Talk:Centrifugal force/Archive 11

New historical section

A historical section is added describing the fundamental role of centrifugal force in thinking about inertial frames and the whole idea of symmetry transformations of physical laws. Brews ohare (talk) 13:06, 1 October 2008 (UTC)

fact template

Harald: Please explain what you are looking for in the sentence that says "fictitious" is being used in a technical sense. The so-called fictitious forces are real in an accelerating frame (in ordinary language), as per this quote also in the article: Kompaneyets, A. S. & George Yankovsky (2003). Theoretical Physics. Courier Dover Publications. p. p. 71. ISBN 0486495329. {{cite book}}: |page= has extra text (help)

"Naturally, the acceleration of a point caused by noninertiality of the system is absolutely real, relative to that system, in spite of the fact that there are other, inertial, systems relative to which this acceleration does not exist. In [the equation for acceleration] this acceleration is written as if it were due to some additional forces. These forces are usually called inertial forces. In so far as the acceleration associated with them is in every way real, the discussion (which sometimes arises) about the reality of inertial forces themselves must be considered as aimless. It is only possible to talk about the difference between the forces of inertia and the forces of interaction between bodies."

Brews ohare (talk) 23:36, 1 October 2008 (UTC)

Brews, please try to read more carefully, and understand what you read, and try to understand the explantions that are provided to you. The above quotation does not say fictitious forces are real. Read carefully. It says the relative acceleration is real (i.e., the relative acceleration is real relative acceleration... very illuminating), and then it says that discussions about the reality of inertial forces themselves must be considered as aimless.

I think Brews presents an interesting problem for Wikipedia. How can we deal with someone who so earnestly and energetically mis-construes everything he reads, and is so utterly determined to promulgate his misunderstandings, novel narratives, and original research throughout a range of Wikipedia articles?Fugal (talk) 15:40, 2 October 2008 (UTC)

Au contraire, mon cher ami. Tu ne comprends rien. If the acceleration is real, as you seem to agree, how can the force be other than real? It is proportional via the mass. That is, "the acceleration of a point caused by noninertiality of the system is absolutely real". "In [the equation for acceleration] this acceleration is written as if it were due to some additional forces. These forces are usually called inertial forces." "...the acceleration associated with them is in every way real." Case closed. Domages. Brews ohare (talk) 16:01, 2 October 2008 (UTC)

As always, Brews' comment is a complete non-sequitur. The expressions "relative acceleration" and "force" have meanings. It was explained to Brews previously that to say a relative acceleration is a real relative acceleration is a trivial tautology (the undefined word "real" serving no purpose), whereas to talk about whether a fictitious force is a real force is at best aimless, as Brews' own reference says, because the word "reality" hasn't been defined, and it can't be dismissed as tautological in this case, because we're comparing "fictitious force" with "force". Now, if by "real force" we mean something that satisfies the Newtonian definition of a force in classical mechanics, then the answer is plainly No, a fictitious force is not a real force in that sense of the word, which is the only relevant sense for this article. This is why fictitious forces are called fictitious forces rather than forces. And this is why most of the modern literature considers the treatment of these acceleration terms as "forces" is (to quote one reference) an abomination. And yet we find Brews blithely proliferating his novel narrative, totally undeterred by being proven wrong time after time after time... Fugal (talk) 22:02, 2 October 2008 (UTC)

It is hard to be patient with such nonsense. Fugal has not parsed the quotation, he has been shown that he doesn't understand it (or will not), and makes unsupported wild statements about "most of the modern literature". And is entirely impolite and unresponsive. I don't know who is watching this debate, but if I'm talking to Fugal, he is beyond reach. Brews ohare (talk) 03:32, 3 October 2008 (UTC)

Having no further objection from Harald, and finding Fugal cannot accept a plain supporting quotation, which he prefers to misconstrue with no supporting argument, I have removed the fact template. Brews ohare (talk) 15:14, 3 October 2008 (UTC)

First line of intro

The introductory line reads: In classical mechanics, when the motion of an object is described in terms of a reference frame that is rotating about a fixed axis, the expression for the absolute acceleration of the object includes terms involving the rotation rate of the frame.[1]

Here are two criticisms of this line:

First, when the motion of an object is described in a rotating reference frame, the acceleration that is observed is not the absolute acceleration, but the acceleration as seen in that frame. The notion of expressing the absolute acceleration in a rotating frame is a bit odd, it seems.

Second, what is meant by absolute acceleration? Here is a quote:

Absolute acceleration (and absolute rotation in particular) must be understood as acceleration (and rotation) relative to absolute space

— Barry Dainton:Time and Space, p. 175

Then one might ask, what is the standing of absolute space? Here are some quotes:

The notions of absolute space absolute time have been branded an unobservable and superfluous metaphysical structure

— Friedel Weinert: The Scientist as Philosopher, p. 116

#The existence of absolute space contradicts the internal logic of classical mechanics since, according to Galilean principle of relativity, none of the inertial frames can be singled out.
#Absolute space does not explain inertial forces since they are related to acceleration with respect to any one of the inertial frames.

— Milutin Blagojević: Gravitation and Gauge Symmetries, p. 5

By the end of the nineteenth century, some physicists had concluded that the concept of absolute space is not really needed...they used the law of inertia to define the entire class of inertial frames. Purged of the concept of absolute space, Newton's laws do single out the class of inertial frames of reference, but assert their complete equality for the description of all mechanical phenomena.

— Laurie M. Brown, Abraham Pais, A. B. Pippard: Twentieth Century Physics, pp. 255-256

So another possible criticism of this introductory line is that it refers unnecessarily to absolute acceleration, and by implication, absolute space, a rather outmoded concept. Brews ohare (talk) 03:42, 2 October 2008 (UTC)

Brews, I urge you to actually study some physics, and specifically the science of dynamics. You're laboring (with very regrettable energy) under some profound misunderstandings. Absolute acceleration does not imply absolute space. The acceleration of any object, when it's motion is described in terms of ANY system of inertial coordinates, is the same, regardless of which system of inertial coordinates we choose. This is the absolute acceleration of the object, and it is the "a" that appears in Newton's equation F = ma. Your failure to understand this is responsible for the huge number of mis-guided edits that you have made (and unfortunately continue to make) in Wikipedia articles. After being compelled by many editors to trim down your bloated novel narrative in this article, I see you've begun re-bloating it with even more novel narrative. Just as you did before, you are adding sections to this article in a misguided attempt to argue for your original research. For example, adding things talking about the obsolete idea of absolute space, as if this somehow refutes the fundamental role of absolute acceleration in dynamics. Brews, please, stop. Just stop. You don't know what you're talking about.

And here on this discussion page you rant about "bastardized accelerations", totally oblivious to the fact that the acceleration evaluated in terms of a rotating frame (i.e., curved time axis) is just as bastardized as an acceleration evaluated in terms of curved space axes, and just as coordinate dependent. An observer can be moving along a curved space axis just as well as he can be moving along a curved time axis. In either case, or combination of cases, the acceleration in terms of his system of reference is bastardized, i.e., it is not the absolute acceleration "a" that appears in Newton's F = ma where F is just the physical forces.

Brews, try to read the following words, and THINK about what they mean: The "a" in Newton's law is explicitly defined as the absolute acceleration when F is defined as the actual physical forces. If you put something other than the absolute acceleration into that equation, it is no longer valid. Whenever you use a bastardized acceleration, you have to bastardize the force correspondingly in order to maintain equality. This is the origin of fictitious forces. Furthermore, any given fictitious forces corresponds to infinitely many different systems of reference, some of which are purely curved in time, and some of which are spatially curved, and some are combinations. This is why (for example) the very same centrifugal force mw2r can be derived either in rotating coordinates or stationary polar coordinates. This is not an accidental coincidence. It applies to every fictitious force in every circumstance. It can be derived in terms of infinitely many systems of reference, just as the case of zero fictitious force can be described in terms of infinitely many distinct systems of reference.

I say again, Brews, you do not have a clue what you are talking about. Please please stop proliferating articles and sections to spread your personal misunderstandings and novel narratives. The latest section you've added to this article is pure novel narrative in the classic Brews style. I urge you to learn some physics before you make any more edits to Wikipedia science articles. Thanks.Fugal (talk) 15:29, 2 October 2008 (UTC)

Hi Fugal: Never was it suggested that the acceleration of an object is not the same in all inertial frames. In fact that is exactly the point of all the quotations (which you ignore): there is no need for "absolute space" nor "absolute acceleration": the word "absolute" is better replaced by a reference to "inertial frames".

How about doing something useful? Brews ohare (talk) 15:55, 2 October 2008 (UTC)

Fugal says: Brews, try to read the following words, and THINK about what they mean: The "a" in Newton's law is explicitly defined as the absolute acceleration when F is defined as the actual physical forces. If you put something other than the absolute acceleration into that equation, it is no longer valid. Whenever you use a bastardized acceleration, you have to bastardize the force correspondingly in order to maintain equality. This is the origin of fictitious forces. Furthermore, any given fictitious forces corresponds to infinitely many different systems of reference, some of which are purely curved in time, and some of which are spatially curved, and some are combinations. This is why (for example) the very same centrifugal force mw2r can be derived either in rotating coordinates or stationary polar coordinates. This is not an accidental coincidence. It applies to every fictitious force in every circumstance. It can be derived in terms of infinitely many systems of reference, just as the case of zero fictitious force can be described in terms of infinitely many distinct systems of reference. Fugal (talk) 15:29, 2 October 2008 (UTC)

The term "fictitious force" originally referred to the forces in a frame due to its rotation or other acceleration. They vanish in a stationary or uniformly translating frame. The term "fictitious force" for arbitrary rearrangement of Newton's second law results in phony forces that are non-zero even in the stationary frame. These phony forces aren't the same as these earlier "fictitious" forces, and causes conflict with the ideas that relate "inertial frames" to frames that do not exhibit fictitious forces. Thanks for the civility. Brews ohare (talk) 16:34, 2 October 2008 (UTC)

For the billionth time, there is nothing more or less phony about one fictitious force than any other fictitious force. Force is defined (in the Newtonian sense) as being associated with absolute acceleration. Fictitious forces are not associated with absolute acceleration, they are associated with phony acceleration. It doesn't matter whether the phoniness is due to curved space axes or curved time axes or a combination of both. This is why all the reputable references that have been provided to you talk about deriving a fictitious centrifugal force in stationary polar coordinates. The fact that you can't understand this is irrelevant. Wikipedia articles are to be based on published sources, not on your original research and novel narratives. Please note that the worst incivility is to persistently violate Wikipedia policy by inserting original research and novel narrative into the article.Fugal (talk) 22:31, 2 October 2008 (UTC)

I have cited reputable references and quoted them at length. So "all the reputable references" you allude to are in fact not "all" of them after all. The "original research and narrative" here is authored by Fugal. Brews ohare (talk) 03:38, 3 October 2008 (UTC)

Fugal says:This is why (for example) the very same centrifugal force m ω²r can be derived either in rotating coordinates or stationary polar coordinates. This is not an accidental coincidence.

In a rotating frame rotating with angular rate Ω every mass m at a radius r seen from the frame (regardless of its trajectory) is subject to a fictitious centrifugal force mrΩ² (of course, there are other fictitious forces too), regardless of its motion or lack of motion. Differently, in a stationary frame, a moving particle with coordinates (r (t) , θ (t) ) has an acceleration involving the term r ( dθ / dt )² = r ω ² where ω = dθ/dt is, of course, zero if the particle moves only radially, and where ω is related to the particle motion and, obviously, there is no Ω because the frame is stationary, not rotating. The two forces mr Ω² and mr ω² have different effects: the first applies to all objects in a rotating frame; the second applies to a particular object moving in a particular manner in a stationary frame. The first is treated as a force in Newton's second law applicable to all objects; the second is a kinematical requirement for a single particle in order that it may pursue its individual trajectory at a position (r, θ).

All that the two forces have in common is a mathematical dependence on the product of a distance and the square of an angular rate; they apply in different manners (as force vs. kinematic requirement) in different frames (non-inertial vs. inertial), and with different interpretations of the angular rate involved (one the angular rate of a frame shared by all objects seen from that frame, the other of an individual object in a particular motion). One is zero in a stationary frame, the other is not. In short, they are not "the very same centrifugal force". Brews ohare (talk) 17:55, 2 October 2008 (UTC)

Again, you fail grasp the fundamentals, and spew out vast amounts of totally misguided verbiage, which is original research on the subject of this article. These discussion pages are not to be used for discussions of the subject of the article, they are to be used to discuss the editing of the article in accord with Wikipedia policy. People have humored you to excess.Fugal (talk) 22:31, 2 October 2008 (UTC)

Again, you fail to address the points raised and sail off into the infinite space of Fugal's expletives. Brews ohare (talk) 03:38, 3 October 2008 (UTC)

Novel Narrative

Here's just one example of the kind of novel narrative that is overflowing in all but the lead and the first section of the current article: In the section entitled "Are Centrifugal forces real?" the concluding sentence is:

From a time-honored viewpoint, REF the simplest explanation is often to be preferred. The simplest explanation often involves fictitious forces.

REF name=Thorpe - Einstein wrote: "Things should be made as simple as possible, but not any simpler" {{cite book :|title=How to think like Einstein: Simple ways to break the rules and discover your hidden genius |author=Scott Thorpe |url=http://books.google.com/books

So here we have a conclusion - one that happens to be contradicted by a majority of the literature on dynamics, but never mind that... what I think is inappropriate is that this conclusion is based on a little homily about "time honored" viewpoints, for which the "reference" is a little grade school primer on "how to think like Einstein" ! This is classic novel narrative. This little book by Thorpe on "how to discover your hidden genius" has no bearing on the subject of this article. To cite this as a "reference" is preposterous.

If this was just an isolated example, we could just correct it and move on, but unfortunately the entire article if rife with #!)*# like this. Granted, most of the citations are at least marginally more relevant, but unfortunately even the relevant references are almost invariably misconstrued. This article is getting better, but it still needs a LOT of work.Fugal (talk) 05:49, 3 October 2008 (UTC)

This is a good example of constructive comment, possibly the first Fugal has made in the last two weeks. It is specific and provides both a particular example from the text and a clear reason for objection. No vague excursions into personal opinion and invective. Brews ohare (talk) 13:31, 3 October 2008 (UTC)

In response to this critique, these sentences have been deleted. Brews ohare (talk) 22:36, 3 October 2008 (UTC)

New section named "Discussion"

The new section is a repeat of Rotating frame of reference with the shortcomings that it is poorly type set, lacks the citations, and merely states some results that are derived in the other article. This section might be shortened to simply state the final result and make a referral to Rotating reference frame. Brews ohare (talk) 14:02, 3 October 2008 (UTC)

I have added citations, links to greater detail and reformatted the equations and symbols. Brews ohare (talk) 22:34, 3 October 2008 (UTC)

The purpose of the removed sub article was different, namely, to point out how to use fictitious forces in solving a problem, not to provide a formula for them. The practical issue in using the forces is the adoption of these forces as if they were real and using them the same way. That is a mind set that affects how the problem is discussed and its math. Brews ohare (talk) 13:43, 3 October 2008 (UTC)

I have somewhat reworded the deleted section and restored it. Brews ohare (talk) 22:34, 3 October 2008 (UTC)

Advantages of rotating frames

The quotes about handling fictitious forces seem necessary to satisfy the need for reassurance exhibited by some editors. Mere statement of the obvious is less convincing. Brews ohare (talk) 16:55, 4 October 2008 (UTC)

As already explained repeatedly, the previous "need for reassurance" was motivated by the incorrect context and presentation in the article. Now that this is being fixed, no one needs any "reassurance" about self-evident facts. The reassurances were needed only when certain editors were peddling confusions and misunderstandings. No need for polemics any more.Fugal (talk) 19:15, 4 October 2008 (UTC)

Redundantly Duplicated Repetitions of the Same (FALSE) Things Over and Over, Repeatedly

The article is rife with repetition. Just to give one example, the concept of introducing fictitious forces to help when working in a rotating frame is explained (rather repetitiously) in the first sections of the article. Then when we get to the section on Fictitious Forces (which doesn't even belong on this article) is starts out

"An alternative to dealing with a rotating frame of reference from the inertial standpoint is to make Newton's laws of motion valid in the rotating frame by artificially adding pseudo forces to be the cause of the above acceleration terms, and then working directly in the rotating frame."

Why must we keep saying this over and over and over....?Fugal (talk) 19:08, 4 October 2008 (UTC)

Oh, and in addition to being redundant, the quoted statement is also false. The pseudo forces are not added to be the cause of the acceleration terms, the pseudo forces are the acceleration terms. Sheesh. The whole article, aside from the header and first section, is a complete mess.Fugal (talk) 19:12, 4 October 2008 (UTC)

Comrade, the language smacks of petty bourgeoisie contamination of the language

"In most introductory physics courses, the centrifugal force is dismissed as an abomination to be avoided by all right-thinking physicists"

I really can hardly barely believe that professional physicists use this kind of language... but some actually do.

It's sort of Monty Python:

“I think that all good, right thinking people in this country are sick and tired of being told that all good, right thinking people in this country are fed up with being told that all good, right thinking people in this country are fed up with being sick and tired. I'm certainly not, and I'm sick and tired of being told that I am”

- (User) Wolfkeeper (Talk) 01:05, 5 October 2008 (UTC)

As always, you miss the point. Taylor is not saying it should be dismissed as an abomination, he is simply, in a droll way, commenting on the exceedingly well known fact that the concept of "centrifugal force" as it is used in this article is generally frowned upon by most physics teachers, because it just consists of giving some accelerations the name "force". Fugal (talk) 01:49, 5 October 2008 (UTC)

I'm not entirely sure that irony in an article like this is a good idea.- (User) Wolfkeeper (Talk) 02:24, 5 October 2008 (UTC)

The only reason for introducing this quote is because Brews continued to challenge the simple statement of fact, which was that "Some authors discourage the use of the term "centrifugal force" to refer to these acceleration terms." A perfectly reputable reference was provided for this well-known fact, but Brews accused me of lying (see New Intro above) and making up the reference, or at best of citing an obsolete reference. Then when he discovered that (as always) he was wrong, instead of apologizing, he responded by saying that this statement from a published reputable source of experts on this subject (7th edition!) is just hearsay(!) and does not cite any reputable source for their statement, and hence Brews suggests that it should be suppressed, so he edited it in a blatently POV way to denigrate and cast doubt on it by saying "According to Beer..." as if they are the only ones who say this, and as if they don't know what they are talking about. Honestly, if direct quotes from reputable sources from recognized experts are to be selectively discredited by Brews according to whether or not they support his (erroneous) POV, then this whole process is a shambles.

So I corrected the article, by supplying the citation from Taylor, who acknowledges even more dramatically that "In most introductory physics courses centrifugal force is regarded as an abomination to be avoided by all right thinking physicists." Note that he says not just "some" or even "many" (as I've worded it in the article), but "most". Of course, Taylor has his own ideas on how the term can be used, as do Beer et al, but the latter certainly do not agree with the usage in the current article (they take the normal/tangential approach), and in any case this is irrelevant to the simple well-known fact that the concept of "centrifugal force" in the sense of this article is not highly regarded among experts in this subject.

Now, some may wonder how Brews could have such a distorted view of this subject. Well, it's fairly apparent that he simply acquired whatever information he possesses about the subject by going to Google books and searching on "centrifugal force". Needless to say, this is going to bring up preferentially books on dynamics that favor the introduction of that term. There are many books on Dynamics that never even introduce the term, because they regard it so disdainful. Then there are many others that mention it once, just to say to the reader "here is something that really stupid people do sometimes, but we will not follow this practice here". Obviously these books will not rank high in Google's hit list. This is a problem with editors who are not really educated on a subject, but who mistakenly think they are educated based on browsing the web. And this doesn't even touch on the fact that Brews invariably misunderstands even the limited selection of texts that he has accessed.

And now we hear from Wolf, in a content-free commentary invoking Monty Python. Very edifying. Honestly, there is a real systemic problem here in the editing of this article. People who have repeatedly demonstrated that they don't know what they are talking about should give some serious thought to taking a less active role in editing the article.Fugal (talk) 01:49, 5 October 2008 (UTC)

The quote from Taylor was a misrepresentation that has been corrected by including the next two lines. Also, Beer and Johnston (and Taylor) actually do not use this restraint in employing the word "force" and provide no citations to support their statements that there is a large body of misguided souls that object. Brews ohare (talk) 19:08, 6 October 2008 (UTC)

In short, neither of these texts adopts the cited view as correct practice, although Fugal's text suggests that may be the case. Brews ohare (talk) 15:55, 6 October 2008 (UTC)

This entire paragraph is unnecessary, and its only consequence is to confuse the reader by providing doubt that centrifugal force is real. I have moved it from the introduction, where it is a distraction, to a separate sub-section. Brews ohare (talk) 13:56, 6 October 2008 (UTC)

I'll take the opportunity to suggest that Fugal use the {{cite book}} template when citing books, instead of his own format, and that he actually provide googlebook links to these sources where possible. In particular the reference: <Halliday and Resnik, "Physics", Wiley, 1978, p 107. "Inertial forces are non-Newetonian... Newton's third law does not apply to them..."> does not appear to be accurate: exact quote, isbn, and google link please. Brews ohare (talk) 15:39, 6 October 2008 (UTC)

Failing any response for a more detailed citation to Halliday and Resnick, I have provided a direct quote from these authors with url and isbn. Brews ohare (talk) 15:12, 8 October 2008 (UTC)

What Is To Be Done?

Here's an overview of the contents of the existing article, and what I think needs to be done regarding each section.

0 Lead - Good, keep

1 Derivation - Good, keep

2 Advantages of rotating frames - Limited value, somewhat redundant, marginal keep

3 Intuition and frames of reference - Novel narrative, delete

3.1 Are centrifugal and Coriolis forces "real"? - Novel narrative, delete

4 Fictitious forces - Merge to Fictitious Force article

5 Uniformly rotating reference frames - Redundant, delete

6 Non uniformly rotating reference frame - Redundant, delete

7 Potential energy - Probably of value, keep and improve

8 Examples - Okay to keep some examples, but should be trimmed WAY down

8.2.4.1 Is the fictitious force ad hoc? - Novel narrative, delete

9 Development of the modern conception of centrifugal force - Not much here

9.1 Role in developing the idea of inertial frames - Could be improved

Fugal (talk) 02:04, 5 October 2008 (UTC)

I've implemented your recommendations 5 and 6. I've revised sections referred to in your items 4 and made it a sub-sub-section. I disagree about section in item 3. Brews ohare (talk) 14:02, 6 October 2008 (UTC)

I've added citations to your item 3 to counter the appearance that this is "novel narrative". These examples are very commonly used, and the interpretation of the examples is equally common. Brews ohare (talk) 04:04, 7 October 2008 (UTC)

I have deleted sub-section ==Is centrifugal force a "force"?== on the basis that it simply raises a POV not advised by Taylor nor Beer & Johnston, although they have been selectively quoted to suggest the contrary. More extensive quotations by the same authors on the same pages that override this false impression were removed by Fugal, and replaced with an undocumented "explanation" of his own devising. Brews ohare (talk) 17:43, 7 October 2008 (UTC)

I'm also gratified to see that the "Derivation" section is rated by you as "good, keep". This derivation simply copies Rotating reference frame. Brews ohare (talk) 16:26, 6 October 2008 (UTC)

Imbalanced disambiguation corrected and improved; now all looks acceptable

The disambiguation strangely referred to centripetal force and to an incomplete list of centrifugal force, curiously lacking the most used alternative meaning. However, there already is a link to the disambiguation page. Thus I removed the incomplete list. Moreover, a clear descriptor of this page is needed at the disambiguation as the title does not make fully clear that this article is about fictitious force. Now I think the disambiguation is both neutral and clear.

Apart of that, I also removed the banner inside the article space as the text has been strongly improved - thanks! Harald88 (talk) 15:41, 5 October 2008 (UTC)

Harald: The link to, for example, Centripetal force, is not a suggestion confusing to the reader, but an aid to the reader who may wish a more complete perspective. As you may know, consulting Wiki has the great merit of guiding the reader to related subjects that may not be immediately recognized as related by the uninitiated reader.

It detracts from Wiki's utility to remove these guiding links.

In the case of Fictitious force, it should be recognized that this link also simply is guidance to an article with a treatment more general than centrifugal force, one that includes all types of fictitious force. Brews ohare (talk) 14:23, 6 October 2008 (UTC)

I'm not against adding more links but as explained before, it is not acceptable to only provide links for a single perspective while deleting all links to the opposite perspective. Moreover, the disambiguation between fictitious and reactive force is essential for the readers, at the start of the article. I'll repair it together with the link to centripetal force. Harald88 (talk) 22:54, 11 October 2008 (UTC)

I think it looks good. Brews ohare (talk) 00:11, 12 October 2008 (UTC)

A suggestion for how to proceed

An agreement was reached in Brews' brief absence, and the dispute tags were removed by Harald, and then Brews returned and immediated proceeded restoring all of his original research and novel narrative and misrepresentations and misunderstandings. It seems clear that Brews knows nothing about, does not understand, and will never agree with, the published reputable sources on this subject. Nevertheless, he appears to believe that his original POV on this subject is so noteworthy that it deserves its own Wikipedia article. Therefore, to help resolve this dispute, I propose that Brews create a new article with the disambiguated title "Centrifugal Force (Brews ohare)". We can then link to this from the main disambiguation page, with a comment like "For Brews ohare's POV on centrifugal force (and other somewhat related ideas) see "Centrifugal Force (Brews ohare)". I really believe this is the only way that Brews will allow the current article to be written in a NPOV way.Fugal (talk) 04:49, 7 October 2008 (UTC)

Statements like those above are extreme, incorrect, inflammatory and not conducive to cooperation. In contrast, I have been helpful in doing clerical work to fix up Fugal's additions with more detailed version of his citations using the standard {{cite book }} template instead of his grab-bag references, and by typesetting of fonts and formatting in his formulas. I have even provided supporting quotations for his viewpoint, which he has deleted with derisive commentary. I have implemented several of his suggestions, deleting two sub-sections. I have supported my actions with clear and careful reasoning (not with polemics and character assassination), and avoided getting excited. Fugal has not. There is no basis for Fugal's hostility and irrational behavior. Brews ohare (talk) 06:21, 7 October 2008 (UTC)

Deletion unwarranted

Deletion of Intuition and frames of reference is unwarranted. All examples in this sub-section are (i) common in the literature (ii) well documented in the article by citations that closely parallel the presentation provided (with links, page numbers and isbn's), and (iii) helpful to the reader, especially the uninitiated reader. It is, therefore, a disservice to the reader and a violation of Wiki policies to delete it summarily. This deletion is not properly supported. Brews ohare (talk) 06:59, 7 October 2008 (UTC)

Inappropriate and off-topic

Fugal: Hence this "centrifugal force" can be defined as "An outward pseudo-force, in a reference frame that is rotating with respect to an inertial reference frame, which is equal and opposite to the centripetal force that must act on a particle stationary in the rotating frame. Since this term is defined as the force that must act on a particle that is stationary in a rotating frame with a given angular speed, it can also be derived as the inertial force on a particle moving in a circle with the same angular speed in stationary polar coordinates.

This topic on particle motion is properly the subject of centrifugal force (planar motion), not of this article, as pointed out on the disambiguation page. Also, this statement suggests by brevity that brief statements are all that is needed. This subject is discussed with the length it requires and discussed correctly in terms of the co-rotating frame at Co-rotating frame. Appropriate citations are provided there that actually support the material presented. An abbreviated obscure formulation in terms of concepts for which no basis has been laid is not needed on centrifugal force (rotating reference frame). Further debate on this issue is really debate about centrifugal force (planar motion), and should take place on that Talk page (where the relevant material is present in detail), not on this one. Brews ohare (talk) 07:27, 7 October 2008 (UTC)

A Unified Article

The arguments that have been put up against having a single unified article seem to be that the centrifugal force that appears in polar coordinates is not the same centrifugal force that appears in the rotating frame transformation equations. I contend that they are indeed exactly the same. But I want to do devil's advocate against Fugal and ask him how does he explain the fact that in rotating frame theory, a centrifugal force acts on a particle which is at rest in the inertial frame, whereas in polar coordinates, there is no such centrifugal force acting? David Tombe (talk) 12:13, 9 October 2008 (UTC)

David: I've replied to your question on Talk: Centrifugal force (planar motion), which seems to me to be the correct venue. Brews ohare (talk) 15:45, 9 October 2008 (UTC)

Brews, It's OK. We can bring the discussion here now because I've been unblocked. I want to see how Fugal makes his case that the centrifugal force as viewed from a rotating frame on a stationary object is the same as a polar coordinates centrifugal force, bearing in mind that the polar coordinates centrifugal force would be zero in that scenario.David Tombe (talk) 16:04, 9 October 2008 (UTC)

Brews, I read your reply on the discussion page of the other article. You were applying Newton's law of inertia to polar coordinates. The two don't mix.

There is zero radial acceleration in circular motion.

Now my sole objective in returning here is to advocate that there should be one single unified article on centrifugal force. I couldn't believe it when you directed the discussion to another talk page that I hadn't even realized existed. Google brings us here. The discussion began here, and this is where I hope that it will finish.

It was bad enough when they separated 'reactive centrifugal force' into a different article. The so-called reactive centrifugal force is a knock on effect which could easily be catered for within a unified article. There will never be a so-called reactive centrifugal force unless it is already being fed by an underlying centrifugal force. In actual fact, it is the tension in a string that supplies the inward centripetal force that is reacting to the outward centrifugal force. The term reactive centrifugal force is a very bad terminology and I haven't been convinced by the sources that were cited.

But as for centrifugal force (planar motion), that takes the biscuit. It just adds to the ever proliferating confusion.

You seems to always want to bring the tangential terms into simple uniform circular motion problems. There is no need to do so. And if angular acceleration is involved, then just bring it in as needs be.

In planetary orbits, the tangential terms vanish. And when we have a circular orbit, the outward centrifugal term exactly cancels with the inward gravity term. There will be no net radial acceleration. I can show you the exact equation that is used in Goldstein's. David Tombe (talk) 10:57, 10 October 2008 (UTC)

Newton's law of inertia in polar coordinates

For uniform circular motion of a particle as seen in an inertial (non-rotating) frame:

${\boldsymbol {F_{cptl}}}=-mr{\dot {\theta }}^{2}{\hat {\boldsymbol {r}}}=m{\boldsymbol {a}}=m{\frac {d{\boldsymbol {v}}}{dt}}=m{\frac {d^{2}\mathbf {r} }{dt^{2}}}=m({\ddot {r}}-r{\dot {\theta }}^{2}){\hat {\boldsymbol {r}}}+m(r{\ddot {\theta }}+2{\dot {r}}{\dot {\theta }}){\hat {\boldsymbol {\theta }}}$

What's wrong with this, David? It is Newton's law in polar coordinates.

${\boldsymbol {F_{cptl}}}=-mr{\dot {\theta }}^{2}{\hat {\boldsymbol {r}}}$

is the impressed centripetal force needed to keep the particle in a circular path of radius r at constant angular rate $\omega ={\dot {\theta }}$ (applied by a spring in tension, say, attached between the moving particle and the center of rotation), and (r, θ) are the moving particle's coordinates. The right-hand side follows from time-differentiation using the chain rule. Details of differentiation are found at rotating reference frame.

Your remark that there is "zero radial acceleration" in circular motion does not square with the usual definition of centripetal force. The standard view is that because the particle velocity is continuously changing direction, that is, exhibits a centripetal acceleration, a centripetal force is necessary to cause the change in direction. Of course the orbital radius does not change magnitude, so ${\ddot {r}}=0$. That is shown in earlier remarks to be a consequence of Newton's law above.

Newton's law as stated above does not invoke an impressed centrifugal force, only a centripetal force applied by the spring in tension.

The only way I can square your remarks with reality is to assume you are adopting the "generalized" coordinates (r, θ) in a Lagrangian formalism and using the "generalized" force of this formalism, which is not the true Newtonian force. See earlier comments concerning Hildebrand. Brews ohare (talk) 21:08, 10 October 2008 (UTC)

Brews, That's simply not how it's done. We either use polar coordinates, in which case we will have centrifugal force. Or we use Newton's law of inertia in Cartesian coordinates, in which case there is no recognition of such a thing as centrifugal force. It is two different languages for expressing the same effect. It's either 'inertia' or it's centrifugal force depending on whether we want to talk the language of X, Y, and Z, or the language of radial and tangential.

When we use polar coordinates to analyze a uniform circular motion problem, we do not involve the tangential terms. The radial equation which we use is centripetal force + centrifugal force = $m{\ddot {r}}=0$

In a gravity orbit, Newton's inverse square law expression would become the centripetal force. If it were an elliptical orbit then the $m{\ddot {r}}$ term would become non-zero and we would have a difficult differential equation to solve. That's how it's done. David Tombe (talk) 01:48, 11 October 2008 (UTC)

Who's we kimosabe? What is this it that's not done? Who are you to say these things?- (User) Wolfkeeper (Talk) 02:26, 11 October 2008 (UTC)

This article is not about coordinate systems, it is about reference frames. The coordinate system used is just a way to describe these psuedo forces that are found in rotating reference frames.- (User) Wolfkeeper (Talk) 02:28, 11 October 2008 (UTC)

David: If you are going to keep me on board, please look at the Newton's law above and tell me specifically what is the matter with it. I think it's correct, and that it predicts uniform circular motion, as it should. It leads directly to your equation $m{\ddot {r}}=0$, and does so without invoking any impressed centrifugal force. Zero centrifugal force is what is expected for an inertial frame. Your pronouncements about "how it's done" don't carry weight by themselves. Remember, this example is a simple one, no gravity involved, just a particle in uniform circular motion attached by a spring to its axis of rotation. Brews ohare (talk) 04:23, 11 October 2008 (UTC)

Brews and Wolfkeeper, It's how it is done in university classical mechanics courses. I'll talk you through it. You have written out the full expression for acceleration in polar coordinates. That's fine. But it cannot be utilized until such times as we give it a physical context. In simple uniform circular motion problems, we normally don't even need to invoke such complications. However, when we deal with planetary orbits where we can have elliptical, parabolic and hyperbolic motion, then we construct a differential equation using the terms in your polar coordinate equation above. The first thing that we do is get rid of the two tangential terms. Doing that follows as a consequence of Kepler's law of areal velocity. This reduces it to a purely radial equation. The inverse square law gravity expression becomes a radially inward term. The centrifugal force becomes a radially outward term and the two sum together to give $m{\ddot {r}}$. That is the differential equation that needs to be solved. However, in the simple case of circular motion, $m{\ddot {r}}$ will be equal to zero. The same principles are involved when the centripetal force is supplied by the tension in a string. The inward centripetal force is exactly balanced by the outward centrifugal force, and $m{\ddot {r}}$ will be equal to zero. This is not my own original research. This is straight out of classical mechanics textbooks and I can supply reliable mainstream sources such as Goldstein's and Williams. Centrifugal force is clearly something which is not restricted to the topic of 'rotating frames of reference'. 'Rotating frames of reference' is always another chapter in the same classical mechanics textbooks that deal with central force orbits. David Tombe (talk) 14:29, 11 October 2008 (UTC)

Newton's laws right out of textbooks

Newton's law is F = m a. You agree my expression for a is correct. The force F in an inertial frame is the impressed force due to identifiable real bodies (the spring). It exerts a tension T. Therefore, Newton's law says

${\boldsymbol {T}}=m{\boldsymbol {a}}=m{\frac {d{\boldsymbol {v}}}{dt}}=m{\frac {d^{2}\mathbf {r} }{dt^{2}}}=m({\ddot {r}}-r{\dot {\theta }}^{2}){\hat {\boldsymbol {r}}}+m(r{\ddot {\theta }}+2{\dot {r}}{\dot {\theta }}){\hat {\boldsymbol {\theta }}}$

Now I adjust the tension T. For uniform circular motion of a particle as seen in an inertial (non-rotating) frame at radius R and angular rate Ω. I set the tension at:

${\boldsymbol {T}}=-mR{\Omega }^{2}{\hat {\boldsymbol {r}}}\ .$

Notice the tension has a unique value and a radially inward direction. Solving the equations with initial conditions at t = 0 (these conditions are part of the set-up phase of the experiment):

$r(t=0)=R\ \mathrm {and} \ {\dot {\theta }}(t=0)=\Omega \ ,$

I get uniform circular motion at angular rate

${\dot {\theta }}=\Omega$

at a radius R, and your favorite result:

${\ddot {r}}=0\ .$

I do not believe there is any error here. Please point one out. Please avoid looking at other examples. This one is very simple. If we cannot agree on the way this one should be handled we are stuck. The same example is discussed as the whirling table where the tension T is provided by a cord attached to a tray of weights. Brews ohare (talk) 15:38, 11 October 2008 (UTC)

Brews, your equation is correct. You just need to know which actual forces to substite for which of the terms. The inward tension replaces the $m{\ddot {r}}$ term, and the $mr{\dot {\theta }}^{2}$ term is the centrifugal force. In circular motion, the two sum together to give zero.

It's no different if gravity is supplying the inward tension. That's exactly how it is done in the texbooks. David Tombe (talk) 19:11, 11 October 2008 (UTC)

David: Your substitutions are incorrect. The force in F = m a, is the tension as I have described. In an inertial frame it has to be a real force from an identifiable source. The acceleration a is as we have agreed upon. Apparently you think the solution's correct prediction done this way is fortuitous. Brews ohare (talk) 21:51, 11 October 2008 (UTC)

Brews, I'm not telling you my own opinions here. I'm telling you what a central force equation looks like as in classical mechanics textbooks. It is a second order scalar differential equation with the variable being the radial distance r. We solve for r. We begin with the total force on the left hand side of the equation, written in the form $m{\ddot {r}}$. Then on the right hand side we list the components of the total force. These will be the inward centripetal force and the outward centrifugal force.

In the special case in which the centripetal force is the inverse square law of gravity, then the solution will be a conic section. (ellipse, circle, parabola, hyperbola, or straight line)

If we consider the very simple everyday cases in which the radial distance is constrained to be constant,such as by the tension in a string, then the inward centripetal force will be constant too, and it will be equal in magnitude to the centrifugal force.

There shouldn't be any argument about this. It's common knowledge to anybody who has studied applied maths at university. If you think that there is no centrifugal force in a planetary orbit then you are going against what is written in reliable university textbooks. David Tombe (talk) 01:33, 12 October 2008 (UTC)

David: If you look at the example under discussion, it does lead to a second order scalar differential equation in the radial direction ${\ddot {r}}=0$. We solve for r(t) using the initial condition and obtain r(t) = R. However, all this is accomplished without following your other prescriptions for substitution. The remainder of your comment is a digression from the example at hand.

The point is that the approach I have outlined works just fine. If you look at your books, you will find they obtained their radial equations the same way. Brews ohare (talk) 03:21, 12 October 2008 (UTC)

Brews, if you use a second order differential equation but then confine your attention to the special simple case of circular motion, you will lose sight of the higher picture. In the more general elliptical case, it is easy to see that the centripetal force inwards is working in tandem with an outward centrifugal force. These two forces will not in general have the same magnitude. However, in the special case of circular motion, the two forces will have the same magnitude. When we then equate the centripetal force to the term for the centrifugal force, this can lead high school students to believe that there only is the centripetal force involved. We need to look at the general elliptical picture in order to see it all more clearly. You need to appreciate the fact that centrifugal force is a reality when actual rotation occurs. This is confirmed by central force orbital theory and I can give you reliable textbook sources. If necessary I will give you exact quotes with page numbers. David Tombe (talk) 09:01, 12 October 2008 (UTC)

Usually the simplest case is the clearest case. From my viewpoint, this example already shows irreconcilable differences between us. The only way to bring us together that I can see is to adopt a Lagrangian formulation. As explained in detail earlier using Hildebrand as a reference, this approach is similar to yours. However, it uses the "generalized" centrifugal force, not the centrifugal force of Newton and the tides. If you want to switch gears to that framework, fine. However, you will have to face the fact that the generalized centrifugal force is different from the centrifugal force of Newton and the tides. Brews ohare (talk) 15:13, 12 October 2008 (UTC)

Brews, this is a situation where the simplest case scenario is not the clearest. The simple case scenario here creates an equality between the magnitudes of centripetal force and centrifugal force. That equality allows the existence of centrifugal force to be concealed behind centripetal force. We need to look at the more general elliptical motion in order to unmask this conjuring trick.

As for Lagrangian, we don't need to go down that road. But since you have brought the subject up, then I assume that you already have a velocity dependent potential in mind to cater for centrifugal force. I'd like to see it. And I'd like to hear how its advocates reconcile it with the idea that centrifugal force is only an illusion as observed from rotating frames of reference. David Tombe (talk) 15:31, 12 October 2008 (UTC)

It's not an illusion as you can prove it exists via mathematical manipulation starting from Newton's laws in inertial reference frames using coordinate transformations.- (User) Wolfkeeper (Talk) 23:48, 13 October 2008 (UTC)

Wolfkeeper, I'm not altogether sure where you stand in all of this. I know that centrifugal force is not an illusion. I have been heavily criticized for having held that belief, and I have been constantly accused of going against what is in the textbooks. So if you also believe that it is not an illusion, can you then please tell me what exactly the argument is about? David Tombe (talk) 00:50, 14 October 2008 (UTC)

If you do a coordinate transformation from an inertial frame of reference to a rotating frame of reference, you find that a pseudo force appears for all objects in the rotating frame of reference that is dependent only on the position relative to the rotation axis of the frame, and is completely independent of the motion of the object within the frame. It appears together with the coriolis pseudo force if the object is moving in the rotating frame. A rough proof of this appears in the article. This is a distinct force from the centrifugal force that appears in polar coordinates that bears the same name, since that force depends on the motion of the object relative to the frame that the polar coordinates are relative to (be it inertial or non inertial). Both are unfortunately termed 'centrifugal force' but they're independent and different. An object can have both types centrifugal forces simultaneously, in the most general case where the polar coordinate axis isn't aligned with the frame rotation axis, then they don't have to act in the same direction, be the same magnitude or have anything else in common.- (User) Wolfkeeper (Talk) 02:44, 14 October 2008 (UTC)

For example if you express a position in longitude, latitude and altitude on the Earth then that is a polar coordinate system relative to a non inertial frame of reference (since the Earth is rotating!). If an aircraft flies around (e.g. Concorde), say it flies west. Then you need to account for: frame centrifugal force, frame coriolis force, coordinate centrifugal force, coordinate coriolis force.- (User) Wolfkeeper (Talk) 02:44, 14 October 2008 (UTC)

The frame centrifugal force depends only on the distance from the frame rotation axis, which in this case depends only on latitude and altitude. The frame coriolis force points at 90 degrees to both the vehicle's velocity relative to the Earth's surface ( ground speed NOT absolute speed!) and the rotation axis vector of the Earth. The polar coordinate forces depend on the vehicle omega around the Earth (vehicle angular speed) and the polar coriolis is an angular term (always). As you can see, even in this non general case, the forces are all completely differently defined, act in different directions and have different magnitudes. (Actually in this case the centrifugal forces are in the same direction, but completely different magnitudes, that's just becasue the polar coordinate axis and the frame rotation axis are aligned, there's nothing deep going on, and wouldn't be true if you were analysing a merry-go-round using polar coordinates centered in the middle refering relative to the Earth-frame)- (User) Wolfkeeper (Talk) 02:44, 14 October 2008 (UTC)

And yes, you can do the same calculation relative to the inertial frame using polar coordinates and get an equivalent result. It might even be easier in this case, other cases it won't be though. That's not the point I'm making at all. My point is, this article is on a particular definition of the term 'centrifugal force' and as I have shown, it is distinct from the polar coordinate usage in just about every way conceivable.- (User) Wolfkeeper (Talk) 02:44, 14 October 2008 (UTC)

Wolfkeeper, within your understanding of centrifugal force as in rotating frames of reference, yes it is indeed different from centrifugal force in inertial frames (as per polar coordinates).

You have stated clearly that you see centrifugal force in rotating frames as applying to all objects within the rotating frame irrespective of their relative motion in the frame.

The quality textbooks are usually silent on whether or not that is the case, and the worked examples always use scenarios in which the objects under consideration are stationary in the rotating frame. In cases when the object under consideration is stationary in the rotating frame, then there is only one universal centrifugal force.

At the moment, I don't intend to argue about which is the correct interpretation. I merely want to highlight what the areas of dispute are. That is one of them. Let's summarize it. Here are two viewpoints,

(A) Centrifugal force, as per in rotating frames of reference, applies to all objects in the rotating frame even if they are at rest in the inertial frame.

(B) Centrifugal force only applies to objects, based on their actual rotation relative to the inertial frame.

Now at the moment, I know that you fall into category (A), whereas I fall into category (B).

Let's meanwhile see if we can establish a key point of agreement to operate from. In the special case in which an object is co-rotating with a rotating frame, such as water in a rotating bucket, do you believe that there is only one universal centrifugal force acting? And do you believe that it is real, and that it can cause the water to climb up the walls of the bucket?

I asked this question before to other editors and they usually ducked the answer by running to hide behind cartesian coordinates and Newton's law of inertia, which is merely a different language for expressing the same effect. I don't expect you to do that, because you were one of the few that had grasped the relevance of centrifugal force in planetary orbital theory. David Tombe (talk) 11:52, 14 October 2008 (UTC)

You say: The quality textbooks are usually silent on whether or not that is the case, and the worked examples always use scenarios in which the objects under consideration are stationary in the rotating frame. I believe this position to be simply untenable. Centrifugal force in the sense that is described in this article (and this article makes no claim that it is the only sense that the term 'centrifugal force' is used) comes out of an equation that contains 2 pseudo forces: a 'centrifugal force' and 'a coriolis force'. The coriolis force is defined in terms of the speed of the particle, whereas the centrifugal force is defined in terms of the position. Given that, even if the examples are simple examples where the objects are not moving, they are only examples and not supposed to be the physics. The physics is that of the equations.- (User) Wolfkeeper (Talk) 18:17, 14 October 2008 (UTC)

On the rotating bucket question, if the bucket is stationary in the rotating reference frame and we are using for the sake of argument a polar coordinate system, then the polar coordinate centrifugal force is zero, and the frame centrifugal force is non zero. There is no such thing in this or any other case of a 'universal centrifugal force'. They are defined differently, and thus are not synonymous and hence are to be found at different places in the wikipedia, under the WP:Wikipedia is not a dictionary policy, where synonymous temrs are kept in a single article, and non synonymous terms separated.- (User) Wolfkeeper (Talk) 18:17, 14 October 2008 (UTC)

Wolfkeeper, for the time being, I don't want to argue about the issue of whether or not the rotating frame equations apply only to co-rotating objects. I just want to highlight what the areas of dispute are.

However, on your second part of the reply, you mention a bucket of water that is co-rotating in a rotating frame. It will then of course have centrifugal potential energy and the water will climb up the walls. Agreed? On what basis do you then conclude that the centrifugal force of the polar coordinates is zero in that scenario? There is an absolute rotation and that is what the polar coordinates cater for. I don't see two centrifugal forces here. I can only see one.

First I wish to point out that there's a very common class of errors that people make in physics, that of taking a frame dependent quantity and trying to move them directly into a different frame of reference without doing the necessary coordinate transformation. For example, kinetic energy is a quantity dependent on the square of the speed relative to the frame of reference, and the kinetic energy of an object can be non zero in one frame and zero in a different frame. If you attempt to mix the kinetic energy from one frame with another frame, you can only have an erroneous calculation. If you stick to calculating in a single frame then everything comes out correctly. You must always do comparisons of frame-dependent quantities in a single frame.- (User) Wolfkeeper (Talk) 18:44, 14 October 2008 (UTC)

I wish to point out that centrifugal force is a pseudo-force, and in every case pseudo forces discussed here are frame dependent.- (User) Wolfkeeper (Talk) 18:44, 14 October 2008 (UTC)

In the rotating reference frame, if you calculate the polar coordinate centrifugal force of the water- the water isn't moving in that frame. The polar centrifugal force is zero. The frame centrifugal force is non zero, proportional to the distance from the origin. They are therefore self-evidently different forces.- (User) Wolfkeeper (Talk) 18:44, 14 October 2008 (UTC)

It seems to me like you are saying that there are two centrifugal forces involved here, but that one of them is zero. Can you give me a scenario in which we would have two non-zero centrifugal forces acting in different directions with different magnitudes. And can you tell me how a bucket of water will react when subjected to these two different centrifugal forces simultaneously? (talk) 18:25, 14 October 2008 (UTC)

Probably, but I just can't be bothered. Sorry ;-)- (User) Wolfkeeper (Talk) 18:44, 14 October 2008 (UTC)

Wolfkeeper, you said,

In the rotating reference frame, if you calculate the polar coordinate centrifugal force of the water- the water isn't moving in that frame. The polar centrifugal force is zero.

The water is moving in the inertial frame and as such the polar centrifugal force will not be zero. Polar coordinates are referenced to the inertial frame. David Tombe (talk) 21:23, 14 October 2008 (UTC)

No, a coordinate system is always used referring to a reference frame, either inertial or non inertial. You can do the polar coordinate system in the inertial frame, and then the polar coordinate centrifugal force is non zero, but the frame centrifugal force is zero (trivially so). However, in the rotating reference frame the converse is true, the polar centrifugal force is zero, but the frame centrifugal force is non zero. This proves without a shadow of a doubt that they are not the same, and that they are defined differently.- (User) Wolfkeeper (Talk) 22:00, 14 October 2008 (UTC)

Wolfkeeper, Let's carefully go over what you have just said. The water rotates with the frame and we are all agreed that a centrifugal force exists from the perspective of the rotating frame of reference. You also agree that if we measure the centrifugal force using polar coordinates referenced to the inertial frame that the result will be non-zero. Well of course it will. It will be the same result because the tangemtial speed will be the same in each case. But now you are introducing a third concept. You are introducing polar coordinates referenced with respect to the rotating frame and claiming that the result will be zero in the above case. And when have you ever known of that system to be used? Can you find a citation for it? I can get you citations regarding rotating reference frames. And I can also get you citations regarding polar coordinates referenced from the inertial frame, which is what is used in orbital mechanics. But I have never heard of anybody using polar coordinates referenced to a rotating frame before. Do you have any citations with examples? It is important for your case to produce any such citations, because so far we have only identified one officially recognized centrifugal force. David Tombe (talk) 00:13, 15 October 2008 (UTC)

Longitude and latitude, altitude is a 3D polar coordinate system expressed in a rotating reference frame. Do I really have to give examples of longitude and latitude used to locate objects? Use of this for firing projectiles on the surface of the earth?- (User) Wolfkeeper (Talk) 01:01, 15 October 2008 (UTC)

This is first term, first year, undergraduate physics; and it's self-evidently completely beyond you.- (User) Wolfkeeper (Talk) 01:01, 15 October 2008 (UTC)

Wolfkeeper, First of all, you were claiming the existence of two centrifugal forces and stating that one of them was equal to zero. I pointed out that no matter which way we look at it, there will only be one centrifugal force. You then introduced polar coordinates as referenced in the rotating frame and added a third centrifugal force which you immediately equated to zero. There is absolutely no need to complicate the issue with all these different ways of describing the phenomenon.

Centrifugal force is always radial. We will always use polar coordinates to describe it. The tangential speed involved will always be measured relative to the inertial frame.

Let's get back to the rotating bucket of water again. The rotating water has got centrifugal potential energy. How many centrifugal potential energies do you see in it?

Wolfkeeper, First of all, you were claiming the existence of two centrifugal forces and stating that one of them was equal to zero. I pointed out that no matter which way we look at it, there will only be one centrifugal force.

You're being completely non-responsive. You can claim that there is only one centrifugal force, but given that the polar coordinate axis and the reference frame rotation axis do not have to coincide, and given that the two centrifugal forces are defined entirely differently, are in general of different size, act in a different direction and vary completely independently you are simply continuing to spout utter and complete nonsense.- (User) Wolfkeeper (Talk) 15:48, 15 October 2008 (UTC)

Wolfkeeper, I would like you to give me an example of a situation in which two different kinds of centrifugal potential energy exist simultaneously. David Tombe (talk) 18:43, 15 October 2008 (UTC)

I could certainly do that. But I'm not going to. I'm not your monkey. You clearly don't understand this topic in any way. All attempts to explain it to you have fallen on deaf ears due to your preconceptions and your complete faith in their inerrancy- and in the face of ample and overwhelming evidence to the contrary. That's really all I have to say to you.- (User) Wolfkeeper (Talk) 19:23, 15 October 2008 (UTC)

Wolfkeeper, centrifugal force is one single topic. If you think that the centrifugal force in rotating frames of reference is different from the cantrifugal force in planetary orbital theory, then the onus is on you to produce citations to justify splitting the topic into more than one article. And I know that you can't do that. David Tombe (talk) 13:43, 17 October 2008 (UTC)

Axe to grind? Try the hardware store. Wikipedia is the wrong venue for this.

Tendentious

Strangely enough, I already did this when the article was scoped, and I've pointed to the material that I used to do this, and it was done in the most balanced way I could come up with at the time, and gave a result which is defensible, and has been defended several times. Whereas you persist in your attempts to give your simply religious faith in a particular view point, which while it may be a defensible POV in and of itself, doesn't align with the weight given on the internet to the various different viewpoints that you can take here.- (User) Wolfkeeper (Talk) 16:31, 17 October 2008 (UTC)

Really, you might like to read WP:Tendentious editing. You have almost every single sign, right down to refusing to indent your material correctly. You might like to ask yourself whether your editing is helpful to yourself or the wikipedia, and is likely to achieve any positive results here. After being here for a considerable time, your biggest achievement is that you've been banned 11 times.- (User) Wolfkeeper (Talk) 16:31, 17 October 2008 (UTC)

Historical development

David: I know you have an interest in the history of (at least) Maxwell's equations. How about the history outlined here in centrifugal force? Maybe following an historical path would be an easier approach to what you want to say?

In particular, the development of the idea of inertial frames as frames where no fictitious forces exist seems to have a long track record and threads all the way through even to general relativity. For example, read closely the discussion in Rotating spheres and the analysis in Centrifugal force. The notion is that if you calculate the tension T in the cord tied between rotating spheres based upon your observations of the motion, one of two things can happen: (i) your measured T agrees with T=m ω² R with ω your actual measured rate of rotation of the spheres, or (ii) it does not. By definition, case (i) is an inertial frame, and case (ii) is a non-inertial frame. In case (ii) you are forced to invent "fictitious" forces to make your calculation of the tension come out right.

Now, you could attempt to argue about this based upon physics, which gets us nowhere. But suppose you look at the historical record, and conclude that this is the view of the historical record (regardless of what the truth might be)? Then a dissenter is placed in a minority position. Is that your case?

If (as I suspect from my reading of the history) you are in a minority position, then so far as Wiki is concerned, you have to present your case as a minority view, rather than attempting to show that it is the correct view. More than that, you have to show that it is not a minority of one, by citing some minority support.

So the question arises in my mind: how do you handle these ideas? Doesn't the historical notion of zero centrifugal force acting on a particle in circular motion when observed from an inertial frame kind of grate against your proposals?

Do you see this historical line of argument bifurcating just for the case of planetary motion, making these problems different from all the other example problems in mechanics? (My view is that the discussion is kinematic in nature, and does not depend upon the particular type of forces involved, nor upon whether paths are conic sections.) Is there any historical thread of documents and discussion to show any such thing?

To summarize: you could drop the approach based upon physical intuition and drop attempts to find "obvious" examples that support one intuitive interpretation rather than another. Instead, you could mount a purely historical argument in the form of the historical record, and who said what, and where matters lie today, and where your minority view fits in. Brews ohare (talk) 20:06, 15 October 2008 (UTC)

I'd like to remind people here that, while some discussion of technical topics is perfectly valid where it contributes to the article, the wikipedia is not a chat room, soapbox, usenet or a discussion forum.- (User) Wolfkeeper (Talk) 03:06, 16 October 2008 (UTC)

I'd like to remind "people" that a contribution to the historical discussion is well within the bounds of the article, which has already such a section. Wikipedia is not a forum for pomposity. Brews ohare (talk) 03:31, 16 October 2008 (UTC)

Brews, At the moment, we can't even seem to pin down what the arguments actually are. I had assumed that the main argument was over whether or not centrifugal force exists on an object that is stationary in the inertial frame as viewed from a rotating frame. I would have said 'no', but everybody else seems to be saying 'yes'. If we could agree that that is the argument, then we could agree to differ.

But it has been further complicated by Wolfkeeper's insistence that even in the co-rotating case in which we all agree that centrifugal force exists, that there is actually another centrifugal force acting at the grand value of zero.

I challenged Wolfkeeper to give me an example in which two separate centrifugal potential energies exist simultaneously. He said that he could, but wouldn't.

I don't think that we are at an arguing stage right now. I think we need to formally collate how many arguments there are. David Tombe (talk) 09:59, 16 October 2008 (UTC)

Who can say what is the best strategy? The following is my suggestion:

Approach the matter historically. The historical arguments made by various participants are clear and citable. That puts them well within Wiki policies. There is no need to "convince" anybody - it's documented.

Here is what I think the record will show.: There are two threads. The Newtonian or vector-form of mechanics is the one outlined above based upon inertial and non-inertial frames. It does not agree with your own view, but it is an historical thread. The second thread is the Lagrangian-Hamiltonian view. The role of inertial frames in this formulation is not necessarily central. It deals with generalized forces, and stresses coordinates, not frames of reference. For example, the generalized centrifugal force is not necessarily the same as the Newtonian vector-mechanics centrifugal force, and in some forms is much closer to your personal take on the matter. Again, a documentable historical thread. (The use of Hamiltonians in Quantum Field Theory and its application to Quantum electrodynamics and the Standard Model does make use of symmetries like Lorentz invariance; however, applications in robotics don't seem to worry much about inertial frames.)

The historical approach side-steps everybody's pet theory about centrifugal force. It is documentable. It is difficult to argue with a quote that says Newton said this "blah-blah": Andrew Motte translation. You're not saying Newton was right; you're saying what Newton said. Beyond debate. Brews ohare (talk) 12:43, 16 October 2008 (UTC)

Brews, I'm saying that there wouldn't be any centrifugal potential energy in a non-rotating bucket of water, no matter from which frame of reference we view it. According to what you say above, Newton would disgaree with me on that point? I don't think so. As regards Maxwell, I did actually introduce quotes by Maxwell on one occasion and they were deleted and dismissed as being inadmissable.

What we need is to catalogue the points of agreement and disagreement.

What about actually beginning with a point of agreement? Are we all agreed that,

" centrifugal force, whether real or not, is a radial effect which can be alternatively described in cartesian coordinates in terms of Newton's law of inertia " ?

Is there anybody who would disagree with that statement. If we are all agreed with that statement, it could form a part of an introduction to a new unified centrifugal force article.

What about you? Do you agree with that statement? David Tombe (talk) 15:08, 16 October 2008 (UTC)

Hi David: It's not my intention to engage in some re-invention of mechanics from different principles, whatever the merits of this enterprise. For example, I've provided the analysis of the rotating sphere problem based on Newton's laws as I understand them. My approach agrees with textbooks, and requires zero centrifugal force in an inertial frame of reference. To fashion a new explanation by positing some "new" axiom like yours to replace one or more of Newton's laws doesn't interest me.

Centrifugal force, in my opinion, stems directly from the two tied rotating spheres and the analysis of the tension in the cord between them, as described above, and in considerable detail here.

If you do look at this discussion, please notice that it is not sufficient to look at a single case, for example, the co-rotating frame. An essential part of the discussion is the explanation of a range of cases, as discussed in the section here, which shows all cases are explained by the very same, identical "standard" general explanation.

My aim in previous two comments was just to suggest an historical tack on the problem might avoid interminable discussion.Brews ohare (talk) 15:17, 16 October 2008 (UTC)

I disagree with that statement David as it says that it is 'alternatively described'. Alternative to what? The way the standard definition describes it? It's pretty clear that you don't like that standard definition of centrifugal force. Tough. Go deal with that somewhere else please. This article is about the definition that is most usually used.- (User) Wolfkeeper (Talk) 18:29, 16 October 2008 (UTC)

I didn't give a definition. I just said it's a radial effect. Newton's law of inertia is an alternative way of describing that effect in cartesian coordinates. Do we agree on that much? David Tombe (talk) 00:45, 17 October 2008 (UTC)

It's not about agreeing, it's about defining a topic so that it is encyclopedic. Encyclopedias grew out of dictionaries, and articles involve a definition that is not about a term, it's about an underlying concept. In this article the consensus seems to be that it's to do with the centrifugal pseudoforce due to rotating reference frames.- (User) Wolfkeeper (Talk) 02:01, 17 October 2008 (UTC)

Reformulation of mechanics

Hi David: You have made no direct response to the suggestion that historical arguments be pursued. Why is that? Instead, it appears that you wish to reformulate Newtonian mechanics based upon some notions of what is centrifugal force. Perhaps you can work backward from that to Newton's laws, but if so, why not just start from them? Brews ohare (talk) 13:52, 17 October 2008 (UTC)

Personally I think that history of centrifugal force could be a good idea. I wondered if it could be merged here or elsewhere, but I think it would sit uncomfortably in this article, as it would contain information outside the scope of this or any current article.- (User) Wolfkeeper (Talk) 16:36, 17 October 2008 (UTC)

Working from sources

I haven't been able to follow these arguments well enough to sort out what seems to be a major three-way argument about centrifugal force is, or how to represent it. Here's my recommendation: each of you provide a link to a book section that can be read on-line (on google books or amazon for example), that develops the topic the way that makes sense to you. Then, we can discuss whether these sources are mutually compatible or not, or whether we really do need two or three quite different presentations to cover how centrifugal force is treated in the literature. Dicklyon (talk) 18:31, 17 October 2008 (UTC)

The problem with your plan is that the potential issues here are not to do with technical accuracy; they're to do with undue weight. There's multiple different ways to skin this cat, and the presentations here and in the other articles are vanilla exposition of mutually exclusive definitions along lines that we have quite reasonable evidence are currently standard ones.- (User) Wolfkeeper (Talk) 18:47, 17 October 2008 (UTC)

My view is that Centrifugal force (rotating reference frame) is somewhat limited in scope but pretty well serves its purpose as an introduction that hits the main points. It is the presentation found in John R Taylor. Classical Mechanics. p. §9.6 p. 344. ISBN 189138922X..

Editor Harald88 has expressed a wish that Reactive centrifugal force be merged with Centrifugal force (rotating reference frame). I believe he is presently satisfied with two articles, properly cross-linked. These two articles very clearly deal with different topics, as one deals with a "fictitious" force, and the other with a "real reactive force" from Newton's third law.

The desire expressed by David for a single article is a dream of his that I do not understand. It is based upon his notion that with the appropriate intuition the entire subject can be summed up in a few lines and (hopefully) without any need for much math. However, his views do not seem to be consistent with standard Newtonian vector mechanics, and when a simple example is offered like the rotating spheres (a classic of Newtonian era), he will not go into detail mathematically to resolve the matter, but tries to introduce different examples that he feels are strongly supportive of his intuition, and that he feels can be explained by exhortation. His intuition leads him into use of polar coordinates, and I'd love to evolve a clearer exposition of how to use polar coordinates with David, but it just isn't going to happen. He feels that Reactive centrifugal force becomes a "knock-on" or footnote in his approach. There is no source presenting David's viewpoint.

Two other editors also have aimed for a unified conception: TimothyRias and Fugal. Their approach to unification stems from a background in general relativity and the treatment of all fictitious forces as generalized forces in the Lagrangian sense, and expressed in the Christoffel tensor. There are two problems with that, neither admitted by these editors. The first problem is that basing centrifugal force on general relativity formalism is like requiring a scratch be treated by a surgeon: who needs all that mechanism? The second problem is that this approach agrees with the Newtonian vector mechanics only in Cartesian coordinates; so, for example, it leads to centrifugal force in polar coordinates even in inertial frames. (That seems to bring up analogies with David, but I don't think they really agree with David). That puts it at variance with the historical development of the concept of inertial frames. Nonetheless, this approach finds its adherents. I think this different approach is better left to yet another article which can be linked to the present one when and if these editors really get it together and write up such a viewpoint. That way, the reader can simply be advised that there is another terminology in use (if they want to read about it), and this article does not have to embroil and embroider the simpler discussion. A typical example of this viewpoint is Francis Begnaud Hildebrand (1965). Methods of Applied Mathematics. Courier Dover Publications. p. pp. 156-157. ISBN 0486670023. {{cite book}}: |page= has extra text (help) and Ludwik Silberstein (1922). The Theory of General Relativity and Gravitation. D. Van Nostrand. p. p. 29. {{cite book}}: |page= has extra text (help).

The unification sought by the abstract formalists is not unification of Reactive centrifugal force and Centrifugal force (rotating reference frame) but unification with material that now appears in Mechanics of planar particle motion, which is better left the way it is.

So, in short, I think everything is just fine the way it is. Brews ohare (talk) 19:24, 17 October 2008 (UTC)

To add two cents to this, the topic of Centrifugal force seems to attract the most tendentious editors I have found anywhere in Wikipedia (and that is saying a lot). Civility just is unheard of, and scoring rhetorical points is the name of the game, not writing an article. Brews ohare (talk) 19:57, 17 October 2008 (UTC)

I've seen worse. That's why I thought focusing on understanding viewpoints relative to sources might be a useful exercise; thanks for going along. I think that anyone who does not back up their position by sources should be shunned and ignored until they do. So far, that's how I feel about both wolfkeeper and david. Wolfkeeper says we have an undue weight issue, but has not clearly identified what are the views whose weights are wrong relative to sources. David is just confused, so can't really produce sources to back up his position. The others I have yet no idea. Dicklyon (talk) 15:24, 18 October 2008 (UTC)

Yeah, I've seen worse too. We don't have people that are paid stooges editing and introducing fake references that misquote people to the degree that they come onto the talk page to complain.- (User) Wolfkeeper (Talk) 18:54, 18 October 2008 (UTC)

My position is that we don't currently have any undue weight. Merging would break various policies though.- (User) Wolfkeeper (Talk) 18:54, 18 October 2008 (UTC)

Brews, you are probably correct that I would end up in disagreement with Fugal further down the line if he is close to Timothy Rias in his thinking. One of the most intense battles in the edit war was between myself and Timothy Rias. And it was over the issue of whether centrifugal force acts on an object that is at rest in the inertial frame as viewed from a rotating frame. I tried to show Timothy Rias that the transformation equations are restricted by their derivations so as to only apply to co-rotating objects. The angular velocity term must apply to the actual object under consideration and as such there is only one centrifugal force as per in polar coordinates. Fugal was meanwhile arguing the point that I am arguing that polar coordinates and rotating frames involve the same one and only centrifugal force. So I'd be interested to see where Fugal stands on my argument with Timothy Rias. But without going into any maths, I think it should be obvious to everybody that if a bucket of water is not rotating, then there will be no water climbing up the sides. There will be no centrifugal potential energy no matter what reference frame we view it from. David Tombe (talk) 00:02, 18 October 2008 (UTC)

No, this is physics. We do maths. So, you're claiming that the equation 9.36 given by a standard textbook, namely Taylor[1] which depends only on 'r' and the frame rotation vector is wrong. Uh huh.- (User) Wolfkeeper (Talk) 01:03, 18 October 2008 (UTC)

But by some complete catastrophic mischance equation 9.35 for the coriolis force has the velocity term ${\dot {r}}$ in it, but 9.36 doesn't? Is that what you're claiming? That's it's all just a mistake David?- (User) Wolfkeeper (Talk) 01:12, 18 October 2008 (UTC)

Wolfkeeper, Centrifugal force is a topic in physics. And the rotating bucket of water example which I have given serves to prove my interpretation of the maths which you are referring to. The centrifugal force term does have a velocity term included. It is implicit in the angular velocity term. Remeber v = rω. Nobody is arguing with this mathematical expression. The argument is about whether the angular velocity term applies to the object under consideration or to the frame of reference. In cases of co-rotation it will be the same in any event, and all text book examples only ever consider cases of co-rotation. The purpose of the bucket of water example was to demonstrate unequivocally that no centrifugal force acts on water that is stationary in an inertial frame of reference, no matter how we look at it. David Tombe (talk) 14:26, 18 October 2008 (UTC)

David, I think the resolution of your argument immediately above in is the definitions. The Taylor book that wolfkeeper linked probably says it explicitly, but it's at least clear from the equations, that the "fictitious forces" in a rotating frame are conventionally divided into two parts: the centrifugal force that acts on ALL objects, proportional to r, and the Coriolis force, that acts proportion to r_dot, so affects only objects that are not stationary in the rotating frame. For the object that's stationary in the inertial frame, but moving in the rotating frame, you need to look at the resultant of these two. So yes, the centrifugal force still applies to the that object that stationary in the inertial frame, but when you add the coriolis force you get the acceleration need to make it appear to be going in circle. Dicklyon (talk) 15:24, 18 October 2008 (UTC)

In a nutshell Dick's explanation is exactly what is said and calculated in the several examples on the page itself, for example Rotating spheres. Brews ohare (talk) 15:30, 18 October 2008 (UTC)

David is far too smart to believe the ever growing and very long list of people that have previously told him that he was full of it on this point. Right David? Much smarter than all of us?- (User) Wolfkeeper (Talk) 19:17, 18 October 2008 (UTC)

Rotating buckets

Hi David: Usually discussion of rotating buckets and rotating spheres are done one after the other, and supposedly illustrate the same point. Newton's idea is that the water is concave when the water rotates relative to absolute space, and others just say it is a definition of absolute rotation. So everybody (even me) agrees that concavity of the water occurs because of absolute rotation.

Let's go into details. Suppose you rotate with the water. Then it is concave, but you don't see any rotation. Accepting that concavity means the water is rotating, you have to conclude that you are rotating too.

So we still agree I think.

Now comes the trouble: how do you explain the concavity? Of course, you can do like Harald and say: "Hey, I'm obviously rotating, so I'll just switch everything over to an inertial frame and say the rotating water requires a centripetal force to circle around, and it goes concave to create a net inward force." This force is provided by piling water up, the further out you go, the bigger the pile up to get the bigger centripetal force.

Now we don't agree, eh? Because I say the kinematics requires an inward force, and piling up the water provides it. The word "Centrifugal" never comes up. Oh-oh.

The centripetal force is a force requirement, not a force per se but a requirement upon the resultant, net force provided by real forces. This requirement must be satisfied by the actual forces in that frame, namely the force due to pile up of the water. The centripetal force is like setting your bank balance: it says if you want a car, here is the balance you need. But without a account to provide the cash, there ain't nothing going on. Centripetal requirement is a wish, nothing more: want concavity? - get this force; got concavity? - you're providing this force.

Or, I can stay in my rotating world. I say: "Hey, the water piles up because there is a centrifugal force." It piles up higher at larger radius because the centrifugal force increases with radius. It piles up until the inward force from piling up is exactly what is needed to balance the centrifugal force. Notice that in this picture the centrifugal force is real to me and is treated in Newton's laws just like the force of gravity is treated. And look, in this rotating frame the word "Centripetal" never came up. Oh-oh.

And here is the last straw in my argument: suppose we are rotating, but not as fast as the water? So it seems to us the water has the wrong concavity according to our observations of its rotation. Then what's the explanation? In the rotating frame we then say the concavity provides the true rate of rotation of the water, and the discrepancy from our calculation is "fixed" by adding just enough centrifugal force to make things come out right. This little experiment decides our rate of rotation. If we don't need any centrifugal force to explain concavity, we are not rotating relative to the universe.

This last is the key point: the bucket provides a general operational definition to determine whether or not we are in an inertial system: If the observed concavity is explained by the observed rotation of the water with no need for centrifugal force, we are inertial (not rotating). Otherwise, not so.

So there is my view of the rotating bucket. I think you agree with only some of it. I further believe that I can support every point made with numerous citations to existing books, most of them in the article already.

You can call me on that, of course, and I will produce them if you cannot find them already in the article. However, I seem to recall going down this path before, and citations did not help to unseat your views that my arguments above are misinterpretations. Equivalently, that my reporting of the literature (all logic aside) is inaccurate. The discussion turned to whether my sources were authoritative, or current, or a majority opinion, or whatever. So I am somewhat dubious that route leads anywhere. Brews ohare (talk) 04:56, 18 October 2008 (UTC)

Brews, you are making it all unnecessarily complicated. You have detected that there is absolute rotation and that it causes a radially outward centrifugal force. That is all there is to the subject. There is nothing more. David Tombe (talk) 14:32, 18 October 2008 (UTC)

David, you've said this before, but I totally don't get where you see an outward force anywhere in the water in the bucket. The particles are all going in circles, which can only happen if there's an inward force to accelerate them (turn them from going off in a straigt line). There is an outward force on the wall of the bucket itself, but that's from the increased water pressure where the water is high. The water is high at the outside because that's the equilibrium that gives all the right inward forces when everything is moving in circles at constant omega. Dicklyon (talk) 15:09, 18 October 2008 (UTC)

Dick, centrifugal force is involved in that equilibrium that you mentioned, but you avoided saying the actual word. You played its presence down. David Tombe (talk) 19:05, 20 October 2008 (UTC)

No, David: I have "detected that there is absolute rotation and that it causes" concavity in the surface of a bucket of rotating water. The quantitative description of this concavity involves centripetal force in an inertial frame of reference (zero centrifugal force), and centrifugal force in a co-rotating frame of reference (zero centripetal force).

Concavity is a universally observed phenomenon. Its explanation is not universal, but frame-dependent. Brews ohare (talk) 15:14, 18 October 2008 (UTC)

As a word of dissatisfaction, I composed the above long discussion to be a very, very clear statement of the "conventional wisdom" on the bucket example. By simply (i) misreading it and (ii) making no detailed observations upon it you are avoiding any benefit that might come from discussion. Brews ohare (talk) 15:21, 18 October 2008 (UTC)

This discussion, should it occur, could take the form of two columns. The left column is titled: "there is no centrifugal force in an inertial frame". The right column is titled "there is a centrifugal force in an inertial frame". In the left column are quotations from a dozen authorities and textbooks supporting the statement at the top. In the right column are David Tombe's reactions to these quotes and citations, which will be of the general tenor that the quotes are (i) commonly held misconceptions shared by the author (textbooks are written for a superficial audience) or (ii) misinterpretations of what is said (for example, they refer to an "inertial frame" but it isn't what you think it is; for example, you can't use polar coordinates in an inertial frame) or (iii) a view once held but that has been superseded (Newton and Einstein lived long ago when terminology had different meanings). How do you propose to proceed from that point? Brews ohare (talk) 16:01, 18 October 2008 (UTC)

My reaction is to simply take the textbook viewpoint (I'd choose Taylor, for example) and say cavalierly that "it's good enough for Wikipedia work." Brews ohare (talk) 16:06, 18 October 2008 (UTC)

Dick and Brews, I was saying that there is no centrifugal force in the non-rotating bucket, and Wolfkeeper was saying that there is. Are you two now trying to tell me that there is no centrifugal force in the rotating bucket? It's starting to look to me as if you guys are turning everything upside down. No centrifugal force with absolute rotation, but centrifugal force when there is no rotation. Please tell me then what we have to do to get centrifugal potential energy in a bucket of water.David Tombe (talk) 20:06, 18 October 2008 (UTC)

I didn't get that from your statement "You have detected that there is absolute rotation and that it causes a radially outward centrifugal force. That is all there is to the subject. There is nothing more." But I'm not saying that there is or is not a "radially outward centrifugal force"; in the rotating system, there is a "fictional force" that outwardly direction; in the inertial system there's not such a force. The potential energy gradient is a part of the equilibrium solution that goes along with the centripetal force needed to make the water move in a circle. What you have to do to get it is to spin and bucket, and the water with it. Dicklyon (talk) 20:13, 18 October 2008 (UTC)

Dick, well then we are obviously in agreement about the rotating system. I'm fully aware that the pressure arises as a result of an equilibrium between the inward centripetal force and the outward centrifugal force. The argument was about the non-rotating system. I was saying that there is no centrifugal force in the non-rotating system but Wolfkeeper has been saying that there is, when we view it from a rotating frame. I asked him where the centrifugal potential energy is in that case. David Tombe (talk) 20:22, 18 October 2008 (UTC)

I don't understand what you think we agree on; I don't understand what outward forces you refer to in "I'm fully aware that the pressure arises as a result of an equilibrium between the inward centripetal force and the outward centrifugal force." I don't see any inward force in the rotating frame, and no outward force in the inertial frame, so whatever it is you're saying we agree on is escaping me. What Wolfkeeper is saying also remains unclear. I still don't see why we can't explain all the viewpoints from sources in one article. Dicklyon (talk) 20:55, 18 October 2008 (UTC)

Because they are actually defined differently. In polar coordinates the centrifugal force depends on the motion of an object, whereas in the rotating reference frame it depends only on position. The associated coriolis forces are also different- in polar coordinates it is always transverse to the radius, whereas in a rotating reference frame it's simply perpendicular to both the motion and the rotation axis of the frame. The frame centrifugal force acts all the time, and has an associated potential energy. The polar coordinate centrifugal force so far as I am aware isn't a conservative force and certainly isn't usually associated with a potential. Ones is a coordinate force, the other is due to a frame coordinate transformation. Under the wikipedias rules, if they're really defined differently they're supposed to be in a different article. There doesn't seem to be enough overlap here other than the name, and that's specifically excluded under the not a dictionary rule. We also have other articles like Coriolis effect that deals with only one of the two meanings of that term and nobody is complaining there. All in all, it seems unnecessary and even unwise to combine them. We also have space issues right now.- (User) Wolfkeeper (Talk) 22:31, 18 October 2008 (UTC)

p.s. Oh yeah, and all the sources I've seen treat them separately as well, including other encyclopedias.- (User) Wolfkeeper (Talk) 22:32, 18 October 2008 (UTC)

I hesitate to engage with Wolfkeeper on this subject. However, I'd say that I only partly agree with him here. The introduction of polar coordinates or Cartesian or whatever, should not change the physics, and it does not: as pointed out earlier, the water surface is concave when the water rotates. The question is how you choose to analyze the situation.

There are several approaches. One is to use a purely vector approach, and refer to inertial and non-inertial frames. Within that approach, as you will find in Taylor, the situation is exactly as described by Dick: I don't see any inward force in the [co]-rotating frame, and no outward force in the inertial frame.

Another approach is to use a Lagrangian with the generalized coordinates (r, θ) and introduce the generalized force as the double-dot of the generalized momenta. Unfortunately, this generalized force is not any one of the vector forces introduced in the previous formulation. Despite that problem, the same terminology is used to describe different things, always a big help. Hildebrand is available on-line to see how this comes about. (Some authors just use the double-dot terms in the acceleration without invoking any underlying framework like Lagrangian mechanics.)

And lastly, one can use the vector approach and put it in polar coordinates. No surprises here. Dick's description still holds good: I don't see any inward force in the [co]-rotating frame, and no outward force in the inertial frame. For an example, see Taylor, pp. 358-359 for a brief discussion of the frame instantaneously co-rotating with a moving particle, which connects the two terminologies.

So, the possible disagreement with Wolfkeeper is only that the confusion of conflicting terminology is not so much a matter of coordinate system, as it is a matter of how one formulates the problem: whether one chooses the Newtonian formulation with Newtonian forces, or chooses the Lagrangian formulation with generalized forces. It would be great if everybody carefully distinguished between "generalized" centrifugal force and centrifugal force in the sense of Newton and the tides, but such care is unusual. Brews ohare (talk) 00:36, 19 October 2008 (UTC)

Brews, you say that Dick's approach is,

I don't see any inward force in the [co]-rotating frame, and no outward force in the inertial frame

I would certainly like to think so. It's my approach too. But my initial dealings with Dick had rather lead me to believe that he was saying the opposite. I thought that Dick had been somewhat reluctunt to see any outward force in the actual rotation scenario.

Anyway, if we're all agreed on the actual rotation scenario, then I think we should now focus attention on the non-rotating scenario as viewed from the rotating frame. I'll open up a discussion section on that as soon as I am sure that we are are agreed on the 'actual rotation' scenario. David Tombe (talk) 13:28, 19 October 2008 (UTC)

Same page yet?

Hi David: So you agree with both the Knudsen and Hjorth analysis of the bucket in the co-rotating frame, and also the analysis of the banked turn in the inertial frame? Brews ohare (talk) 16:01, 19 October 2008 (UTC)

Brews, I haven't actually looked at it yet. But I have never objected to the idea of centrifugal force or centrifugal potential energy in co-rotating situations. My problem has been with the idea that centrifugal force is present when an object is not rotating relative to the inertial frame. I have been having to argue with people who have been claiming that a centrifugal force exists on stationary objects in the inertial frame, while at the same time denying the existence of centrifugal force in actual rotation situations. David Tombe (talk) 23:22, 19 October 2008 (UTC)

Hi David: Well, before we assume we are all on the same page here, please look closely at these examples. Brews ohare (talk) 00:40, 20 October 2008 (UTC)

I remain very confused about whether I agree with David or not. I don't really have a position on how this stuff should be presented, which is why I was seeking sources to help clarify the positions of others. But I do think I understand the physics, at least basically. I'm still trying to understand what David's trying to tell me. In particular now, what is the "actual rotation scenario" that he refers to and says we agree on? Dicklyon (talk) 04:02, 20 October 2008 (UTC)

I am surprised that David thinks we are close to agreement on the rotating bucket from both the inertial and the co-rotating frame of reference. Maybe that will become definite when he looks more carefully at the two examples Knudsen and Hjorth analysis and banked turn. Do you, yourself, have any comments on these examples or their presentation? Brews ohare (talk) 04:48, 20 October 2008 (UTC)

That bucket analysis looks OK, and in agreement with the source. The linked page doesn't specifically mention that "the centrifugal force" referred to there is a "fictitious force", but going back to earlier pages that becomes clear. That's the only way an outward force and corresponding potential come into the picture. The banked turn looks OK, too, though the drawing is poorly done and confusing (the one in the book at ref 5 is much more clear). It makes sense that it's in the centripetal force article, since that's how it's treat in the source, which doe not introduce centrifugal force until several pages later, as a fictitious force in a non-inertial frame. It's also linked to, and treated again in, reactive centrifugal force, which cites (ref 4) a source that defines cetrifugal force as this outward reactive force. Since these treatments are consistent with the cited sources, I'm happy with them. I still don't know what treatments are common in sources, or even if there are others that someone is proposing. It's clear at least that centripetal in inward, and that centrifugal is outward and has two very different interpretations, one a fictitious force (e.g. on the car) and the other a reaction force (the force felt by the road when the car goes around the curve). Dicklyon (talk) 05:43, 20 October 2008 (UTC)

Dick: Thanks for the comments. I tinkered a bit with the banked turn illustration; maybe it's better. Brews ohare (talk) 09:19, 20 October 2008 (UTC)

Dick, you've got reactive centrifugal force wrong. In a swerving car, a centrifugal force acts on the car. The car transmits a knock on effect to the road. That knock on effect is an action. It is not a reaction. There is no reactive centrifugal force. It is all one subject. The knock on effect would never happen unless there was a centrifugal force to feed it in the first place. And the references that are cited in the reactive centrifugal force article are totally out of context. David Tombe (talk) 19:12, 20 October 2008 (UTC)

I find David's comment confusing. To describe a "centrifugal force acts on the car" we must be in a non-inertial frame, probably the frame attached to the car. Within this frame, David's comment makes sense. However, in an inertial frame, the road is the active agent providing the normal force that keeps the car on track. In this inertial frame, the horizontal component of the normal force from the road provides the centripetal force demanded by circular motion. In this inertial frame the car (subject to the force from the road) exerts a force of reaction upon the road, of which the radial component is the reactive centrifugal force. It is essential to attach terminology to the appropriate frame of reference, and not let it float about like it had an independent existence. Brews ohare (talk) 20:46, 20 October 2008 (UTC)

Confusing indeed. David oscillates between agreeing and saying things like the above. The statements "a centrifugal force acts on the car" and "There is no reactive centrifugal force" need to at least include which frame he's in, in order to be interpretable; as they stand, I can't tell whether I agree with him, or whether he is disagreeing with me. I'm not sure what distinction he means between action and reaction, but it seems irrelevant. And he goes cryptic and elliptic again with "the references that are cited in the reactive centrifugal force article are totally out of context" instead of being specific about which references and what the problem is. Dicklyon (talk) 05:25, 21 October 2008 (UTC)

Both of you need to stop switching into the language of Newton's law of inertia. We have a definite physical effect which is best described in polar coordinates. It is a radially outward force that arises when actual rotation occurs. We don't need to confuse the issue by considering reference frames. The rotating bucket experiment shows that the physical effects and conclusions are frame independent.

Maybe we should do a section on Newton's law of inertia to clarify this point and emphasize the fact that centrifugal force is a radial effect that cannot be properly described using cartesian coordinates. David Tombe (talk) 11:08, 21 October 2008 (UTC)

Maxwell and Centrifugal Force

Brews, I just want to add that Maxwell used that very outward expansion effect to account for magnetic repulsion. In hydrodynamics, centrifugal force shows up as grad (A.v). Imagine two north poles facing each other. The field lines spread outwards. If each line is the axis of a tiny vortex, you can see how centrifugal force is causing the repulsion. David Tombe (talk) 14:37, 18 October 2008 (UTC)

This seems like a complete non-sequitur. Maybe a link to the relevant Maxwell passage would be useful so we could try to interpret what you're saying in terms of what Maxwell said. Dicklyon (talk) 18:04, 18 October 2008 (UTC)

Unfortunately it's not a non-sequitur if you understand where David is coming from. He's trying to rewrite basic physics without going through all that bother of having to learn it properly.- (User) Wolfkeeper (Talk) 18:58, 18 October 2008 (UTC)

Dick, Page 165 in the actual paper, page 5 of the pdf file, second paragraph down in this web link. It's Maxwell's 1861 paper,

[2] David Tombe (talk) 20:10, 18 October 2008 (UTC)

Thanks. I don't see any interpretation there about "outward", "inward", or otherwise, so I'm still not clear what you were trying to say about it. Dicklyon (talk) 22:02, 18 October 2008 (UTC)

Dick, Somehow I didn't expect that you would. What you claimed to be non-sequitur was actually a response to the fact that Brews is genuinely interested in electromagnetism and that he has previously expressed an interest in getting a deeper understanding of the magnetic vector potential A. It was also a response to Brews' suggestion about having a historical section to highlight historical attitudes to centrifugal force. I stated that Maxwell had used centrifugal force to account for magnetic repulsion. You challenged me to provide a citation. I provided the citation. The citation quite clearly confirms what I said. If you can't see that, then I think we will have to admit that there exists a serious problem here with the interpretation of plain English. David Tombe (talk) 13:35, 19 October 2008 (UTC)

I'm only questioning your interpretation of Maxwell's writing as "Maxwell used that very outward expansion effect"; I didn't see support for that particular interpretation there. Dicklyon (talk) 14:43, 19 October 2008 (UTC)

Dick, I wasn't seriously expecting you to see support for that interpretation. But I would expect other people to. Would a quote by Bernoulli be more helpful?

“All space, according to the young [John] Bernoulli, is permeated by a fluid Aether, containing an immense number of excessively small whirlpools. The elasticity which the Aether appears to possess, and in virtue of which it is able to transmit vibrations, is really due to the presence of these whirlpools; for, owing to centrifugal force, each whirlpool is continually striving to dilate, and so presses against the neighbouring whirlpools."

David Tombe (talk) 23:41, 19 October 2008 (UTC)

Interesting. So in this example the outward force you refer to is the force that the rotating stuff impresses on the other stuff that keeps it from expanding (like the pressure that the rotating water puts on the wall of the bucket). That's the centrifugal reaction force. The net force on the rotating bits is still inward.

Dick, one minute you accept the outward centrifugal force. The next minute you deny it. And you are very wrong in saying that the outward expansion effect of a vortex is a reaction. It is very much an action. David Tombe (talk) 11:04, 20 October 2008 (UTC)

Right; what I accept depends on the context of the words around it, which is usually where the meaning come from, by stating for example what frame of reference you're in, and whether you mean the "fictitious" centrifugal force, or the reaction force, or an inward centripetal force. If I sometimes misinterpret you because you've forgotten to state which frame of reference you mean, I apologize. As to what's an action or reaction, I'm not sure I see the distinction; I don't understand your comment "you are very wrong in saying that the outward expansion effect of a vortex is a reaction," since I don't believe I ever commented on "the outward expansion effect"; my comment on the "outward force" was meant to mean that it is the force on the surroundings that is equal and opposite to the centripetal force that is making things go around; that is, it's what has been called the centrifugal reaction force or reactionary centrifugal force or something like that; this is not meant to say that one thing is an action and that another is a reaction. See for example this 1892 Nature article or this book. Dicklyon (talk) 05:49, 21 October 2008 (UTC)

Dick, this whole 'reactive centrifugal force' concept is wrong. In the situations in which it exists, it is the centripetal force that is reacting to a centrifugal force. There would be no force on the side of the door of a swerving car unless there was centrifugal force to begin with. Without centrifugal force, there would be no inward centripetal force acting.

The argument that centrifugal force and the so-called reactive centrifugal force are different because they act on different objects is true. And they don't even have to have the same magnitude. But they are both manifestations of one single underlying effect. A centrifugal force acts on object A. Object A then contacts object B. There is a knock on effect. The magnitude of that knock on effect depends on the degree to which object B yields. Object B might exert an inward centripetal force that totally cancels the outward centrifugal force. On the other hand it might only exert a lesser centripetal force which partially cancels the centrifugal force. The action-reaction pair in the latter case will be at the value of the partial cancellation. But it will have been entirely fed from the original centrifugal force.

The best linear analogy for studying this is the elevator. Gravity is always constant just like the centrifugal force in the above example. But weight varies according to the yield of the floor of the elevator. When the floor is accelerating downwards, the weight and the normal reaction form a low value action-reaction pair. When the elevator is accelerating upwards, they form a high value action-reaction pair.

Always compare centripetal force to normal reaction, and gravity to centrifugal force to get the correct linear anlogies.

I tried to look at your references but they didn't open up like that other one. Should I try again. David Tombe (talk) 10:46, 21 October 2008 (UTC)

Knudsen and Hjorth

I added the Knudsen and Hjorth analysis to the section on Potential energy. Any comments? Brews ohare (talk) 04:32, 19 October 2008 (UTC)

Brews, I haven't actually checked out your edits yet. But I ought to point out to you that the stored energy in the rotating bucket of water is not technically centrifugal potential energy. It is hydrostatic potential energy. However, it has indeed been the result of a transfer from centrifugal potential energy. Centrifugal potential energy is actually just tangential kinetic energy. In a Keplerian orbit, we can use the areal constant to obtain a purely position dependent term for centrifugal potential energy.

The rotating bucket of water would probably be amenable to a Lagrangian analysis. The Lagrangian method is all about conservation of energy. It can be good for certain problems but it also loses the cause. Centrifugal force in Lagrangian formulation will simply merge into kinetic energy.

The gyroscope is analyzed using Lagrangian mechanics. It deals with the conservation of energy and the constraints, but it loses the actual cause as to why the gyroscope doesn't topple over. David Tombe (talk) 23:31, 19 October 2008 (UTC)

I am unsure what you would like to do with your first remark: change terminology a bit? Brews ohare (talk) 09:29, 20 October 2008 (UTC)

For purposes of the discussion in flow, I am more interested in whether you agree with the figures showing the force diagrams in both Potential energy and in the banked turn. Brews ohare (talk) 09:29, 20 October 2008 (UTC)

Brews, I wasn't recommending any changes on the rotating bucket section for the time being. The principles are simple, but the detailed analysis is anything but simple. I'm even having second thoughts about whether or not it would be amenable to a Lagrangian analysis. I'd need more time to think about how this problem should be analysed.

The principles involved are that centrifugal force makes the water want to go outwards. Inward centripetal force prevents it from going outwards. This creates a hydrostatic pressure gradient. There is then an up/down equilibrium that involves gravity. The analysis will be very complicated because it involves the intermolecular forces. It's not a single particle problem and it's not a rigid body problem. It's actually a very complicated problem.

But meanwhile, can we get a statement of agreement on the following,

Outward radial centrifugal force occurs when actual rotation occurs, but that this effect can also be described in cartesian coordinates using Newton's law of inertia, without reference to centrifugal force.

We need to get that clear before we can start looking at the non-rotating scenarios. David Tombe (talk) 10:59, 20 October 2008 (UTC)

Brews, I've just looked at the Knudsen and Hjorth reference. Page 144 confirms everything that I have been saying all along. We only get centrifugal force when there is absolute rotation. There is no centrifugal force in a stationary scenario even if we view it from a rotating frame.

The edit war has been caused by people who have tried to turn everything upside down and deny centrifugal force when it really exists yet claim to see it in situations where it clearly doesn't exist.

The problem that we will be up against now will be as in the Maxwell reference. I would fully expect some editors to deny that that is what page 144 is saying. David Tombe (talk) 11:41, 20 October 2008 (UTC)

David: Page 144 discusses whether the water has a concave surface when it rotates relative to what? The fixed stars or absolute space. That question is not relevant here, and is explored further in Bucket argument. We all absolutely agree that absolute rotation of the water leads to a concave surface. In making this factual observation upon which all observers agree (regardless of their frame), the word "centrifugal" does not come up. That word and the word "centripetal" arise and are part of an explanation of the observation of concavity. This explanation is observer dependent. Maybe you are just being a bit sloppy here, and maybe I am being pedantic, but I get the idea that, for you, "concavity" and "presence of centrifugal force" are synonymous. That is not my usage, and not that of the texts. We cannot allow usage that permits confusion of an observation with its explanation. Brews ohare (talk) 15:42, 20 October 2008 (UTC)

Brews, yes, but page 143 only mentions centrifugal force. There is no mention of centripetal force in this topic. It's a constraint that is built into the geometry. David Tombe (talk) 18:57, 20 October 2008 (UTC)

David, you have to go back to the start of section 6.4 on p. 116 and realize that by centrifugal force he always means the fictitious force in a rotating frame; he also mentions the distinction with centripetal there. And example 6.9 on p.133 he treats the case that you've brought up, about a rotating frame and a particle at rest (non-rotating) in the lab frame; and just as we've said there is still a centrifugal force on that non-moving particle, and also a Coriolis force, and the net is just the centripetal force needed to make the particle move in a circle in the rotating frame. It really does all work, if you just accept the definitions and apply them where they apply. You say "We only get centrifugal force when there is absolute rotation." That much is true, if by "when there is absolute rotation" you mean when the reference frame has absolute rotation. But then you say "There is no centrifugal force in a stationary scenario even if we view it from a rotating frame." Not clear what you mean by "stationary scenario" here, but I don't see support for this idea on p.144. And it's really hard to imagine that your statement "Page 144 confirms everything that I have been saying all along" is verifiable, as what you've been saying all along has not been sufficiently clear or consistent to test. Dicklyon (talk) 06:20, 21 October 2008 (UTC)

Dick, Yes I checked it out. This is where the textbooks become self contradictory. Coriolis force is unequivocally a tangential force. This follows from the derivation in both polar coordinates and in rotating frame transformations (which is actually the same derivation but within the context of a particle that is stationary in a rotating frame).

So no matter what that example says, those transformation equations cannot be applied to the stationary object because it doesn't possess the angular velocity that was used in the derivation.

Also, the Coriolis force never acts in the radial direction and it doesn't have an associated potential energy that could cancel the centrifugal potential energy.

And also, the result doesn't give circular motion. We are in polar coordinates so we need a counter balancing force in order to keep the radial distance constant.

This is a clear example of somebody having extended the application of certian equations beyond their remit. They have lost the plot. They have lost the lessons of the rotating bucket experiment. And that is what has caused all this endless confusion. David Tombe (talk) 11:17, 21 October 2008 (UTC)

I understand that it contradicts you, but where does it contradict itself? Where does anyone imply that Coriolis force is only tangential? That would not work, and you can see. As to polar versus cartesian, you keep bringing that up, but I've seen no case where the choice of coordinates can affect the math or the vector equations, or anything else except maybe the intuitive explanation. See for example p.103 where they do the Coriolis force in 3-space Cartesian coordinates. Your statement "We are in polar coordinates so we need a counter balancing force in order to keep the radial distance constant" is nonsense, and is perhaps at the base of your difficulties. Dicklyon (talk) 15:12, 21 October 2008 (UTC)

No Dick, see the section on this below. David Tombe (talk) 21:52, 21 October 2008 (UTC)

Look in this text, or the cited Taylor text, or whatever. The Coriolis force is a cross product of the frame's omega times the frame-relative object velocity. So the force is in the plane of rotation, orthogonal to the object's frame-relative motion. If the motion is tangential, the Coriolic force is radial, and vice-versa. An object moving in a circle in the frame has a Coriolis force that's inward or outward, depending on the direction of rotation. Dicklyon (talk) 22:30, 21 October 2008 (UTC)

Dick, I'm fully aware of that. The restriction to the tangential direction is not overtly stated in the final result. The restriction is implicit in the derivation. Have you ever looked at the derivation? David Tombe (talk) 22:47, 21 October 2008 (UTC)

Analyzing the Parabolic Water Surface

Brews, this is just for your information. In the non-rotating water, there is a vertical hydrostatic pressure gradient which arises as result of downward gravity acting in opposition to the upward normal reaction of the bottom of the bucket.

When we rotate the water, we add an extra centrifugal force which changes the direction of this hydrostatic pressure gradient.

In the textbook analysis, we ignore both the normal reaction of the bottom of the bucket and also the centripetal reaction of the side of the bucket as these are covered automatically by the constraints of the geometry. The centripetal force in this case is to the centrifugal force what the normal reaction of the bottom of the bucket is to gravity.

We concern ourselves with the two active forces. These two active forces are the downward gravity, and the outward centrifugal force. The resultant of these two forces is at an angle, from which we can calculate the relationship between r and h and get the equation for a parabola.

The gravitational potential energy and some of the centrifugal potential energy has been converted into hydrostatic potential energy. A full analysis would be very cumbersome and not suitable for this article.

You have got the right idea. But could you not somehow simplify the wording in the article even for this simplified analysis? You have a tendency to introduce too many mathematical symbols and cloud the issue. Also, there is no need for a reference to Coriolis Force at the header because the Coriolis force doesn't come into this analysis at all. David Tombe (talk) 13:42, 20 October 2008 (UTC)

Last things first: I don't see "Coriolis force" in the header; I see "Potential energy". Brews ohare (talk) 16:19, 20 October 2008 (UTC)

On to the explanation.We agree that the force on the body of water is transmitted to the bucket walls. Then the reaction force from the bucket walls is transmitted back to the water surface as the normal force F_n. As indicated in the article, to get the shape of the surface, all that is needed is the fact that this force is normal to the surface, which is the consequence of inability of the water to support shear, and equilibrium of the surface element of water, which requires this reaction force from the bucket walls at its location be not only normal but equal to –( F_Cfgl + F_g). I see no conflict with your explanation, although it does fill in some details buried in your phrase "The resultant of these two forces is at an angle, from which we can calculate the relationship between r and h and get the equation for a parabola." I do not see how this explanation "clouds the issue", nor how it is any more complex than your own. Brews ohare (talk) 16:19, 20 October 2008 (UTC)

Your statement "The centripetal force in this case is to the centrifugal force what the normal reaction of the bottom of the bucket is to gravity." can be interpreted so that I would agree with it. However, I am uneasy with it because it implicitly involves looking at matters from two disparate frames, leaving it to the reader to fill in the switch. That kind of thing invites confusion. Brews ohare (talk) 16:19, 20 October 2008 (UTC)

Your statement: "When we rotate the water, we add an extra centrifugal force which changes the direction of this hydrostatic pressure gradient." introduces the notions that enter the "potential energy" approach to the problem. Maybe you would like to propose some wording changes there? Brews ohare (talk) 16:27, 20 October 2008 (UTC)

Brews, you are doing what is called a qualitative treatment. There is nothing wrong with that. It is a standard method used in university physics. And it is good enough for this article.

I just wanted you to be aware however that a qualitative treatment falls short of being a full analysis. And sometimes a full analysis is not even possible. This would be a tricky one to do a full analysis for because it involves inter-molecular forces.

What your qualitative treatment does is to rationalize the parabolic surface in terms of the downward gravity and the outward centrifugal force, which are the only two active forces involved. But it falls short of actually explaining why the water rises. I'm not criticising you for that, but I notice that you have perhaps fallen into the trap of assuming that all the necessary physical explanations are inherent in this qualitative treatment, and that you are then trying to explain them using hand waving explanations about shear stress.

You've got a good grasp of the physics of the situation now. It's just a case of writing a coherently worded section. It is already the best section in the whole article, and it could be made better. David Tombe (talk) 17:03, 20 October 2008 (UTC)

Good point. The explanation does explains the shape of the water surface based upon the observation of equilibrium, but does not explain why equilibrium is expected. Have I got it? Brews ohare (talk) 17:54, 20 October 2008 (UTC)

Brews, Yes. It doesn't explain why that particular equilibrium is expected. And this same lack of understanding extends to many scenarios in mechanics.

We start mechanics using point particles. But once we move into rigid bodies, it becomes alot more difficult. We often use N for normal reaction and work out its value from equations that are based on observation. But we never get an explanation as to why N does what it does. The value of N from the same surface varies according to the circumstances.

The situation then gets even worse for spinning rigid bodies. A gyroscope is analyzed using Lagrangian mechanics. That rationalizes the balance in the motion in terms of conservation of energy. But it falls short of explaining why the spinning gyroscope doesn't actually topple over in the first place.

Another big mystery in classical mechanics is the rattleback. They think they know the explanation, but they don't. The rattleback needs rolling friction to function, but sliding friction impedes its operation. And clearly the rolling friction can't be causing the reversal torque, and neither can the downward gravity. Something else is causing that reversal torque.

But you can watch the motion of a rattleback and rationalize it all with conservation of energy. However, we fall short of actually pinning down the force that causes the reversal of angular momentum.

I would bet that the reversal of angular momentum is caused by an interplay of real centrifugal torque, due to assymetry, and real Coriolis force at the inter-molecular level.

Likewise, I'll bet that Coriolis force at inter-molecular level is involved in inclined planes, screws, and why a column of water doesn't stay upright unsupported, and also as to why the parabolic equilibrium occurs in the rotating bucket of water.

But having said that, Coriolis force plays no officially recognized role in the rotating bucket of water and so it would be better if you removed that reference to Coriolis force near the top of that section.

And when you are writing an encyclopaedia article and you come across something which you don't fully understand that is not directly related to the main point, then you should find a formula of words that side steps that issue altogether.

In other words find a shortened coherent way of writing that section such as to draw attention to the key points. The key points are,

(1) Absolute rotation induces centrifugal force.

(2) Centrifugal force has an associated potential energy.

(3) The parabolic surface on a rotating bucket of water can be explained by making a differential equation out of the ratio of the two active forces involved, ie. downward gravity and outward centrifugal force. David Tombe (talk) 18:51, 20 October 2008 (UTC)

David, I think we all agree on all that, except that to be clear, one needs to specify that the "outward centrifugal force" is a "fictitious" force, and that this analysis is only applicable in the co-rotating frame. In the inertial frame, there is no outward centrifugal force. Right? Dicklyon (talk) 22:26, 20 October 2008 (UTC)

Dick, When something is stationary in the inertial frame, then there is no centrifugal force acting on it. But we can still observe the paraboloic water surface of absolute rotation from an inertial frame of reference. The rotating bucket observations do not depend on our frame of observation.

This is where the confusion seems to come in. The introduction to the article gives the impression that centrifugal force is something which can only be observed from a rotating frame of reference. That is a total misinterpretation of the topic 'rotating frames of reference' and it shouldn't be used as a basis to introduce the subject 'centrifugal force'.

Centrifugal force arises in the topic 'rotating frames of reference' when an object is co-rotating with that frame. If an object is not co-rotating with that frame, or only partially co-rotating, then it will have a centrifugal force based on its own actual angular velocity.

That is what the rotating bucket experiment demonstrates. It's all quite simple. If there is actual rotation, there will be centrifugal force induced. If there is no actual rotation, then there will be no centrifugal force.

Regarding the term fictitious, I presume you mean that when centrifugal force is analyzed in cartesian coordinates in an inertial frame, that the term vanishes and that the effect is described by Newton's law of inertia. David Tombe (talk) 10:08, 21 October 2008 (UTC)

Hi David: You say "The introduction to the article gives the impression that centrifugal force is something which can only be observed from a rotating frame of reference."

This statement is almost true. A true statement would be: "Centrifugal force is something that can be observed only from a non-inertial frame of reference."

You object to this statement because you identify the term "centrifugal force", which is an explanatory term used in rotating frames, with "concavity of rotating water surface", which is an indisputable observation in any frame of reference. The equating of "concavity" and "centrifugal force" must be eradicated, I think. Brews ohare (talk) 14:25, 21 October 2008 (UTC)

You say:"That is what the rotating bucket experiment demonstrates. It's all quite simple. If there is actual rotation, there will be centrifugal force induced. If there is no actual rotation, then there will be no centrifugal force."

That is not correct. A correct statement is:"''That is what the rotating bucket experiment demonstrates. It's all quite simple. If there is actual rotation, there will be a concavity of rotating water surface induced. If there is no actual rotation, then there will be no concavity of rotating water surface induced." Brews ohare (talk) 14:40, 21 October 2008 (UTC)

An additional correct statement would be: "If there is actual rotation, there will be a concavity of rotating water surface induced. In a co-rotating frame this concavity is explained in terms of centrifugal force. In an inertial frame this concavity is explained by the need to generate centripetal force to support the circular motion. That centripetal force is generated by deformation of the water surface so the force normal to the surface has sufficient radial component to provide the required centripetal force." Brews ohare (talk) 14:50, 21 October 2008 (UTC)

Furthermore, it does not matter whether you used Cartesian or polar coordinates, in either frame. The answer is the same, which is that centrifugal force, as typically defined, is zero accept in frames that have some rotation. The kind of centrifugal force you find in inertial frames is according to another distinct defitio, the reactive centrifugal force; it's not a force on the particle moving in a circle, but rather a force that particle exerts on other things in reaction to the centripetal force that's making it move in a circle. Dicklyon (talk) 15:17, 21 October 2008 (UTC)

Verbal pre-amble

I've put some explanation in words in the potential energy section. Maybe they can be improved upon? Brews ohare (talk) 19:15, 20 October 2008 (UTC)

Brews, That is an improvement. Most important is that you comprehend the topic. Then you can gradually improve on the wording over a period of time as you read over it again. I'll make a few suggetsions. The equations are necessary but you could tidy them up a bit. I don't like the capital omegas that you use for angular velocity. Also, try and avoid subscripts and superscripts. Try to simplify the symbolism. It is only a qualitative treatment and so the full vector symbolisms aren't necessary.

Basically, all there is is gh and rω^2. Those are the only two relevant expressions.

Also, I would tend to get rid of all that stuff about the tides. Centrifugal force is a uniform effect with the Earth's rotation whereas the tides are an oscillatory effect and so I can't see the relevance. We need to shorten the article, and that is an example of the kind of chaf that could be deleted. We don't need to go into five body problems and Lagrange points.

And are you sure about the reasons that you have given regarding shear stress and why the water rises up? I don't think that that is a satisfactory explanation. You may be better simply by-passing that issue altogether.

And I'm sure that you have now realized that the entire rotating bucket experiment is frame indepedent. We don't need to analyze it from a rotating frame. The physical effects and conclusions are manifestly clear no matter what frame of reference we observe it all from. David Tombe (talk) 10:23, 21 October 2008 (UTC)

Why does the water rise up? The argument given is pretty simple. Here is a repeat:

When rotation is present, centrifugal force lowers the energy of regions at larger r relative to those at smaller r. This potential gradient tends to drive water to larger radius away from smaller radius. Inasmuch as the total volume of water in the bucket is fixed, and water is incompressible, and it has to fit inside the bucket, movement of water from smaller r to larger must increase the depth at larger r relative to smaller r. Increased depth can be achieved only at the cost of work against gravity. When the energy advantage due to centrifugal force balances the disadvantage of greater height, movement of water equilibrates leaving the equilibrium surface concave.

Do you have any specific objection to this argument? Would you say it differently? Brews ohare (talk)

I agree that the tides things ought to go. The relevant potential there is a combination of centrifugal with gravitational, and I don't see how the current argument applies. Why does the water go to different heights around the equator when the centrifugal equi-potential there is circular? Dicklyon (talk) 15:20, 21 October 2008 (UTC)

The Big Question

The discussion is splitting into too many threads. As a result of the recent discussions, it is now clear that this entire controversy boils down to the answer to one single question.

Some textbooks like to create the scenario in which a stationary object is viewed from a rotating frame of reference and then account for the artifact circular motion in terms of a radially outward centrifugal force and a radially inward Coriolis force.

Try and do this with the bucket of water. Observe a stationary bucket of water from a rotating frame of reference centred on the bucket. There will be no paraboloic surface. So where is the supposed centrifugal potential energy? The supposed Coriolis force doesn't have an associated potential energy. Coriolis force doesn't cause changes in energy. Coriolis force only ever causes changes in direction. So the Coriolis force cannot be used to account for why the centrifugal potential energy has been cancelled out.

So the question is, where is the centrifugal potential energy in a stationary bucket of water as viewed from a rotating frame of reference?

This question is the ultimate proof that some textbooks have been over extending the application of the rotating frame transformation equations.

The solution is therefore to play this aspect down in the main article and to concentrate on scenarios in which the centrifugal force is unequivocally apparent. David Tombe (talk) 12:46, 21 October 2008 (UTC)

Hi David: I will attempt to summarize some of what you have said, and provide a response.

Some textbooks like to create the scenario in which a stationary object is viewed from a rotating frame of reference and then account for the artifact circular motion in terms of a radially outward centrifugal force and a radially inward Coriolis force.

This is a true statement, and it is done in the article as well. Inasmuch as the Coriolis force is a whole new kettle of fish, I recommend this topic be dropped from this discussion until the simpler case is decided. Brews ohare (talk) 13:52, 21 October 2008 (UTC)

So the question is, where is the centrifugal potential energy in a stationary bucket of water as viewed from a rotating frame of reference?

The answer, which I doubt you agree with, is that the centrifugal force is omnipresent in the rotating frame, and corresponding potential energy always is present as well. Introduction of a "test body" will reveal this field, and absence of a test body does not mean the field went away. Brews ohare (talk) 13:52, 21 October 2008 (UTC)

So the Coriolis force cannot be used to account for why the centrifugal potential energy has been canceled out."

The centrifugal potential is not canceled out. It is always present. The force due to this potential is conservative and given by the gradient of the centrifugal potential. The presence of this conservative force does not preclude the action of the non-conservative Coriolis force, and the net force on an object, as always, is the vector sum of all forces present. Brews ohare (talk) 13:52, 21 October 2008 (UTC)

It is evident that discussion of the Coriolis force will not simplify the discussion, which already is going nowhere. Let's stick to the simple case. Brews ohare (talk) 13:52, 21 October 2008 (UTC)

Those "simple cases" would have to exclude David's favorite: stationary object object viewed from a rotating frame. You can't do that one without Coriolis force. But until he understands and accepts that there's a consistent analysis that applies to that case, in reliable sources, he should stop bothering us about it. Dicklyon (talk) 15:24, 21 October 2008 (UTC)

Dick, I've got a reliable source here. Page 144 of the reliable source that we have been referring to gives a quote from Newton's Principia.

"The effects by which absolute and relative motions are distinguished from one another, are centrifugal forces, or those forces in circular motion which produce a tendency of recession from the axis"

He couldn't be more clear in his meaning. When a bucket of water is actually rotating, there will be centrifugal force and we will see this from the parabolic surface. If a bucket of water is only observed in relative rotation, no such effects will be observed. There is no centrifugal force in a stationary bucket of water no matter how we view it. The textbook application of rotating frame transformations to the latter scenario is quite wrong. David Tombe (talk) 23:05, 21 October 2008 (UTC)

Coriolis force

Contrary to my best judgment, which is to leave this discussion to later, here is the explanation of the flat water in the rotating frame of reference

If a bucket of water with a flat surface is observed in the rotating frame, located let's say at the origin of the frame, all observers (inertial and rotating) agree that the water in the bucket is not rotating because the surface is flat.

The issue as always is how to explain the observation. For the stationary observer the explanation is "The water is stationary and it also looks stationary to us. End of story."

For the rotating observer, matters are more complex. A test body shows that all co-rotating masses are subject to centrifugal force. A test body also shows that all bodies that appear to move are subject to Coriolis force and centrifugal force. Again, that applies to a sample volume of water in the bucket.

In particular, a sample volume of water from the water in the bucket appears to be in uniform circular motion. That is to say it is subject to both Coriolis and centrifugal forces.

The apparent circular motion of our water sample (or of a test body mirroring the circular motion) has a kinematic requirement for a centripetal force in the rotating frame. That is, circular motion requires a force to explain non-straight-line motion. These rotating observers use a test body to find that a test body in circular motion generates this centripetal required force as the vector sum of the Coriolis force due to its apparent motion and the centrifugal force, which is motion independent. These two forces add to provide precisely the kinematic force requirement on the water sample. Gravity forces are not part of the discussion, which involves only the radial direction, not the vertical. Hence, the water does not need to pile up, and the water surface remains flat. The entire argument is provided in exhaustive mathematical detail in the article. Brews ohare (talk) 13:52, 21 October 2008 (UTC)

Brews, I'm glad to see that you are thinking about it. You have at least realized that there is a case to be answered. But at the end of the day, the water surface is flat no matter from which frame of reference we view it. If we attempt to introduce a centrifugal force in the rotating frame we end up in a state of total contradiction, because the flat surface tells us that there is no centrifugal force. Bringing in the Coriolis force has no bearing on it because there is no Coriolis potential energy that could possibly cause a cancelling tension. The easiest conclusion to come to is that the textbooks have got it wrong on this one. And I could point to at least three other flaws in the textbook argument.

Does it not make sense to you that centrifugal force occurs during absolute rotation and that it doesn't occur when there is no rotation? Can you not see that centrifugal force is an absolute effect that arises in connection with absolute motion? David Tombe (talk) 15:06, 21 October 2008 (UTC)

David, it is indeed awkward that in the rotating frame there's a centrifugal force on the still flat water. But it's only awkward, due to the chosen definitions of the centrifugal and Coriolis fictitious forces. It's NOT contradictory, and does not describe different physics, nor get a different answer, than analysing in the inertial frame, in a coordinate system of your choice. So get over it. Dicklyon (talk) 15:27, 21 October 2008 (UTC)

David: You say: "the water surface is flat no matter from which frame of reference we view it. If we attempt to introduce a centrifugal force in the rotating frame we end up in a state of total contradiction, because the flat surface tells us that there is no centrifugal force."

Yes, the water is flat. In the rotating frame, however, the flat surface does not mean there is "no centrifugal force". It means that there is not only a centrifugal force. Brews ohare (talk) 15:37, 21 October 2008 (UTC)

You say: "there is no Coriolis potential energy that could possibly cause a canceling tension."

That seems to suggest that non-conservative forces (Coriolis force, e.g.) cannot exert an influence. Why would that be? There is no need that all forces be expressed as gradients of a potential. They still are real. Brews ohare (talk) 15:37, 21 October 2008 (UTC)

By the way, textbooks do sometimes get things wrong. When that happens, your choices are to cite others that say they got it wrong, or at least books that get it right, or to publish your criticism in a reliable source; putting your analysis into the article before it appears in a reliable source is WP:OR. In this case, however, they got it right. Dicklyon (talk) 15:30, 21 October 2008 (UTC)

David: You say: "Does it not make sense to you that centrifugal force occurs during absolute rotation and that it doesn't occur when there is no rotation? Can you not see that centrifugal force is an absolute effect that arises in connection with absolute motion?"

I am repeating myself here. The term "centrifugal force" is not synonymous with "absolute rotation". Rather, "centrifugal force" is a term restricted to use in explanations made by rotational observers, like "meows" are used by cats to describe their experiences. In inertial frames, centrifugal forces don't come up. David, you have to face the fact that your use of "centrifugal force" as a synonym of "absolute rotation" is your own choice of usage, and is at variance with standard terminology. Brews ohare (talk) 15:50, 21 October 2008 (UTC)

I'm just glad we have David Tombe here to point out the contradiction that unaccountably everyone in the history of physics has missed. We are truly blessed in that regard, here on the Wikipedia. That the obvious state of total contradiction exists is a terrible indictment on the state of modern physics. I'm just going to go burn all my books, because David Tombe's argument has convinced me. I'm also going to start a picket line at CERN, since that design is based on modern physics, and those overeducated dumbos that work there are obviously incompetent fools. Oh yeah, and don't expect me online anymore; I no longer believe in quantum physics, and that's the principle that silicon chips work on. And to think, David Tombe was banned, and we nearly missed out!!!!- (User) Wolfkeeper (Talk) 18:00, 21 October 2008 (UTC)

Wolfkeeper, I'm not sure if the implications of all this have any relevance to quantum mechanics or what goes on at CERN. The implications are in electromagnetism and the missing term in the Lorentz force which accounts for magnetic repulsion. David Tombe (talk) 23:14, 21 October 2008 (UTC)

In your sarcasm, you mix up modern with classical physics. Still, good point. As wikipedians we are constrained to follow the field, so we won't actually be able to benefit from David's insights. Dicklyon (talk) 19:07, 21 October 2008 (UTC)

Sorry folks, but I find this kind of comment out of place and distasteful. Whatever else, the discussion with David has led to improvement of the article. And trying to explain something is what the article is about: it's not about being understandable to a clique of the indoctrinated. Brews ohare (talk) 19:31, 21 October 2008 (UTC)

You're right. Sometimes one gets frustrated and resorts to sarcasm, but it's not the best way forward. Sorry I joined in. Dicklyon (talk) 19:42, 21 October 2008 (UTC)

Dick: Thanks for the note of moderation. Of course, I'm guilty myself of such things, especially when the editor involved takes a snotty attitude that I'm a dunce and therefore worthy mainly of scorn and ridicule. Matters do progress better when the guidelines in the template at the top of the page are followed. Brews ohare (talk) 19:57, 21 October 2008 (UTC)

Electromagnetism can be defined by Maxwell's equation. It's not always well understood by people (even Maxwell himself) that Maxwell's equations are equivalent to Special Relativity. This article is about Newtonian Mechanics.- (User) Wolfkeeper (Talk) 00:04, 22 October 2008 (UTC)

Wolfkeeper, Special relativity isn't even about the same thing as Maxwell's equations. One is about time dilation, mass increase, and length contraction in moving particles. The other is about the relationship between charge, currents, electric fields, and magnetic fields. My point was that centrifugal force is the missing fourth term in the Lorentz force. Maxwell had it in one of his early papers. It's interesting to note that on the Eric Weisstein link on Lorentz Force that he has substituted the Coriolis vXB term for the centrifugal grad(A.v) term in equation (8). I don't know what he was playing at. See the link yourself,

[[3]] David Tombe (talk) 18:15, 22 October 2008 (UTC)

Figure on Lagrange points

What is the pertinence of this figure to the topic?

Delete: I recommend it be removed. Brews ohare (talk) 13:15, 21 October 2008 (UTC)

Brews, I agree. Remove all chaf. David Tombe (talk) 15:07, 21 October 2008 (UTC)

Tides

I removed the earliest reference to tides, but left in the reference in the historical section. In the historical section it plays a role as an early introduction to the idea of centrifugal force as "artificial gravity", which motivated the development of general relativity by providing an analogy, as indicated in the various citations in this section. Brews ohare (talk) 15:58, 21 October 2008 (UTC)

Notation

David: You say: I don't like the capital omegas that you use for angular velocity. Also, try and avoid subscripts and superscripts. Try to simplify the symbolism. It is only a qualitative treatment and so the full vector symbolisms aren't necessary.

In response, Ω is a very commonly used notation for the angular rate of a frame. Virtually all the sources cited use this notation in their vector formulations for the fictitious forces, in particular Arnol'd and also Taylor.

Subscripts are used as in F_g, F_Cfgl so that the same symbol F can be used for "force" for all types of force. That seems better to me than using, for example, ${\boldsymbol {G\ ,C}}$.

Any specific suggestions? Brews ohare (talk) 17:30, 21 October 2008 (UTC)

Brews, it's only a minor issue but I would have tended to use the lower case omega. Also, I would have tried to avoid the force symbol altogether and lead in with the actual accelerations g and ω^2r, having introduced them in the text. David Tombe (talk) 21:47, 21 October 2008 (UTC)

The lower case is more often used for the angular velocity of objects, points, or particles; upper case for the frame. Dicklyon (talk) 22:22, 21 October 2008 (UTC)

The Knudsen and Hjorth example uses lower case. David Tombe (talk) 23:08, 21 October 2008 (UTC)

Reactive Centrifugal Force

Dick, You have got this whole 'reactive centrifugal force' concept wrong. In the situations in which it exists, it is the centripetal force that is reacting to a centrifugal force. There would be no force on the side of the door of a swerving car unless there was centrifugal force to begin with. Without centrifugal force, there would be no inward centripetal force acting.

I have no quarrel with calling the centripetal force the reaction and the centrifugal the action; the action of the car on the road (or person against the door) is centrifugal, and the reaction of the road on the car (or door on the person) is centripetal. What's the difference? The point is that the force on the object in circular motion is inward, and the equal and opposite force on something else is outward. Dicklyon (talk) 07:26, 22 October 2008 (UTC)

The argument that centrifugal force and the so-called reactive centrifugal force are different because they act on different objects is true. And they don't even have to have the same magnitude. But they are both manifestations of one single underlying effect. A centrifugal force acts on object A. Object A then contacts object B. There is a knock on effect. The magnitude of that knock on effect depends on the degree to which object B yields. Object B might exert an inward centripetal force that totally cancels the outward centrifugal force. On the other hand it might only exert a lesser centripetal force which partially cancels the centrifugal force. The action-reaction pair in the latter case will be at the value of the partial cancellation. But it will have been entirely fed from the original centrifugal force.

Yes, both are different descriptions of the same physics; the act on different bodies, and are in different reference frames. The rest I don't follow; what do you mean by a "knock on effect"? And what is this cancellation you're speaking of? A balance of forces? On what? Dicklyon (talk) 07:26, 22 October 2008 (UTC)

The best linear analogy for studying this is the elevator. Gravity is always constant just like the centrifugal force in the above example. But weight varies according to the yield of the floor of the elevator. When the floor is accelerating downwards, the weight and the normal reaction form a low value action-reaction pair. When the elevator is accelerating upwards, they form a high value action-reaction pair.

I'm not familiar with that definition of weight. I suppose you mean like the reading of a scale that one is standing on? I understand that when you're accelerating, that will not be equal to the force of gravity. Still, I don't see how this analogy is applicable. Maybe you need to clarify with an example of what your object A and object B are, and what happens when you're forces aren't balanced. Dicklyon (talk) 07:26, 22 October 2008 (UTC)

Always compare centripetal force to normal reaction, and gravity to centrifugal force to get the correct linear anlogies. David Tombe (talk) 21:54, 21 October 2008 (UTC)

David: Have you abandoned the earlier discussions? Taking up Reactive centrifugal force seems to be opening up new areas of dispute. I assume you are aware that the article Reactive centrifugal force and its examples do not agree with your comments above? Brews ohare (talk) 22:10, 21 October 2008 (UTC)

In particular, I have made the following statement: "David, you have to face the fact that your use of "centrifugal force" as a synonym of "absolute rotation" is your own choice of usage, and is at variance with standard terminology." Do you have a response to this observation? Brews ohare (talk) 22:18, 21 October 2008 (UTC)

Brews, I brought that down here because Dick didn't reply to it above, yet he expressed some misinformed views about reactive centrifugal force in a reply to another edit.

Now I've replied, interlinearly above. And I'm with Brews on the string, below. Dicklyon (talk) 07:26, 22 October 2008 (UTC)

I can't imagine any practical illustration which would contradict what I have said above, especially since all your illustrations are restricted to circular motion in which case the centrifugal force and the centripetal force will always be numerically equal. The point is that the floor of a rotating space station only exerts a normal reaction when the object on the floor is already being subjected to outward centrifugal force. Likewise the tension in a string only arises when the weight on the end of it pulls it taut due to its outward centrifugal force. David Tombe (talk) 22:26, 21 October 2008 (UTC)

David: The rotating sphere example discusses the tension in the string extensively, for a variety of cases. Do you agree with that discussion and those examples? Brews ohare (talk) 23:45, 21 October 2008 (UTC)

Centrifugal Potential Energy in Rotating Frames of Reference

Dick, first of all, have you ever followed the derivation of the rotating frame transformation equations through line by line? The principle is identical to that used to derive the polar coordinate expressions. In the latter case, the Coriolis term is specifically stated to be tangential. In the former case, in which a context has been given in the form of referencing a fixed point in a rotating frame, you will find that the Coriolis term is also strictly in the tangential direction.

No, and I'm not likely to follow it if you don't give me a specific reference to which derivation you mean. Dicklyon (talk) 22:19, 21 October 2008 (UTC)

The derivation is based on considering the motion of a point that is fixed in a rotating frame of reference. The angular velocity ω which prevails throughout the analysis applies strictly to the point that is fixed in the rotating frame. The centrifugal force term applies to that point and the expression ω^2r comes about when we have considered the limit as dr and dθ tend to zero, in which case it is a purely radial effect. Since the Coriolis term makes up the other side of the right angle triangle, it is a purely tangential effect.

You cannot apply this transformation equation to a stationary particle in the inertial frame as viewed from a rotating frame.

And you cannot point the Coriolis term in the radial direction.

David: These statements are at the lease debatable, and in my opinion not generally true, though perhaps true in some cases. For example, the so-called acceleration transformation formula found in very many texts applies to an accelerating particle in general motion: (see R. Douglas Gregory (2006). Classical Mechanics: An Undergraduate Text. Cambridge UK: Cambridge University Press. p. Eq. (17.16), p. 475. ISBN 0521826780.)

$\mathbf {a} _{A}=\mathbf {a} _{B}+2\ {\boldsymbol {\Omega }}\times \mathbf {v} _{B}\$ $+{\frac {d{\boldsymbol {\Omega }}}{dt}}\times \mathbf {x} _{B}\ +{\boldsymbol {\Omega }}\times \left({\boldsymbol {\Omega }}\times \mathbf {x} _{B}\right)\ ,$

where subscript "A" refers to an inertial frame and "B" to a non-inertial frame. According to this result the Coriolis force is inward radial in the example of a stationary body that is viewed from a rotating frame. Brews ohare (talk) 00:45, 22 October 2008 (UTC)

And even if you do all that, you are still left with a net inward force. In order to have a circular motion, you need to have a net zero radial force. You would know that if you had studied planetary orbital motion. But that is one important sourced topic which has been consistently disallowed from this article.

And if you don't wish to acknowedge those mathematical arguments, the proof of the pudding is in the eating.

With a bucket of water, there is a parabolic surface when actual rotation occurs. That parabolic surface is attributed to centrifugal potential energy. That is a scalar quantity which is frame independent.

David: No, the parabolic surface is attributed to absolute rotation. Its explanation in the rotating frame involves centrifugal potential energy. Brews ohare (talk) 23:22, 21 October 2008 (UTC)

When there is no rotation, there is no parabolic surface and there is no centrifugal potential energy. You cannot create the centrifugal potential energy and the parabolic surface simply by observing it from a rotating frame of reference.

David: You are ambiguous here. If there is no rotation of the water there is no parabolic surface. If there is rotation of the frame of reference there is centrifugal potential energy, regardless of what experiment one does in the rotating frame, including looking at buckets of water. Brews ohare (talk) 23:25, 21 October 2008 (UTC)

So the textbooks which push this ridiculous line have got it completely wrong. They have completely lost sight of physical reality. They have become so totally blinkered with the maths, that they have forgotten the restrictions implicit in the derivations which led to the formulae in the first place. David Tombe (talk) 22:17, 21 October 2008 (UTC)

I disagree; the books describe the physical reality correctly. Can you point to any reliable sources that do it your way? Dicklyon (talk) 22:21, 21 October 2008 (UTC)

I can point to reliable sources which contradict what it says in different chapters in the same book. I have also supplied reliable sources for orbital mechanics which have been dismissed. These related to the radial equation and the need to balance forces in circular motion.

You say that the books describe the physical reality correctly. If a bucket of water is not rotating, it has a flat surface. It therefore contains no centrifugal potential energy. A book which tries to tell us that a centrifugal force exists in this situation, if we view it from a rotating frame, is not describing physical reality correctly.

David: Yes, if the water is not rotating wrt absolute space, it has a flat surface. If we observe that water from a rotating frame, it is subject to a centrifugal force, however, that is overcompensated by a Coriolis force. This situation was described above. Brews ohare (talk) 23:29, 21 October 2008 (UTC)

And I would guess that you have never studied the mathematical derivation in question to know whether it contains restrictions of application or not.

This is not a question of reliable sources. This is a question of why some sources are being dismissed and others promoted in order to turn the whole physical reality of centrifugal force upside down and emphasize that it exists on stationary objects when viewed from a rotating frame but that it doesn't really exist in actual rotation situations.

David: At this point you are becoming tendentious. You need to develop this argument carefully with actual sources and verifiable quotations. You might begin with, say, two of the "dismissed sources" and what they have to say that is being ignored. Brews ohare (talk) 23:32, 21 October 2008 (UTC)

You yourself saw a Maxwell source which indicated unequivocally that he considered magnetic repulsion to be caused by outward expansion of vortices. Nobody was asking you to accept Maxwell's explanation. But you attempted to deny that Maxwell was even saying that at all. That was after a very quick casual glance. But I have studied that paper for years, and I can assure you that that is exactly what Maxwell was saying. It's a question of reading plain English. David Tombe (talk) 22:39, 21 October 2008 (UTC)

David: The use of vortices by Maxwell is a difficult subject that actually requires an historian's skills to untangle the meaning of verbiage then vs. verbiage now, never mind what the merit of these vortex theories is in today's physics. This topic is best left for another discussion. Brews ohare (talk) 23:36, 21 October 2008 (UTC)

Brews, what you are saying is that although centrifugal force causes the parabolic surface on a rotating bucket of water, the centrifugal force vanishes when we observe it from the inertial frame, but the parabolic surface remains.

How do you then account for the rising water and the parabolic surface in the inertial frame without centrifugal force? You can't use centripetal force because it was there anyway in the rotating frame and it played no part in your qualitative treatment of the parabolic surface.

No, there is no centripetal force in the rotating frame; everything is static in the bucket example, so there's no acceleration, hence no need for centripetal force. Dicklyon (talk) 15:46, 22 October 2008 (UTC)

Careful here! Centripetal force is a real force, and hence appears in every frame! There's no acceleration in that case because it's cancelled by the centrifugal force.- (User) Wolfkeeper (Talk) 17:46, 22 October 2008 (UTC)

Wolfkeeper: Centripetal force can appear in any frame, but in the co-rotational frame the water appears to be stationary, so there is no need for the co-rotational observer to request any centrifugal force. There is no kinematic requirement based upon their observations. In the co-rotational frame the equilibrium is set up between (i) gravity, (ii) normal reaction force of water, and (iii) centrifugal force. There is no centripetal force in this example. Brews ohare (talk) 20:36, 22 October 2008 (UTC)

Both centripetal force and centrifugal force are radial forces and both are described in polar coordinates. Yet you seem to think that one of these two forces only exists if we view a situation from a rotating frame of reference? David Tombe (talk) 12:02, 22 October 2008 (UTC)

No, the coordinate system is completely irrelevant. The vector equations usually don't specify or require any particular coordinate system. And yes, by definition, the centrifugal force as defined only exists in the rotating frame, and is a "fictitious" force designed to make f=ma work in that frame even though it's not an inertial frame. Dicklyon (talk) 15:46, 22 October 2008 (UTC)

Dick, you've just contradicted yourself. Is the concave surface caused by centrifuagl force or not? David Tombe (talk) 18:04, 22 October 2008 (UTC)

David: No, I am saying everybody sees concavity of water when it is in absolute rotation. But observers that co-rotate see a static equilibrium between "centrifugal forces" and the inward resultant of gravity and normal force of the water beneath, while those that do not rotate (the stationary guys) say its the inward resultant of gravity and normal force of the water beneath producing the centripetal force demanded by what they see as circular motion. Everybody agrees on three things: (i) the water is in absolute rotation (its surface is concave), (ii) gravity is at work, and (iii) the water below the surface produces a normal restoring force. How you assemble these facts depends on observer. The explanation varies with observer, just like a universally observed "war" may be "economic struggle" or "good vs. evil" depending on your perspective. "Centrifugal force" participating in equilibrium is one observer's viewpoint. Circular motion requiring "centripetal force" is the other viewpoint. "Centrifugal" is in only one observer's dictionary, "Centripetal" only in the other's. What's so hard about this is that you insist that "Centrifugal force" is a concomitant of "Absolute rotation": one implies the other; it's not the case except in your own idiosyncratic usage. "Absolute rotation" of the water is a synonym for "concavity of the water surface", and need have nothing to do with "centrifugal force", depending upon your frame of reference. Take a look at David P. Stern. Brews ohare (talk) 14:00, 22 October 2008 (UTC)

Idiosynchratic usage

David: What's so hard about this is that you insist that "Centrifugal force" is a concomitant of "Absolute rotation": one implies the other; it's not the case except in your own idiosyncratic usage. "Concavity of the water surface" is an operational definition for "Absolute rotation" of the water, and its explanation need have nothing to do with "centrifugal force", depending upon your frame of reference. Take a look at David P. Stern. Brews ohare (talk) 16:54, 22 October 2008 (UTC)

David: Maybe you are just being a bit sloppy here, and maybe I am being pedantic, but I get the idea that, for you, "concavity" and "presence of centrifugal force" are synonymous. That is not my usage, and not that of the texts. We cannot allow usage that permits confusion of an observation with its explanation. Brews ohare (talk) 15:42, 20 October 2008 (UTC)

David: In particular, I have made the following statement: "David, you have to face the fact that your use of "centrifugal force" as a synonym of "absolute rotation" is your own choice of usage, and is at variance with standard terminology." Do you have a response to this observation? Brews ohare (talk) 22:18, 21 October 2008 (UTC)

Brews, it was also Newton that linked centrifugal force with absolute rotation. You can see the quote from the Principia at about page 144 in the reference that you provided. The concave surface on a rotating bucket of water is caused by centrifugal force. You even did a qualitative treatment for the parabolic surface using centrifugal force. You are agreed that centrifugal force is the cause of the parabolic surface in the rotating frame of reference. It's an absolute physical effect, so how could the cause be any different for people sitting watching the rotating bucket? David Tombe (talk) 18:00, 22 October 2008 (UTC)

Ah, but this article isn't on Newton's usage of the term. That usage is fairly uncommon these days, but it's over at Reactive centrifugal force.- (User) Wolfkeeper (Talk) 18:34, 22 October 2008 (UTC)

Wolfkeeper is correct on the usage by Newton. And centrifugal force is not an absolute effect; concavity of the absolutely rotating water is an absolute effect. Centrifugal force is an artifact used in explanation, and is unnecessary in an inertial frame, by definition of an inertial frame. Brews ohare (talk) 20:43, 22 October 2008 (UTC)

I take it that your direct answer to my question about your usage is:

"Whether modern usage agrees with me or not, my usage of the term should be the commonly used term, because I believe (whether or not I am alone in this belief) that "centrifugal force" is a physical effect that is frame- and observer-independent."

If you would rephrase this interpretation of your position, please do so.

The next step is to support your usage (hopefully in a modern contest) by citing sources that employ your usage. That is, sources that say:

"Centrifugal force is found in inertial frames."

I believe that can be done, but not in the context of the bucket experiment. For example, you could cite Hildebrand. However, that puts you in the "generalized centrifugal force" camp, and outside of Newtonian vector mechanics. Brews ohare (talk) 21:27, 22 October 2008 (UTC)

Brews, There is no such thing as reactive centrifugal force as a distinct topic from centrifugal force. And it is not reactive anyway. It is pro-active. There shouldn't be a separate article to cover reactive centrifugal force, and for that matter, if you are going to have it at all then the rotating bucket should be over there and not in this article, because the rotating bucket has got nothing whatsoever to do with frames of reference. Centrifugal force is an outward pressure that comes with rotation. It doesn't matter what frame we observe it from. Did you once see Newton talking about 'reactive centrifugal force' when he was describing the outward physical effects of absolute rotation? No. Newton recognized just one centrifugal force and so did Maxwell and so did Bernoulli.

In fact, there is no room for centrifugal potential energy in an article that deals with so-called frame dependent fictitious forces. As for generalized centrifugal force, the Lagrangian formulation merely merges centrifugal force with kinetic energy and proves my point that it is present in the inertial frame. David Tombe (talk) 21:38, 22 October 2008 (UTC)

WE HAVE BEEN TOLD.- (User) Wolfkeeper (Talk) 22:24, 22 October 2008 (UTC)

The generalized centrifugal force approach does place centrifugal force in an inertial frame. That is exactly what I said, isn't it? The other part of what I said is that this approach is outside Newtonian vector mechanics, which by definition says there is no centrifugal force in an inertial frame. Want chapter and verse on inertial frames and fictitious forces? It is there a'plenty in the various Wiki articles, from sources as varied as Landau & Lifshitz, Arnol'd, Taylor, Gregory etc. etc. See Non-inertial reference frame for some quotes. "Generalized" centrifugal force is a different breed of cat. See Hildebrand Dignath et al. IMechE Lenarcic et al'. Brews ohare (talk) 21:49, 22 October 2008 (UTC)

David: You might find it interesting to read about Newton and Huygens in Topper, who describes Newton as coining the term "centrifugal", and Huygens with coining the word "centrifugal". For the ball swinging on a rope, "centripetal" is the force on the ball exerted by the rope, and "centrifugal' is the force exerted by the ball upon the rope. Being action and reaction they are equal and opposite. There appears to have been some controversy among historians over what Newton actually meant. See Shea. This confusion appears now to be resolved among historians. Meli quotes Newton as saying in the third person: "the centrifugal endeavor is always equal to the force of gravity and is directed in the opposite direction because of the third law of motion in Newton's Principia Mathematica." All this historical debate underlines the importance of using modern sources in this Wiki article. Brews ohare (talk) 03:47, 23 October 2008 (UTC)

Brews, This all comes down to your misinformed belief that centrifugal force does not exist in the inertial frame of reference. Well you are quite wrong. I'm sorry that this argument then has to come down to the issue of sources and citations because I don't like having to resort to sources for something that is so basic.

I have here the Herbert Goldsetin 'Classical Mechanics' textbook which I used at university. There is a chapter on central force orbits which doesn't even touch on the topic of rotating frames of reference. It reduces the planetary orbital equation to a one dimensional scalar equation in the radial distance. It does this by combining the centrifugal force term with the Keplerian areal constant to obtain an inverse cube law expression. And in black and white on page 76 is says,

"The significance of the additional term is clear if it is written as $mr{\dot {\theta }}^{2}=mv_{\theta }^{2}/r$, which is the familiar centrifugal force"

Then over on page 78 when describing the motion in an unbounded orbit he says,

"A particle will come in from infinity, strike the "repulsive centrifugal barrier", be repelled, and travel back out to infinity - - -"

So long as you continue to believe that centrifugal force can only be acknowledged in rotating frames of reference, then you will forever remain confused about this topic. Where did you get the idea that centrifugal force only exists in rotating frames of reference? The children in the garden know that you don't have to be inside a bucket of water that is swung over your head to observe that centrifugal force stops the water from pouring out. David Tombe (talk) 11:27, 23 October 2008 (UTC)

David, the only kind of centrigual force in an inertial frame is the outward force that an object moving in a circle exerts on whatever is pushing or pulling it inward to accelerate it sideways. There's an article on that called reactive centrifugal force. If there's some third meaning of centrifugal force that we've missed, we can take a look at it; is that book available any place we can look at? Can you scan a few pages and send them to us? Does any other book approach the topic this way? It sounds to me like the "one dimensial scalar" approach is sort of like converting into a non-inertial frame connecting the two bodies, so that all motion is along a line; in that frame, centrifugal force exists as an outward force. Otherwise, what is this outward force coming from? Classically, gravity is the only force operating on planets. Dicklyon (talk) 15:21, 23 October 2008 (UTC)

No Dick, we've been over this before. That force is not reactive, and it needs a centrifugal force to feed it. And there shouldn't be a separate article to cater for that effect. Wolfkeeper created that separate article during an edit war. In my opinion he did so to remove all examples that showed that centrifugal force had real effects. David Tombe (talk) 16:57, 23 October 2008 (UTC)

Like here's a book that does it your way. Based on Hamiltonians and manifolds and such, it gets a "repulsive" centrifugal force. I'm pretty sure this is due to projecting into the frame of just distance, but someone else needs to help interpret. Dicklyon (talk) 15:43, 23 October 2008 (UTC)

I've been content to just watch this play out with the least number of people confronting David. However, for the benefit of everyone currently involved, the use of Goldstein was brought up awhile back near the end of July. The full quote of Goldstein on page 76 reads (with my own emphasis added):

The equation of motion in r, with ${\dot {\theta }}$ expressed in terms of l, Eq. (3.12), involves only r and its derivatives. It is the same equation as would be obtained for a fictitious one-dimensional problem in which a particle of mass m is subject to a force $f'=f+{\frac {l^{2}}{mr^{3}}}$. The significance of the additional term is clear if it is written as $mr{\dot {\theta }}^{2}=mv_{\theta }^{2}/r$, which is the familiar centrifugal force.

Later in the book (pg 176), Goldstein states with regard to orbits and the centrifugal force:

If we analyze the motion of the Sun-Earth system from a frame rotating with Earth, it is of course just the balance between the centrifugal effect and the gravitational attraction that keeps the Earth (and all that are on it) and Sun separated. An analysis in a Newtonian inertial frame gives a different picture. As was described in Section 3.3, the angular momentum contributes to the effective potential energy to keep the Earth in orbit.

And with that, I will go back to the bleachers. I have no further desire to engage in this debate except to help provide and assess reliable sources. Cheers. --FyzixFighter (talk) 15:49, 23 October 2008 (UTC)

FyzixFighter, So what you're saying is that although Goldstein points out in one chapter that centrifugal force provides the outward repulsive effect in planetary orbits, that in another chapter he says that this cause is only so in a rotating frame of reference. And what cause does he then give for this repulsive effect in the Newtonian inertial frame? He gives some formula of words "the angular momentum contributes to the effective potential energy to keep the Earth in orbit" which when stripped down, means exactly the same thing as centrifugal force. Because if it's not centrifugal force, then what is it? And anyway, polar coordinates in general are referenced to the inertial frame of reference and they contain a centrifugal force term that is used in planetary orbital theory. It strikes me that you are all trying far too hard to write off centrifugal force where it really exists, but all far too keen to highlight it where it doesn't exist. Nothing wrong with rotating frame transformation equations. But whoever was the first to liberate them from their terms of reference and extend their application to non-rotating objects, made a big mistake. And it seems that alot of editors here want to make that mistaken aspect the flagship of the whole topic, and palm all other aspects of centrifugal force into other articles such as polar coordinates and reactive centrifugal force.David Tombe (talk) 16:29, 23 October 2008 (UTC)

FyzixFighter, I've just looked at page 176 and I can't see anything that remotely relates to what you have quoted above. We may be looking at different editions. Your quote mentions section 3.3 which is actually the very section that I was quoting from in the first place which attributes the cause to centrifugal force. Therefore your quote essentially means that it is not centrifugal force but rather the explanation in section 3.3 which IS centrifugal force.

Your attempt to undermine my source hasn't been very convincing. David Tombe (talk) 16:50, 23 October 2008 (UTC)

These are taken from the most recent edition (2002) in the local university library. As I see it, Goldstein isn't contradicting himself since he says in the first instance that the centrifugal force only appears in the "fictitious one-dimensional problem" that gives the same equation of motion for r, not in the actual orbital scenario itself. The rest of your argument about polar coordinates and angular momentum=centrifugal force is your own original synthesis, and is therefore outside the realm of wikipedia. I have provided the quotes so others can see for themselves whether Goldstein supports your claims or not. From my reading of Goldstein, he does not support your claim that the centrifugal force is present in the inertial frame. Beyond that, I refuse to debate anything not referenced to reliable sources (ie original interpretation/analysis/synthesis of the physics/math). --FyzixFighter (talk) 17:35, 23 October 2008 (UTC)

And who wrote the preface? And what chapter might I find your page 176 in in my 1980 edition. Section 3.3 is quite clear in its meaning. It does the one-dimensional scalar equation in r. Kepler's areal constant is subsituted into the centrifugal force term to get an inverse cube law expression for centrifugal force. It's a matter of reading plain English. But I wouldn't be surprised if the other editors here would decide to read into it that Goldstein didn't really have centrifugal force in mind. I have become accustomed to these blatant denials of plain English in quotes by Newton, Bernoulli, and Maxwell. Basically, you have committed yourself to a view of centrifugal force which is such that it is only an illusion in rotating frames of reference. You are not alone in this way of thinking. But I can assure you that you are totally wrong. And sources and references mean nothing in this argument because you will simply deny plain English that doesn't suit you. David Tombe (talk) 18:16, 23 October 2008 (UTC)

Two terminologies

Hi Folks: I seem to be talking to myself here. This controversy has three aspects.

1. D Tombe: David believes in centrifugal force like he believes in the fixed stars. It is out there, a real physical thing independent of any observer. This view is his alone. Although a few phrases from the literature (see below) appear to support some of his statements, his overall view of the reality of centrifugal force attempts the impossible task of combining both of the two views presented next.
2. There is the Newtonian vector mechanics view. This view has a long historical thread outlined in the article here, and fully documented. In this view there is zero fictitious force in an inertial frame, and in particular, zero centrifugal force in a frame that does not rotate. Further sources and discussion are everywhere: Fictitious force, Rotating reference frame, Bucket argument, Non-inertial reference frame, Reference frame, Inertial frame, Mechanics of planar particle motion. I am not citing Wiki to support the argument: I am saying that these articles contain numerous sources and quotations that establish this viewpoint beyond any reasonable doubt. Repeating these quotes here is unnecessary when a click on the links will provide them. David knows these sources exist. He knows they are irrefutable masters of the subject. This view also appears on line and in textbooks. I have pointed out as a typical example David P. Stern. My conclusion is that David is beyond reach, that he will not come to grips with these sources and will insist upon his views regardless of how many authorities are against him.
3. The Hamiltonian-Lagrangian approach. Naturally this approach has a large following. It focuses upon generalized coordinates and generalized forces. Although it often is said that the Lagrangian has to be written down in an inertial frame to begin with, the whole point of the method is to find and adopt the most efficient set of generalized coordinates to identify all the conserved quantities and reduce the number of variables to a minimum. Inertial frames have no particular interest or unique role once the Lagrangian is given. I have cited numerous texts, and apparently a few more are out there, where the entire notion of inertial frames is lost sight of following the initial formulation of the Lagrangian. This method does not use the Newtonian framework and is a much more "elegant math" approach to mechanics. As with many abstract mathematical approaches, the participants are dying for a physical peg to hang onto to bring some vividness to their methods. So when polar coordinates come up, the terms that look similar to the centrifugal and Coriolis terms are called by that name, even though the physical interpretation of these terms shows they are non-zero in inertial frames. In other words, they are not the same things that are called by these names in Newtonian vector mechanics. I have cited numerous sources that take the Lagrange-Hamiltonian approach. You have found more.

It is unfortunate that there is this dichotomy in the literature. It cannot be argued away. Taylor has shown the instantaneous co-rotating frame, in which the particle has momentarily only an apparent radial motion, provides a point of contact between these views John R Taylor (2005). Classical Mechanics. University Science Books. p. §9.10, pp. 358-359. ISBN 1-891389-22-X. At the chosen instant t₀, the frame S' and the particle are rotating at the same rate....In the inertial frame, the forces are simpler (no "fictitious" forces) but the accelerations are more complicated.; in the rotating frame, it is the other way round..

To conclude: what more can be said on this subject? It seems to me to be completely settled, sourced and explained. Brews ohare (talk) 17:01, 23 October 2008 (UTC)

Brews, you say that it's my view alone but that a few phrases from the literature appear to support it. Those few phrases come from Newton, Bernoulli, Maxwell, and Goldstein's classical mechanics textbook. They also come from texts on Lagrangian and Hamiltonian mechanics.David Tombe (talk) 17:49, 23 October 2008 (UTC)

David: Your vague allusions to sources hardly can confront the very specific and at-length quotations referred to above. In addition, I would disqualify consideration of Newton, Bernoulli, Maxwell because these authors' statements require an historian to disentangle the evolution of meaning over time, and are the subject of very extensive discussion by historians even to this day, as I have pointed out to you specifically in the case of Newton. Brews ohare (talk) 18:32, 23 October 2008 (UTC)

Brews, the meanings of the sayings of Newton, Bernoulli, and Maxwell don't require specialists to interpret them. The meanings are quite clear if you want to see them. They contradict modern ideas such as that centrifugal force is only an illusion in rotating frames of reference. David Tombe (talk) 19:00, 23 October 2008 (UTC)

The Herbert Goldstein Editions

The first edition was 1950. Herbert Goldstein wrote the preface at Cambridge, Massachusetts in March 1950. My edition is the 1980 edition. He wrote the preface to it in January 1980 at Kew Gardens Hills, New York.

In the second edition preface, he mentions his reasons for the need for a new edition and he states that that there has been a revolution in the attitude towards classical mechanics. He then states that he has attempted to steer a course somewhere midway between these two attitudes.

Nevertheless, he still firmly links the outward repulsion in planetary orbits to centrifugal force as per the quote from section 3.3 above.

So I'd be interested to know what edition FyzixFighter is quoting from. I'd be interested to know if Herbert Goldstein is still writing the prefaces. For if FyzixFighter's quote from the new page 176 is correct, and I have every reason to believe that it is correct, then it would appear that somebody somewhere is trying to re-write classical mechanics and to write off centrifugal force. They do so in a clumsy way by denying it and then making up a formula of words to describe the contents of section 3.3 which is exactly as it always was. My quote on this above was,

He gives some formula of words "the angular momentum contributes to the effective potential energy to keep the Earth in orbit" which when stripped down, means exactly the same thing as centrifugal force.

David Tombe (talk) 17:14, 23 October 2008 (UTC)

Your 'stripping down' constitutes entirely transparent original research.- (User) Wolfkeeper (Talk) 17:54, 23 October 2008 (UTC)

Wolfkeeper, I don't follow your logic. I gave a source which clearly mentioned centrifugal force as having a real physical effect and totally outside the context of rotating reference frames. FyzixFighter claims that on page 176 of the same book it says otherwsie but neverthless refers back to the very section in question where my quotes came from. My 1980 edition doesn't have FyzixFighter's quote on page 176. So if somebody has added that quote into a newer edition then we need to know why. The quote is self-contradictory. It says that there is no centrifugal force in the inertial frame but then refers us to an alternative explanation which actually turns out to be the very section that attributes the cause to the centrifugal force, and which I have taken my quotes from. So where's the original research? David Tombe (talk) 18:07, 23 October 2008 (UTC)

I have the 1950 edition. Below is an excerpt.

Chapter 3 is about "The two-body central force problem" The problem is discussed using a Lagrangian:

$L=T-V={\frac {1}{2}}m\left({\dot {r}}^{2}+r^{2}{\dot {\theta }}^{2}\right)-V(r)\ .$

Goldstein determines that the angular velocity and the radius are related to the angular momentum as:

$mr^{2}{\dot {\theta }}=\ell \ .$

p. 61: Designating the force along r, $-{\frac {\partial V}{\partial r}}$, by f(r)...yielding a second order differential equation involving r only:

$m{\ddot {r}}-{\frac {\ell ^{2}}{mr^{3}}}=f(r)$

It is the same equation as would be obtained for a fictitious one-dimensional problem in which a particle of mass m is subject to a force

$f'=f+{\frac {\ell ^{2}}{mr^{3}}}\ .$

The significance of the additional term is clear if it is written as

$mr{\dot {\theta }}^{2}=m{\frac {v_{\theta }^{2}}{r}}\ ,$

which is the familiar centrifugal force. An equivalent statement...is that of a one-dimensional problem with a fictitious potential energy:

$V'=V+{\frac {1}{2}}{\frac {\ell ^{2}}{mr^{2}}}\ .$

Remembering that the effective "force" is the negative of the slope of the V' curve, the requirement for cirular orbits is simply that f' be zero, or:

$f(r)=-{\frac {{\ell }^{2}}{mr^{3}}}=-mr{\dot {\theta }}^{2}\ .$

We have here the familiar elementary condition of a circular orbit, that the applied force just balances the "reversed effective force" of centripetal acceleration.

What can be made of this? Very little, I'd say, because the discussion is phrased about a "fictitious" one-d problem, and its interpretation in terms of the "real" problem is not disclosed. Brews ohare (talk) 18:35, 23 October 2008 (UTC)

Brews, That's the bit where I took my quotes from. Goldstein is quite clear about the fact that centrifugal force is involved in the planetary orbit. You can see the words very clearly. We're not arguing about whether it is real or fictitious. And you can't get off the hook by drawing attention to the term 'one-dimensional'. That simply means that he has eliminated the theta (angular) terms and reduced it to a one-dimensional scalar equation in r. He did that by substituting Kepler's areal constant into the centrifugal force expression and getting a position dependent inverse cube law expression for the centrifugal force. I cannot possibly see how you could ever argue in a court of law that this page does not involve centrifugal force. And if you go over to page 78 you will see his line about the repulsive centrifugal barrier.

What we need to know is more about the 2002 edition. Why is there a bit on page 176 of the 2002 edition which denies the involvement of centrifugal force in inertial frames and then claims that the explanation is in sec. 3.3 which is the section which you have copied above, and which very much involves centrifugal force. It seems to me that new editors have been involved who want to write centrifugal force out. And I have just found out that the 2002 edition was edited by Poole and Safko to reflect today's physics curriculum. See this web link [[4]]

David Tombe (talk) 18:44, 23 October 2008 (UTC)

I'd say that transferal to the one-d problem is tantamount to a switch to the co-rotational frame of reference, where the classical Newtonian picture and the view of the Wiki article agree that centrifugal force is all you need. The argument of Goldstein is like the potential argument in this discussion. Brews ohare (talk) 18:47, 23 October 2008 (UTC)

Brews, Co-rotation ultimately means actual rotation in the context. The r is the actual radial distance and the centrifugal force comes about due to the actual tangential velocity. Centrifugal force is a real outward force that is induced by actual rotation. It is as simple as that and you are making it all so complicated by tangling it up with frames of reference. David Tombe (talk) 18:55, 23 October 2008 (UTC)

To phrase it a bit differently, Goldstein has eliminated the angular (rotational) aspect of the problem by treating the angular momentum as a constant of the motion, and consequently switching to a frame of reference where there is no rotation, and instead a centrifugal energy term; a co-rotational frame using a potential energy. Brews ohare (talk) 18:59, 23 October 2008 (UTC)

To support this view, see Whittaker and [5]. Brews ohare (talk) 19:57, 23 October 2008 (UTC)

Brews, has he involved centrifugal force in planetary orbits or not? David Tombe (talk) 19:03, 23 October 2008 (UTC)

David: I have not found any other discussion of planetary orbits in my edition of Goldstein. Brews ohare (talk) 19:06, 23 October 2008 (UTC)

And neither can I in mine. So we'll just have to wait until FyzixFighter tells us more about what chapter his page 176 is in in his 2002 edition. David Tombe (talk) 19:12, 23 October 2008 (UTC)

Page 176 in the 2002 3rd edition is in section 4.10 "The Coriolis effect" in chapter 4 "The Kinematics of Rigid Body Motion". --FyzixFighter (talk) 19:17, 23 October 2008 (UTC)

This is Section 4-9, p. 135 in the 1950 Edition. It is the same as the corresponding sections in Taylor, Arnol'd and others, deriving the "acceleration transformation law" as Gregory calls it. The terminology here for centrifugal force and Coriolis force is exactly the usual Newtonian vector mechanics interpretation. To quote, p. 135:

To an observer in the rotating system it therefore appears as if the particle is moving under the influence of an effective force F_eff:

${\boldsymbol {F_{eff}}}={\boldsymbol {F}}-2m\left({\boldsymbol {\omega \times v_{r}}}\right)-m{\boldsymbol {\omega \times }}\left({\boldsymbol {\omega \times r}}\right)\ .$

There is no discussion of planetary motion in this section of this edition. However, it appears from the above equation and its discussion in Goldstein that Goldstein has adopted the traditional Newtonian vector mechanics view, which evaluates the centrifugal force (which Goldstein identifies as the last term) as zero in a frame that does not rotate, and as non-zero in one that does, regardless of the actual motion or apparent motion of an observed object. Brews ohare (talk) 19:36, 23 October 2008 (UTC)

Centrifugal Potential Energy

If centrifugal potential energy only exists in the rotating frame, how is that energy expressed in the inertial frame? How is the parabolic surface on the rotating water explained in the inertial frame without using the centrifugal force expression? David Tombe (talk) 19:34, 23 October 2008 (UTC)

If centrifugal potential energy only exists in the rotating frame, then that energy does not exist in the inertial frame. The parabolic surface in the inertial frame is required in that frame because the water rotates in the inertial frame. That means it has a circular motion, requiring a centripetal force. That force is provided by a distortion of the water surface that makes the normal restoring force of the water beneath the surface have a horizontal inward component of exactly the right value to provide the centripetal force. The normal restoring force of the water beneath the surface is transmitted from the bucket walls that constrain the water to stay inside the bucket. This constraining force is transmitted by the incompressible water to the surface of the water. Brews ohare (talk) 19:44, 23 October 2008 (UTC)

This question is off-topic here, as this article is about rotating reference frames; and in any case, talk pages are not a place to ask basic physics questions.- (User) Wolfkeeper (Talk) 20:03, 23 October 2008 (UTC)

Brews, Why does the rotating water need a restraining force to keep it inside the bucket? Is there some kind of outward moving tendency that comes with rotating water by any chance?

And how can you explain something with centripetal force in one frame and with centrifugal force in another frame. They are in the complete opposite direction, and centripetal force is present in both frames? David Tombe (talk) 20:04, 23 October 2008 (UTC)

Wolfkeeper, did you think that I was just asking that question because I didn't know the answer? It was a debating point related to the topic of the article. That topic is 'centrifugal force'. This is the centrifugal force article. It was you that added in the extra bit in brackets about rotating reference frames. David Tombe (talk) 20:06, 23 October 2008 (UTC)

I don't have to speculate on such things. This is offtopic. Please take it elsewhere.- (User) Wolfkeeper (Talk) 20:12, 23 October 2008 (UTC)

How can it be off topic when there is a section in the article with that title? David Tombe (talk) 20:15, 23 October 2008 (UTC)

I do believe this discussion is relevant to the article about rotating frames. David poses what is apparently a rhetorical question: Why does the rotating water need a restraining force to keep it inside the bucket? Is there some kind of outward moving tendency that comes with rotating water by any chance?

The answer to this question is that the bucket forces the water to travel in a circular path. Otherwise it would proceed in a straight line. The situation is analogous to the ball whirled at the end of a string. It is not an indication of centrifugal force unless you switch to the co-rotating frame.

Next David asks: And how can you explain something with centripetal force in one frame and with centrifugal force in another frame? They are in the complete opposite direction, and centripetal force is present in both frames?

To answer the last point first, in the co-rotational frame there is zero centripetal force because the water appears stationary in that frame. That is why centrifugal force is necessary in this frame to explain the concave surface. To answer the first question: centripetal force is required in the inertial frame because the water is apparently in uniform circular motion in this frame, and that motion kinematically requires a centripetal force. That force is provided by the concave surface. Brews ohare (talk) 20:18, 23 October 2008 (UTC)

Brews ohare (talk) 20:18, 23 October 2008 (UTC)

FyzixFighter's Reference

On page 179 of the 1980 edition of Herbert Goldstein's 'Classical Mechanics', it says,

Incidentally, the centrifugal force on a particle arising from the earth's revolution around the sun is appreciable compared to gravity, but it is almost exactly balanced by the gravitational attraction to the sun. It is, of course, just this balance between centrifugal force and gravitational attraction that keeps the earth (and all that are on it) in orbit around the sun.

In 2002,[[6]] two men altered this to read,

If we analyze the motion of the Sun-Earth system from a frame rotating with Earth, it is of course just the balance between the centrifugal effect and the gravitational attraction that keeps the Earth (and all that are on it) and Sun separated. An analysis in a Newtonian inertial frame gives a different picture. As was described in Section 3.3, the angular momentum contributes to the effective potential energy to keep the Earth in orbit.

FyzixFighter introduced this edited quote as a quote from Goldstein, although I suspect that he was totally unaware that it was actually a tampering with what Goldstein had originally said. FyzixFighter, having produced this edited quote, then said,

"And with that, I will go back to the bleachers. I have no further desire to engage in this debate except to help provide and assess reliable sources."

FyzixFighter's quote referred us to section 3.3 which actually contradicts what the quote says. The quote claims that angular momentum rather than centrifugal force is involved in keeping the earth in orbit.

This quote is a blatant attempt to re-write classical mechanics within a new vision which doesn't involve centrifugal force in inertial frames. The quote is strange in that it puts forward angular momentum as an alternative explanation yet anybody knows that it is the centrifugal effect that comes with angular momentum which keeps the planets in orbit. And it is inaccurate because it implies that section 3.3 contains an explanation other than centrifugal force, which it doesn't.

These two editors of the 2002 edition of Goldstein, when Goldstein was already 79 years old, have attempted to alter what was Goldstein's view regarding the role of centrifugal force in planetary orbits. David Tombe (talk) 19:56, 23 October 2008 (UTC)

These remarks are an exaggeration, as the 1950 edition leaves no doubt as to Goldstein's view of centrifugal force as always being present in a rotating frame; and never present in a stationary frame, regardless of the motion of any observed object. See above. Brews ohare (talk) 20:07, 23 October 2008 (UTC)

Brews, They are not an exaggeration. Goldstein's views are in his actual quote above. Not the amended quote that FyzixFighter supplied. David Tombe (talk) 20:11, 23 October 2008 (UTC)

David, please address the formulas for centrifugal force derived and discussed by Goldstein here that present an entirely Newtonian traditional view of centrifugal force as always being present in a rotating frame; and never present in a stationary frame, regardless of the motion of any observed object. Brews ohare (talk) 20:23, 23 October 2008 (UTC)

Mr brews, I could not find any thing in my 1950 edition of Goldstein that confirms what you say above. Please be more specific.71.251.177.111 (talk) 15:45, 24 October 2008 (UTC)

The equation developed by Goldstein, as referred to here has the properties that centrifugal force always is present in a rotating frame (that is the formula is non-zero if ω is non-zero); and never is present in a stationary frame (that is, always vanishes if ω=0), regardless of the motion of any observed object. Does that help? Brews ohare (talk) 15:50, 24 October 2008 (UTC)

Brews, I don't know if it helps anonymous 71.251.177.111. But I can assure you that Goldstein says nothing of the sort. David Tombe (talk) 11:31, 25 October 2008 (UTC)

The formula is derived on the pages cited here. Brews ohare (talk) 16:55, 25 October 2008 (UTC)

Yes, but where does he say that centrifugal force is never present in a stationary frame? David Tombe (talk) 18:35, 25 October 2008 (UTC)

David: Come on; a stationary frame has ω = 0 . If we accept the formula derived for centrifugal force, it is zero when ω = 0. Maybe you are suggesting that Goldstein proposes that his formula for centrifugal force in a rotating frame is only "part" of the centrifugal force? Where does he say that? Brews ohare (talk) 21:09, 25 October 2008 (UTC)

Fluid mechanics

A more microscopic analysis is outlined, including links to various topics in fluid mechanics. The actual motion of the water in the rotating bucket can be quite complicated. Brews ohare (talk) 15:46, 24 October 2008 (UTC)

Brews, isn't that what I told you further up the page? What you did was only a qualitative treatment. But that is good enough for this article, and I doubt if it would be possible to do an accurate analysis that involves the inter molecular forces.David Tombe (talk) 18:28, 24 October 2008 (UTC)

You were right about the treatment being approximate. I confess to surprise that this simple problem shows up some very fundamental difficulties that apparently can be resolved even approximately only by introducing things like vortex solutions. Brews ohare (talk) 19:00, 24 October 2008 (UTC)

You merely established your parabolic surface using the gradient of the centrifugal force to gravity, but you never explained what causes the water to rise upwards in the first place. It will actually be a knock on effect beginning with the centrifugal force, and it might even involve intermolecular Coriolis force. David Tombe (talk) 18:28, 24 October 2008 (UTC)

In the inertial frame, my view is that the water wishes to travel in a tangential path unless constrained. The bucket wall intervenes. The water then cannot travel tangentially, and its only degree of freedom is to travel up the bucket wall. When that happens, a centripetal force is produced that insures circular motion. If we start from a flat surface and begin to rotate, part of the work involved in acceleration of the water is work in distorting the surface against the force of gravity, I'd assume. Sort of analogous to stretching the spring in a centrifugal clutch. Brews ohare (talk) 19:11, 24 October 2008 (UTC)

Anyway, what did you think of the revisionism in the 2002 Goldstein? We should be grateful to FyzixFighter for having brought it to our attention. Goldstein's statement on planetary orbits on page 179 of the 1980 edition is quite different from the Poole and Shaftoe amended statement on page 176 of the 2002 edition. What does it say in your 1950 edition? David Tombe (talk) 18:28, 24 October 2008 (UTC)

My 1950 edition of Goldstein treats planetary motion only in the equivalent one-D formulation, which is the equivalent of going to a co-rotational frame. (See Whittaker and [7].) In this frame he says (p. 79) "the force of attraction is just balanced by the centrifugal force". This statement is expected in the co-rotating frame. Brews ohare (talk) 18:54, 24 October 2008 (UTC)

Tombe's views

Brews, [Goldstein] says nothing about the co-rotating frame. It quite clearly introduces the problem within the context of plane polar coordinates referenced with respect to the inertial frame. Equation 3.12 is in that very format. He then likens it to a fictitious one-dimensional problem. The one dimensional potential energy graph for your curiosity is in fact identical to the inter-molecular force graph.

When Fugal was arguing with you, it was already accepted that centrifugal force existed in polar coordinates in the inertial frame. The problem in that argument was about whether it was the same centrifugal force as the one in rotating reference frames. I was backing Fugal on the idea that they are one and the same centrifugal force.

But now you have changed the nature of the argument. We are once again back to where I was before Fugal entered the arena. You are all denying that centrifugal force can exist at all outside of rotating reference frames.

And despite my very clear citations from Goldstein, you are still trying to deny it. Goldstein is quite specific about the fact that centrifugal force occurs in plane polar coordinates with respect to the inertial frame. The Lagrangian link to kinetic energy wouldn't make any sense otherwise.

Goldstein does not mention rotating frames in his analysis. And on page 78, he talks about the 'repulsive centrifugal barrier'.

On page 179 he makes his position very clear and we have seen, thanks to FyzixFighter, that that statement was tampered with in 2002.

And when we return to where we were when Fugal was here, then you will see that your interpretation of Goldstein in terms of the co-rotating frame merely confirms what Fugal and I have been saying, which is that they are all one and the same effect and you have no reason to siphon this material off into a separate article on polar coordinates. David Tombe (talk) 11:22, 25 October 2008 (UTC)

David: With regard to Goldstein.

1. See Carmichael and Whittaker. I don't think you want to argue with Whittaker, whose book is the definitive, world-renowned statement on this subject. The one-D formulation is tantamount to switching to a co-rotational frame, whether or not those words are used by Goldstein. In this frame there is no centripetal force, and only centrifugal force and gravity.
2. In Section 4-9, p. 135 in the 1950 Edition, Goldstein presents the same formulas as the corresponding sections in Taylor, Arnol'd and others, deriving the "acceleration transformation law" as Gregory calls it. The terminology here for centrifugal force and Coriolis force is exactly the usual Newtonian vector mechanics interpretation. To quote, p. 135:

To an observer in the rotating system it therefore appears as if the particle is moving under the influence of an effective force F_eff:

${\boldsymbol {F_{eff}}}={\boldsymbol {F}}-2m\left({\boldsymbol {\omega \times v_{r}}}\right)-m{\boldsymbol {\omega \times }}\left({\boldsymbol {\omega \times r}}\right)\ .$

This equation developed by Goldstein has the properties that centrifugal force (identified explicitly by Goldstein as the last term above) always is present in a rotating frame (that is the formula is non-zero if ω is non-zero); and never is present in a stationary frame (that is, always vanishes if ω=0), regardless of the motion of any observed object. Brews ohare (talk) 16:23, 25 October 2008 (UTC)

In sum, Goldstein provides you no support. Brews ohare (talk) 16:23, 25 October 2008 (UTC)

With regard to my position: I have indicated the following:

1. Your views contradict every major textbook that adopts the Newtonian vector-mechanics viewpoint. Goldstein is just one of many authors who do not support your view. Many of them are even more explicit about it, providing refutation in words, as well as math. Innumerable citations and quotations to this effect are ignored by you.
2. You might find some support for your views in the literature that uses Lagrangian methods and generalized centrifugal force, for example Hildebrand. So far this alternative has not been discussed much. It does not support your view that your thinking is compatible with the Newtonian vector-mechanics viewpoint.
   Although it is not clear from this discussion page, I'd guess that Fugal adopts this view, plus your mistaken view that it is the same as the Newtonian vector mechanics view, despite the fact that the generalized centrifugal force is non-zero in inertial frames, and the Newtonian vector mechanics centrifugal force is zero in inertial frames. (Fugal says that although all these authors adopting the Newtonian vector-mechanical view do say that there is zero centrifugal force in inertial frames, their idea of an inertial frame is implicitly defined by them as restricted to the use of Cartesian coordinates. Fugal's interpretation of these authors is untenable given the vector formulation of F_eff above, which can be used in any coordinate system, and always vanishes when ω = 0, regardless of coordinate system.) Brews ohare (talk) 16:23, 25 October 2008 (UTC)
3. A connection between the two viewpoints exists in the instantaneous co-rotating frame at the exact moment when the observed particle appears to have only a radial motion because the instantaneous co-rotating frame temporarily tracks the angular motion of the observed particle. That situation is described by John R Taylor (2005). Classical Mechanics. University Science Books. p. §9.10, pp. 358-359. ISBN 1-891389-22-X., links given above and in the Wiki articles. You have not engaged with this example.

None of the above is new to you, although you do not discuss it head-on and prefer to reiterate your positions as though no attempt at dialog with you has been made. Brews ohare (talk) 16:23, 25 October 2008 (UTC)

Brews, Goldstein supports my views exactly otherwise I wouldn't have quoted it. He mentions nothing about co-rotating frames.

Are you now retreating away from your earlier position that there is a centrifugal force in polar coordinates that is different from the centrifugal force in rotating frames? Is it back to 'rotating frames only' again, now that Fugal has gone? David Tombe (talk) 18:33, 25 October 2008 (UTC)

David, you say: Goldstein supports my views exactly. You refuse to read Whittaker? He does not support your view of the One-D model. You refuse to address Goldstein's adoption of the vector formula for F_eff?

David, you say: Are you now retreating away from your earlier position that there is a centrifugal force in polar coordinates that is different from the centrifugal force in rotating frames? You refuse to understand the difference between "generalized" centrifugal force à la Hildebrand and Newtonian vector-mechanics centrifugal force à la F_eff?

How can I talk to you when you are so unresponsive? Brews ohare (talk) 18:39, 25 October 2008 (UTC)

Modern Revisionism

Brews, the details no longer matter when citations are being systematically dismissed. My position on centrifugal force is exactly as per Newton, Bernoulli, Maxwell, and also Herbert Goldstein. The response to citations from these sources is always something like, (i) They were talking about a different centrifugal force, or (ii) we cannot accept original sources, or (iii) we would need a historian to interpret what they were trying to say, despite the fact that their statements on the subject were in plain English, or (iv) we would need a secondary source which states that Maxwell believed that centrifugal force was real, or (v) that Goldstein didn't involve centrifugal force in planetary orbital theory, despite having explicitly mentioned it in the analysis etc.

The most interesting citation of all came from FyzixFigher. It was the altered version of Goldstein's 1950 statement which appeared in the revised 2002 version. Goldstein's original statement read,

Incidentally, the centrifugal force on a particle arising from the earth's revolution around the sun is appreciable compared to gravity, but it is almost exactly balanced by the gravitational attraction to the sun. It is, of course, just this balance between centrifugal force and gravitational attraction that keeps the earth (and all that are on it) in orbit around the sun.

But in 2002, this was altered to read,

If we analyze the motion of the Sun-Earth system from a frame rotating with Earth, it is of course just the balance between the centrifugal effect and the gravitational attraction that keeps the Earth (and all that are on it) and Sun separated. An analysis in a Newtonian inertial frame gives a different picture. As was described in Section 3.3, the angular momentum contributes to the effective potential energy to keep the Earth in orbit.

That says it all. Somebody somewhere, probably about fifty or sixty years ago decided to shift the angular velocity term in rotating frame transformation equations from the object to the frame, and make the equations apply to stationary objects. This is a total nonsense. It's up to you whether or not you want to believe it. David Tombe (talk) 15:14, 26 October 2008 (UTC)

David: Very specific criticisms of your interpretation of Goldstein have been presented in Tombe's Views above. You have addressed none of them. The revisions of Goldstein's original statements you mention above, which post date the 1950 edition, do not impact any of these criticisms of your interpretation of Goldstein. You also have not replied to anything else said in Tombe's Views above. Brews ohare (talk) 15:45, 26 October 2008 (UTC)

Brews, my interpretation of Goldstein is that he dealt with planetary orbital theory using centrifugal force in polar coordinates, referenced to the inertial frame. He doesn't mention rotating frames of reference. It is you that has linked his treatment to the co-rotating frame. And ironically, it was you and Wolfkeeper that were trying to tell Fugal that the rotating frame centrifugal force is different from the polar coordinates centrifugal force.

If you fully comprehend centrifugal force, you will see that it is one single topic. All these forks to polar coordinates and reactive centrifugal force merely indicate a lack of comprehension of the topic by the authors. David Tombe (talk) 12:12, 27 October 2008 (UTC)

There is no need to "interpret" Goldstein. The 1950 analysis is here and uses the One-D model. This model is described by Carmichael and by Whittaker as being in the co-rotational frame, which makes entire good sense inasmuch as no One-D model can rotate - rotation takes more dimensions. To quote:

"we may replace the consideration of a system which is constrained to rotate uniformly about an axis by that of a system for which this rotation does not take place. The imaginary forces which are introduced in this way to represent the acceleration effect of the enforced rotation are often called centrifugal forces.

Yes, Goldstein doesn't talk about co-rotation; but that is what he is doing. He uses a model in which rotation does not take place.

Goldstein also uses the standard vector expression for centrifugal force that vanishes in a non-rotational frame, completely in accord with the rest of the literature.

So what possible basis is there for your interpretation of Goldstein? It consists simply of quoting a few lines here and there with no regard for the mathematical context, and ignoring sections (like the vector analysis of F_eff ) that don't suit your interpretation. Why not give this up and switch to Hildebrand for support? Brews ohare (talk) 15:07, 27 October 2008 (UTC)

Brews, which way do you want to play it? Do you want to hear my analysis of the situation or do you want me to base my arguments on sources? Everytime I give my own analysis there is usually at least one editor that refuses to debate the issue and merely demands citations. So I decided to give a few citations from Goldstein. Goldstein deals with planetary orbital theory in polar coordinates, using centrifugal force. After having reduced the centrifugal force term to an inverse cube law force by using the areal constant, he then likens the orbital equation to the fictitious one dimensional problem. That is sufficient to prove my point that we don't need to involve rotating frames of reference for centrifugal force to be present. You then come along with your own interpretation which is that what Goldstein was doing is equivalent to the co-rotating frame. And you are absolutely correct. David Tombe (talk) 19:17, 27 October 2008 (UTC)

Hi David: It is good to know I am absolutely correct, but it seems a bit optimistic to think that we actually are now in agreement about Goldstein. As for which way to play? It seems to me that your intuition has to be backed up by citations, as intuition is a very personal thing, and one man's intuition is another's fantasy world. Brews ohare (talk) 23:23, 27 October 2008 (UTC)

Brews, you are correct that Goldstein's treatment is exactly equivalent to an object co-rotating in a rotating frame, providing that we don't have to declare whether we believe the angular velocity ω to be attached to the frame, or to the object. And yes, it is equivalent to a one dimensional problem in r. I should further add that it is equivalent to Boscovich's force law, although Boscovich doesn't seem to have identified centrifugal force as being the cause of the repulsive force. He assumed that he had united gravity with inter atomic forces. Well to a certain degree he had done just that. The inter-atomic force graph and the one dimensional orbital equation of force are identical. They both have the stability node which Goldstein refers to as the repulsive centrifugal barrier.

But let's not lose sight of what the edit war is about. The edit war is about why the co-rotating frame and the one dimensional polar equation are the same. I say they are the same because ω applies to the object, and not to the frame.

At one point, you were arguing with Fugal that the two centrifugal forces were different. I was siding with Fugal in the belief that they are one and the same thing. But the real argument comes when we consider particles that don't have the angular velocity of the rotating frame. That's when the issue of 'who owns the ω?' becomes crucial. I say that the object owns the ω. You say that it's the frame that owns the ω.

I maintain that it is the height of nonsense to extrapolate the rotating frame transformation equations to objects that don't have the angular velocity of the frame. The whole derivation begins with the angular velocity applying to an object fixed in the frame. Somebody somewhere about 60 years ago lost sight of the physics, and put an example in a textbook that involved applying these equations to stationary objects not connected to the rotating frame. This mistake was then propagated into other textbooks and scientific journals.

The amendments in the 2002 edition of Goldstein are the clearest example of the revisionism that has come with this erroneous way of thinking. The modern editors obviously didn't feel comfortable with the way that Goldstein described things. Goldstein didn't involve rotating frames in his treatment of planetary orbits, so Poole and Shaftoe felt that they had to amend his statement on this to involve the issue of frames of reference. They further claimed that his treatment of planetary orbits explained the stability in terms of angular momentum and not centrifugal force. This claim was unfounded as can be seen by referring to the relevant section.

This is a way of thinking that is hard to comprehend. We can all see that centrifugal force comes about with absolute rotation. We can see the real physical effects. It is sheer delusion to think that a stationary object as viewed from a rotating frame is being subjected to two mutually cancelling fictitious forces. This idea involves swinging the Coriolis force into the radial direction and attributing an angular velocity to a particle that is not rotating. It is completely wrong, and it has totally confused the topic. David Tombe (talk) 01:35, 28 October 2008 (UTC)

David: To you it seems "sheer delusion", but that is exactly what all the textbooks that employ the vector F_eff formula do. It's my impression that you have decided that virtually all texts post 1900 are subject to erroneous revisionism. I guess that if you are right, Wikipedia is forced to do the same, except perhaps in an historical article about what people once thought. As regards whether ω belongs to the frame or to the particle, the intermediate case where the frame is neither co-rotating nor stationary shows that ω belongs to the frame. See Centrifugal_force_(rotating_reference_frame)#General_case. Further discussion of this point should envelop the detailed analysis of this section and attempt to show where it is incorrect, if you think it is incorrect. Brews ohare (talk) 03:07, 28 October 2008 (UTC)

Brews, In Goldstein,ω applies to the planets. He doesn't mention rotating frames. All the more interesting is the amended statement on page 176 of the 2002 edition where Poole and Shaftoe try to unwrite what Goldstein wrote in the 1950 and 1980 editions. So it's not as clear cut as you make out. David Tombe (talk) 11:03, 28 October 2008 (UTC)

Including archives, ~750k of talk page here

That's as big as a book; and not a small book, and a spectacularly boring and repetitive book at that.

And to be honest, the article seems to be devolving. Encyclopedia articles in my experience do not consist of 50-60% of 'examples'.

And I'd like to know why general sections like potential energy seem to have suddenly become a specialised case of 'rotating bucket' rather than being a general topic in its own right. This isn't my idea of an encyclopedia article; it's veering dangerously close to 'how to' in my opinion.

Encyclopedia articles are supposed to be all about a topic, not just give a bunch of examples and let the reader fill in the blanks in between. We should say this topic is defined as X, and it has features T,U,V and Z and it relates to these other topics A,B,C in the following ways.

It currently reads more like a magazine article.

All in all, it's not going well IMO.- (User) Wolfkeeper (Talk) 02:14, 28 October 2008 (UTC)

Wolfkeeper: The section Rotating bucket: fluid mechanics shows interestingly that the simple idea of potential energy is simple mainly because it is very approximate. Personally that caught me by surprise. Maybe it did you too. Each example contributes a useful insight to the topic, and none of them duplicate each other. Each example arose originally as a result of some debate on the Talk page, and did not arise out of the blue. In addition, most textbooks treat some or even all of these examples, suggesting a number of authors felt they contributed to understanding the subject. If a reader has no interest in reading all the examples, they can cherry pick - no skin off their nose. Brews ohare (talk) 02:59, 28 October 2008 (UTC)

I think it makes sense to pare the examples, too. We should only use examples that are in sources, and treat them without too much space, preferably. Dicklyon (talk) 06:06, 28 October 2008 (UTC)

Dick, which sources? If we use the Goldstein 1950 edition or 1980 edition, there won't be any examples involving particles that are stationary in the inertial frame. I don't even have any evidence so far that that has chaged with the 2002 edition, despite some revisionism in the main text. David Tombe (talk) 11:05, 28 October 2008 (UTC)

Dick: It would be helpful to understand your reasoning, and not just your conclusion. In particular, how does it harm the reader to have the examples? Personally I found them rather enlightening. Brews ohare (talk) 14:52, 28 October 2008 (UTC)

Perhaps we could take the examples one by one and look at what they bring to the article. Wolfkeeper has focused upon the bucket example, which may be a good starting point because its evolution is recent. Initially it had only the potential energy argument. I doubt anyone would suggest its removal. To this was added the Newton-force balance and then the Fluid mechanical arguments. Taking the last first, it connects the potential energy approach to a more fundamental one, and supports one of Wiki's strengths, namely, its ability to connect the reader to related topics and deepen the reader's understanding. I find the need for vortex solutions in this example fascinating. I'd oppose its deletion. The Newton-force argument connects with the Wiki articles on banked turns, and again it supports the Wiki strength of connecting the reader to various facets of a topic and linking to related articles. The force balance argument is a very fundamental analysis methodology, and showing it here is helpful to the reader. Brews ohare (talk) 15:57, 28 October 2008 (UTC)

BTW, all these examples are thoroughly cited, so there is no question about accuracy. Brews ohare (talk) 16:03, 28 October 2008 (UTC)

Brews, I'd also oppose its deletion. It's all about making the subject more interesting. Centrifugal force ultimately traces back to tiny vortices. The potential energy section, the planetary orbital section, and the fluid dynamics section are the most interesting in the article. All we need now is to generalize the title and the introduction. A section on rotating frames could point out that while in planetary orbital theory, ω belongs to the object, but that in rotating frames, it belongs to the frame and that in co-rotating situations, the two are equivalent. We needn't touch on the controversy about the artificial circle. David Tombe (talk) 16:35, 28 October 2008 (UTC)

Centrifugal Force in Hydrodynamics

Brews, I'm glad to see that you are learning, and that you have now arrived in the realm of hydrodynamics. This brings us full circle.

Consider the vector $\mathbf {A}$ to be the fluid momentum. If we differentiate it with respect to time we get,

$-{\frac {{\mbox{d}}\mathbf {A} }{{\mbox{d}}t}}=-\nabla \phi -{\frac {\partial \mathbf {A} }{\partial t}}+\mathbf {v} \times \mathbf {B} +\nabla (\mathbf {A} \cdot \mathbf {v} )\,$

where,

$\mathbf {B} =\nabla \times \mathbf {A} .$

is the vorticity.

The $\nabla (\mathbf {A} \cdot \mathbf {v} )\,$ term above appears as the centrifugal force term in equation (5) in Maxwell's 1861 paper. It is used to account for magnetic repulsion which is not catered for in the modern Lorentz force. Centrifugal force is the missing fourth term of the Lorentz Force.

Clearly the other terms include the Coriolis force and what you have been calling the Euler force. Do you remember the battle to get the Euler force overtly recognized? They wanted to bury it inside $\mathbf {E} ,$ so that nobody could see what was going on. David Tombe (talk) 15:05, 28 October 2008 (UTC)

Too long

Brews, your recent work has pushed the article over 90 KB. This is about 3x longer than the recommended size for a complete article. There's just way too much here for it to be effective as an encyclopedia article. No mechanics text spends half that much space on this topic. Think about moving the extensive examples into a subsidiary article, or re-org with summary style, or just prune away parts that people are less likely to care about, and let's see if we can get back to a decent size and effective article. Dicklyon (talk) 17:18, 28 October 2008 (UTC)

Here are some examples:

• Earth 101 kilobytes
• Moon 88 kilobytes
• Group (mathematics) 88 kilobytes
• Maxwell's equations 86 kilobytes
• Special relativity 80 kilobytes
• Sarah Palin 97 kilobytes
• Barak Obama 119 kilobytes
• Madonna (entertainer) 92 kilobytes
• Britney Spears 91 kilobytes

It appears that Centrifugal force is approaching celebrity status. However, I don't find it less important or less interesting than any of the above. What is the perspective upon what makes something "effective as an encyclopedia article"?

Personally, I'd envision an article as effective if: (i) It provided information up front to satisfy the casual reader who perhaps wants only to know what the subject is about. That is handled by the lead-in. (ii) It provides links to fill in details that might not interest everyone. (iii) It provides links to related topics that maybe the reader would find illuminating but perhaps are not an obvious connection (iv) It would provide sufficient examples to allow the reader to actually apply the topic to a question that may have drawn the reader to the article in the first place.

I do not find the actual length of the article to be very relevant to any of this, as long as the article is easy to navigate.

Breaking the article up into specific topics can be useful if one can identify a more specific question that the reader might wish to pose. Because the question can be posed in various ways and Wiki does not provide a search engine, the reader must either pose the topic in the exact words of an article, or go to a general article and look for links.

Would you recommend, for example, that a list of examples be given in the present article, and each example separately dealt with on its own page? If you are worried about space, rather than access, this approach definitely will take more memory.

For example:

To see centrifugal force applied the question of absolute rotation as determined by a rotating bucket of water, see Centrifugal force (rotating bucket)

To see centrifugal force applied the question of planetary motion, see Centrifugal force (planetary motion)

To see centrifugal force applied to the question of absolute rotation using tied rotating spheres, see Centrifugal force (rotating spheres)

To see the connection between Coriolis force and centrifugal force, see Centrifugal force (dropping ball and parachutist) and also Centrifugal force (rotating spheres)

To see the historical development of the concept of centrifugal force and its connection to the concept of inertial frames, see Centrifugal force (historical development). Brews ohare (talk) 17:54, 28 October 2008 (UTC)

Following up on this discussion, I have moved the rotating spheres example to Rotating spheres on the grounds that already there is a Bucket argument page, so why not the other Newtonian example on its own page? Down to 77 kilobytes.Brews ohare (talk) 19:05, 28 October 2008 (UTC)

I also moved the alternative explanations of the bucket experiment to Bucket argument. Now down to 61 kilobytes. Brews ohare (talk) 23:19, 28 October 2008 (UTC)

Brews, one of your main problems seems to be an inability to focus on key points. The article could most certainly be substantially shortened.

For a start, the introduction could be reduced to,

Centrifugal force is the outward force that is associated with rotation.

Next, you could drop that section on the derivation.

You could also drop the section on 'advantages of the rotating frame', because there are none.

The bucket argument could be substantially reduced to state that a parabolic surface arises during actual rotation, due to centrifugal force.

The planetary orbital equation could be reduced to a single equation and a statement of the solution as being either a parabola, hyperbola or an ellipse.

I once put in a much shorter section on planetary orbits but it was swiftly deleted on some specious pretext.

The fluid dynamics section could be reduced to the equation which exposes centrifugal force.

Why not begin with a skeleton article on that framework, and then beef it up if it looks too thin? David Tombe (talk) 19:57, 28 October 2008 (UTC)

Hi David: Maybe you have me diagnosed. Another problem is this: I have developed virtually the entire page with all citations, quotations, derivations and diagrams. That process evolved along with me, and I found solving all these examples taught me a lot. I'd like to believe another reader would find this process helpful as well, but obviously it depends on the reader. Brews ohare (talk) 20:06, 28 October 2008 (UTC)

Here is a related point: the details that are included in the examples allow the reader to think them through themselves without too much head scratching. The simple statement of results is very suspicious in Wikipedia because its authoritativeness is doubtful. So the opportunity to actually reason through the argument adds a lot to credibility, and including some detail makes it easier to follow along than searching through all the citations and splicing them together. Brews ohare (talk) 20:10, 28 October 2008 (UTC)

It might make the article more inviting to go back to the earlier organization that puts the more mathematical sections last. There appears to be a distaste for math among many editors. Brews ohare (talk)20:22, 28 October 2008 (UTC)

Brews, it's an ongoing process. You start with a skeleton outline and build on it. But you must focus on the key points. As long as you are sure that you comprehend the topic, you shouldn't need to go over the top in justifying any point, because it is only an encyclopaedia article. It is not a textbook. It's only when somebody challenges a point that one needs to consider sources and citations. Think about the main situations in which centrifugal force arises. Planetary orbits is probably the most important of all. Hydrodynamics is controversial because it leads straight into Maxwell's and Helmholtz's theories of electromagnetism, but for that reason, I would want to keep it. That's why I supported your fluid dynamics section, albeit that it would need to be drastically trimmed. The rotating bucket of water is an excellent illustration of the principle and also of centrifugal potential energy. The centrifuge device is a good practical example. Artificial gravity is also an interesting topic and it includes the effect which has been wrongly siphoned off into a different article called by the misnomer 'reactive centrifugal force'. David Tombe (talk) 20:26, 28 October 2008 (UTC)

Actually I like your idea for an intro. The present intro goes back to Fugal who produced this exercise in obfuscation to allow him to ease into a curvilinear Christoffel symbol obscurantist version of centrifugal force, which never actually got written. I have tried to use your introductory sentence in a revised lead; we'll see how it flies. Brews ohare (talk) 20:29, 28 October 2008 (UTC)

Brews, I never got a chance to find out exactly what Fugal was ultimately driving at, but I supported his idea that centrifugal force is one single topic, and that it can exist outside of the context of rotating frames. I had to observe your debates with both Paolo.dt and Fugal from a distance. I thought at first that I understood Paolo's points, but as with Fugal, the debate ended up in a huge confusion about coordinates and frames and I doubt if anybody was following the details.

In retrospect, I think that in both cases, the argument was about ownership of the angular velocity ω vector. In planetary orbital theory, the object owns ω. In the co-rotating situation, we don't need to make the distinction. But in the stationary situation in the inertial frame as viewed from the rotating frame, as is dealt with in some textbooks, then the frame owns the ω. It is this latter concept that I totally object to, and I never got to hear either Paolo's or Fugal's view on that.

At any rate, I don't think that rotating frames should be mentioned in the introduction. There should be a special section on them.

Do take note of the balatant revisionism that was injected into the 2002 edition of Goldstein. That is very important. Goldstein clearly thought along the lines that the object owned ω. But in 2002, the revision of his quote tried to transfer ownership of ω to the frame. David Tombe (talk) 13:44, 29 October 2008 (UTC)

Hi David: We have not really agreed upon this "ownership of ω" question. My view is that centrifugal force vanishes for observers within a rotating frame when the frame Ω = 0, regardless of what the observed object is doing. (It is evident that when Ω = 0, the frame is inertial, and according to most authors, centrifugal force is zero in an inertial frame.) Contrariwise, if Ω of the frame is non-zero, centrifugal force always exists, regardless of what the observed object is doing.

From a different viewpoint, if you are seated upon the object, the object takes over. The centrifugal force seen by the object depends on the radius of curvature of your trajectory ρ in the fashion of a radially outward force from the center of curvature with a magnitude v² / ρ. Brews ohare (talk) 13:58, 29 October 2008 (UTC)

Fantasy Physics for Equivalentists

Brews, When a textbook deals with planetary orbits, the ω is owned by the planet. When the same textbook deals with rotating frames of reference, ownership of ω goes to the frame. In the case of co-rotating objects it doesn't make any difference whether we consider ω to belong to the frame or to the object. Most old textbooks only deal with co-rotating examples. However, there are modern textbooks which have extrapolated the rotating frame transformation equations to deal with non-co-rotating objects, and in these examples, the frame has stolen the ω. This is not real physics. It is a kind of fantasy physics for equivalentists. It doesn't intersect with the real world. David Tombe (talk) 15:34, 29 October 2008 (UTC)

What would be your description of the parachutist example? The parachutist co-rotates, so I guess there is no problem?

Then what about the dropping ball example? The ball is stationary in the inertial frame, but appears to be in circular motion in the rotating frame. I'd guess your explanation would be different from the article in this case? I seem to recall some debate over the Coriolis force. Has your viewpoint changed? Brews ohare (talk) 16:16, 29 October 2008 (UTC)

Do you agree with the skywriter example? Brews ohare (talk) 16:45, 29 October 2008 (UTC)

Brews, I would say that the last sentence in the introduction,

Instead, centrifugal force originates in the rotation of the frame of reference within which observations are made

is fundamentally wrong. That is the revisionist viewpoint as was being pushed by the amendments in the 2002 edition of Goldstein. The rotating bucket of water clearly demonstrates that centrifugal force originates in actual rotation of the object in question.

On the skywriter example and indeed in all of your examples, there is both centripetal force and centrifugal force acting in the radial direction, no matter how you look at it.

On Coriolis force, I haven't changed my position. It is a tangential force that either needs to be physically applied or to involve vorticity in space. It is certainly not involved in any of your circular motion problems. David Tombe (talk) 18:21, 29 October 2008 (UTC)

David: You say: I would say that the last sentence in the introduction,

"Instead, centrifugal force originates in the rotation of the frame of reference within which observations are made"

is fundamentally wrong. I think we'll have to agree to disagree about this point. To me the statement that there is no centrifugal force in the inertial frame, and moreover, by definition:

${\boldsymbol {F_{Cfgl}}}{\overset {\underset {\mathrm {def} }{}}{=}}-m{\boldsymbol {\Omega \times }}({\boldsymbol {\Omega \times r}})\ ,$

with Ω the angular rotation vector of the frame and ${\boldsymbol {r}}$ the location of the object under observation, regardless of whether ${\boldsymbol {r}}$ varies in time, make this sentence of the introduction inescapable.Brews ohare (talk) 19:13, 29 October 2008 (UTC)

You say: On the skywriter example and indeed in all of your examples, there is both centripetal force and centrifugal force acting in the radial direction, no matter how you look at it.

I'm a bit unsure of what you are saying here. I'd say that centripetal force appears in the inertial frame because the plane is in an arc, exhibiting curved motion, while centrifugal force appears to the pilot because the plane appears to be stationary, yet requires lift to stay in its position, suggesting the existence of the centrifugal force that must be fought against. I've added a reference to support this view. So, if "no matter how you look at it" means regardless of the frame of reference, again we would have to disagree. Brews ohare (talk) 19:24, 29 October 2008 (UTC)

You say: On Coriolis force, it is certainly not involved in any of your circular motion problems. This comment applies to dropping ball example. Your view appears to me to contradict the cited references (and the mathematical derivation given). Is there any point in pursuing this matter? Brews ohare (talk) 19:13, 29 October 2008 (UTC)

You say: The rotating bucket of water clearly demonstrates that centrifugal force originates in actual rotation of the object in question. Pardon me for being a stick-in-the-mud here, but my understanding is that the rotating bucket "clearly demonstrates how to detect actual rotation of the object in question". In fact, it says absolutely nothing about centrifugal force, in my opinion. Brews ohare (talk) 19:23, 29 October 2008 (UTC)

Brews, some wikipedian once told me that I had the patience of a saint when I continued for months calmly trying to convince an errant editor of the error of his ways. But the only reason I did was that he was a dynamic IP editor and blocking his IP had been ineffective. Here, you're showing a similar ridiculous degree of patience with an actual person who hasn't done anything to get blocked, but continues to insist on a bizarre and inconsistent interpretation of mathematical physics that can't be found in any text. Are you a saint, or what? Are you thinking that you'll pull off a miracle and eventually get through to him, or just fill his time to keep him from doing harm? If he thinks that a clarification in the content of his text is dangerously revisionist, and doesn't understand the distinction between "fictitious" and "fantasy", and can't accept that outward forces in inertial frames are reaction forces, then why are you continuing to engage him? Maybe a simple question to David will help him contemplate his stuff: on a planet acts an inward (centripetal) gravitational force; this force is all that's needed to describe the acceleration, and hence the orbit, of the planet; the reaction is an outward (toward the planet) pull on the sun; what is centrifugal force in this scene? Dicklyon (talk) 04:59, 30 October 2008 (UTC)

Dick: I have found that although David and I do not agree, discussion with him has led to improvements in the article. That has made the article too big, so some discussions have moved elsewhere, but the net result is positive. Brews ohare (talk) 07:25, 30 October 2008 (UTC)

Dick, the problem here is that there are textbook sources that give ownership of the angular velocity ω to the object, and there are other textbook sources that give ownership of the angular velocity ω to the frame of reference. The problem seems to be in writing a coherent article which gives a balance to these two conflicting points of view. Goldstein doesn't give any worked examples that involve the latter approach, yet the latter approach has dominated the article so far. Regarding your assertion that the centrifugal force in planetary orbits is only a reaction, you are quite wrong. You have got absolutely no basis whatsoever upon which to make that assertion. Goldstein is quite clear on the point that both the centrifugal force and the gravity force act in tandem to produce the ellipses, hyperbolae, or parabolae of planetary orbits. His relevant quote is at the top of page 179 in the 1980 edition. David Tombe (talk) 10:52, 30 October 2008 (UTC)

But this centrifugal force in Goldstein is due to reducing to a 1-D problem via frame rotation. In an inertial system, gravity is the only force, right? Dicklyon (talk) 17:57, 30 October 2008 (UTC)

No Dick, Goldstein doesn't mention frame rotation in his treatment of planetary orbits. The centrifugal force is mentioned explicitly and the angular velocity is owned by the planet and referenced to the inertial frame. David Tombe (talk) 01:17, 31 October 2008 (UTC)

David: I am disappointed that you did not reply to my comments above Dick's input. You also have never taken a serious look at Hildebrand, who might be close to what you are looking for. Brews ohare (talk) 14:50, 30 October 2008 (UTC)

Brews, I was still thinking about a response to those comments above Dick's. I acknowledge that in textbook chapters that deal with rotating frames of reference, the angular velocity is deemed to be owned by the frame. In co-rotation situations, this fact doesn't matter one way or the other because the angular velocity is shared between the frame and the object. My point has been that the derivation of those equations restricts their application to co-rotational situations. I base this on the fact that the derivation focuses on a point that is fixed in the rotating frame. Gold standard textbooks such as Goldstein's will only ever treat examples that involve co-rotation, although they tend to be silent on whether the equations can be extrapolated to cater for non co-rotational situations. There are indeed some sources that use these transformation equations for non-co-rotational situations. I believe that these sources are quite wrong and they are in total contradiction with other sources that firmly place ownership of the angular velocity with the particle. Both these sources can't be correct. The point is that we need to highlight this issue and then decide upon the balance of treatment in the main article. Originally, during the edit war in May, the article used the non-co-rotational situation as the flagship for centrifugal force, and all my attempts to introduce examples of actual outward centrifugal force where being swiftly deleted. My opponents were adopting a bizarre upside down approach in which centrifugal force was being denied where it really exists, yet being promoted where it doesn't exist at all. As for Hildebrand, I haven't looked at it yet. You seem to think that it backs up my point of view. If that is so, then what exactly is the problem? We know exactly where the point of disagreement is. It is in the non-co-rotational scenario. That is where I disagree with some textbook chapters. But there have also been attempts to deny the contents of actual sources which confirm that centrifugal force is owned by the objects in planetary orbital theory. All we need to do to improve the article is remove all references to rotating frames from the title and introduction, and then deal with all these situations in separate sections in the main article. There would of course be an article on rotating frames of reference. But there would also be articles on planetary orbits, hydrodynamics, centrifuge devices, artificial gravity, and centrifugal potential energy. David Tombe (talk) 17:47, 30 October 2008 (UTC)

David: You say:My point has been that the derivation of those equations restricts their application to co-rotational situations. I base this on the fact that the derivation focuses on a point that is fixed in the rotating frame. I don't see the derivation that way. It is based upon locating a moving particle in frame A at location x_A(t) that appears in frame B to be located at x_B(t) . The time dependence means the location is not fixed; it follows a moving particle under observation in both frames. The derivation at Fictitious force proceeds from there. That is a very general basis, not restricted in the way you suggest. Brews ohare (talk) 23:39, 30 October 2008 (UTC)

You say: There are indeed some sources that use these transformation equations for non-co-rotational situations. I believe that these sources are quite wrong and they are in total contradiction with other sources that firmly place ownership of the angular velocity with the particle. Both these sources can't be correct. You don't say exactly which sources you have in mind. However, there are what I have called "two terminologies" and they do not agree. It is not that one is right and one is wrong. However, it can be said that one is consistent with the standard connection between inertial/non-inertial frames and the absence/presence of fictitious forces, while the other terminology is not consistent. The conflict of terminologies has been raised before, and you seem unwilling to look into it. Brews ohare (talk) 23:39, 30 October 2008 (UTC)

You say: As for Hildebrand, I haven't looked at it yet. You seem to think that it backs up my point of view. If that is so, then what exactly is the problem? The problem is that it has some things in common with your viewpoint, but I suspect it is not 100% what you want. You might have to modify your stance to be able to adopt this view. Who but you can say whether this is OK? Brews ohare (talk) 23:39, 30 October 2008 (UTC)

Brews, the rotating frame transformation equations deal with a point that is free to move in any fashion. But that point is rooted through another point that is fixed in a rotating frame. We hence get a vector triangle and we concern ourselves with two sides (1) origin to fixed point in rotating frame, and (2) Fixed point in rotating frame to the free point.

The angular velocity throughout the entire analysis is the angular velocity of the point that is fixed in the rotating frame. The linear velocity that is used in the Coriolis force term is the velocity of the free point relative to the fixed point in the rotating frame. The expression ω^2r for centrifugal force only applies when the two sides of the triangle dr and dθ tend to zero. When that happens, dθ becomes a pureley tangential effect. dr therefore becomes a purely radial effect and hence so does the velocity in the Coriolis force term.

The maths is identical in principle to the maths in the derivation of the polar coordinate expressions for acceleration. The Coriolis force terms and the centrifugal force terms correspond exactly in both cases. There is absolutely no question of having two different kinds of centrifugal force.

The only reason that you could possibly think that they are different is because some textbooks have unlawfully extrapolated the centrifugal force term in the rotating frame transformation equations to apply to non-rotating objects. Likewise they have also applied the Coriolis force term to any direction, and liberated it from its constraint to the tangential direction.

There is clearly a mistake in the literature, and if you don't see it, then we'll have to agree to differ on that point. Meanwhile, by all means write about rotating frames of reference as you want to see it, as per some textbooks. But one should not dominate the entire article on centrifugal force with this aspect, as has been done previously, and is still being done in the title and the introduction. The frame does not own the angular velocity. That is not physical reality.

There are other topics that involve centrifugal force, where this controversy doesn't have to be either involved or mentioned. Some examples are (a) Centrifugal Potential Energy, (b) The rotating bucket of water, (c) Planetary orbits, (d) Artificial Gravity, (e) centrifuges, and more. David Tombe (talk) 01:53, 31 October 2008 (UTC)

David, your position remains most puzzling. All the sources say that centrifugal force is a fictitious force, induced by a rotating frame of reference. Even in Goldstein, it's the projection into the 1D separation distance (that is, a non-inertial frame rotating with the planet) that gives rise to centrifugal force. As always, there's no real outward force due to rotation, except for the reaction force, the other end of the centripetal force, which is the subject of a different article. You have not been able to show any other outward force, because there is not any other. You keep claiming that your own favorite book did it differently, yet hte latest edition was clarified to make it clear that it was not intended differently. Even without that clarification, it was consistent with all other sources that treat fictitious forces. Goldstein even resolves the net effective radial force into the conventional "centrifugal" and "Coriolis" components, but doesn't mention the name of the latter term as most do; this term makes a difference when the motion is non circular and the radial component of Coriolis force is therefore nonzero, but whatever you call them the answer comes out the same. Dicklyon (talk) 03:43, 31 October 2008 (UTC)

Dick, All sources do not say that centrifugal force is a fictitious force, induced by a rotating frame of reference. The Goldstein doesn't involve rotating frames of reference when treating planetary orbits. The angular velocity belongs absolutely to the planets. Centrifugal force IS involved. It works in tandem with the inward radial gravity force. The Coriolis force is not involved in the analysis, apart from when in gets eliminated due to Kepler's law of areal velocity. And the centrifugal force is not a reactive force. It doesn't even always equal the inward gravity force in magnitude.

So what point exactly are you trying to make?

In fact, I'll repeat Goldstein's statement at the top of page 179,

Incidentally, the centrifugal force on a particle arising from the earth's revolution around the sun is appreciable compared to gravity, but it is almost exactly balanced by the gravitational attraction to the sun. It is, of course, just this balance between centrifugal force and gravitational attraction that keeps the earth (and all that are on it) in orbit around the sun. David Tombe (talk) 17:35, 31 October 2008 (UTC)

Ownership of ω

David: You have made an error in your reading. You say:

the rotating frame transformation equations deal with a point that is free to move in any fashion. But that point is rooted through another point that is fixed in a rotating frame. We hence get a vector triangle and we concern ourselves with two sides (1) origin to fixed point in rotating frame, and (2) Fixed point in rotating frame to the free point.

Your statement is inaccurate. The vector triangle is (i) between the origin of the inertial frame A and the moving point, the vector x_A (t), (ii) between the origin of the rotating frame B and the moving point, the vector x_B (t) and (iii) the vector joining the origins of the two frames X_AB (t), which may move relative to one another. There is no fixed point, except perhaps the origin of the inertial frame A. Please look over the derivation in Fictitious force much more carefully. Brews ohare (talk) 05:11, 31 October 2008 (UTC)

You say:

The maths is identical in principle to the maths in the derivation of the polar coordinate expressions for acceleration. The Coriolis force terms and the centrifugal force terms correspond exactly in both cases. There is absolutely no question of having two different kinds of centrifugal force.

There are similarities in the two derivations. However, there is not an exact correspondence. In the case of the polar coordinates analysis that is done in an inertial frame, the angular rate is that of the particle (ω) in the inertial frame where the polar coordinates reside. These terms exist independent of the frame, and depend only upon the particle. There is only one frame. the inertial frame. I hope that it is apparent that working in polar coordinates in an inertial frame is in no way tantamount to introducing any rotation of the frame itself. Any coordinate system can be used in this frame: for example, arc length s(t) along the particle path, oblate-spheroidal, etc. etc., and no choice affects the state of motion of the inertial frame.

On the other hand, the Fictitious forces argument explicitly relates an inertial to a rotating frame, so the angular rate of the frame (Ω) appears in the fictitious forces. (The angular rate of the particle as seen from the rotating frame also is present, if you choose to use polar coordinates in the rotating frame.) There are two frames: the inertial frame and the rotating frame. Brews ohare (talk) 05:11, 31 October 2008 (UTC)

Very possibly we have here an understanding of the "ownership of ω" problem. If you do polar coordinates in an inertial frame, the particle "owns ω". That has to be true, because nothing else in this problem can rotate. There is no frame rotating. If you do the Fictitious forces derivation, of course there is a rotating frame, and what the particle does is arbitrary: it may or it may not rotate, depending upon just what particle motion you choose to solve. Naturally the frame "owns Ω" (the frame rotation) and the particle motion has yet to be specified. If you introduce polar coordinates in the rotating frame the particle rotation ω (relative to the rotating frame) becomes an explicit variable. Then we have "joint ownership": the particle owns ω and the frame owns Ω. Polar coordinates in a rotating frame spells all this out in mathematical detail. For example, when the origins of the rotating and inertial frames coincide, the acceleration in the inertial frame ${\ddot {\boldsymbol {r}}}$ becomes:

${\frac {d^{2}\mathbf {r} }{dt^{2}}}=({\ddot {r}}-r\omega ^{2}){\hat {\mathbf {r} }}+(r{\dot {\omega }}+2{\dot {r}}\omega ){\hat {\boldsymbol {\theta }}}-\left(2r\Omega \omega +r\Omega ^{2}\right){\hat {\mathbf {r} }}+\left(2{\dot {r}}\Omega \right){\hat {\boldsymbol {\theta }}}\ .$

The leading two terms in ω are the standard polar coordinate terms for acceleration of the observed object (as seen in the rotating frame). The final two terms in Ω are the "standard" fictitious forces that vanish when Ω = 0 , that is, in an inertial frame. Please don't blow it off: take the time to read Polar coordinates before replying. It may settle matters at last. Brews ohare (talk) 13:17, 31 October 2008 (UTC)

Brews, The vector triangle in the derivation of the rotating frame transformation equations is exactly as I said above. The velocity vector has to be relative to a fixed point on the rotating frame for the transformations to make any sense at all. David Tombe (talk) 17:39, 31 October 2008 (UTC)

I take it that "exactly as I said above" means that you agree with me, but that I misunderstood you. Figure 2 at Fictitious force leaves little doubt about the geometry. The coordinate vector of the particle as observed in the rotating frame has to be relative to the origin of the rotating frame. The velocity and acceleration are independent of this origin, but do depend upon the state of rotation of the frame. That is not a restriction of generality, but a statement of the transformation under derivation.

How do you respond to the #equation? Brews ohare (talk) 17:49, 31 October 2008 (UTC) Brews ohare (talk) 17:44, 31 October 2008 (UTC)

Brews, No. I was referring to what I had said. Anyway, there have been a number of editors over the last year who have stringently tried to defend the notion that the coordinate frame transformation equations can be applied to objects that are not co-rotating. We have been over the arguments a few times. There have been many attempts to draw attention away from the simple underlying principle behind the transformation equations, which is that the motion of a particle relative to the inertial frame is split into two components. (1) The motion of a fixed point on the rotating frame relative to the inertial frame, and (2) the motion of the particle in question, relative to that fixed point.

We are just going to have to agree to differ on this issue. You believe that the coordinate frame transformation equations apply to non-co-rotating objects. That is your choice. I don't believe it. The question now remains as to what balance you wish to portray in the main article in relation to examples of this folly.

My own view is that the balance should be given in favour of examples in which either (1) the angular velocity belongs to the particle, or (2) the particle and the frame are co-rotating. David Tombe (talk) 18:12, 31 October 2008 (UTC)

David: Your response is unduly vague. A proper argument with the thesis you present should, at a minimum, present the mathematical objection to the already available derivation that makes transparent the mathematical origins of your suggested restrictions and limitations. A more complete presentation of your thesis would provide an alternative mathematical formulation not subject to these restrictions, which would, of course, reduce to the already presented argument in the appropriate limiting cases.

I am left of the opinion that you have a personal intuition about the subject, but that it transcends your ability to pinpoint the math. For example, you do not have any idea what might be wrong with the math in Polar coordinates, leaving your argument in the unenviable position of being simple speculation. Brews ohare (talk) 18:30, 31 October 2008 (UTC)

You say:

the motion of a particle relative to the inertial frame is split into two components. (1) The motion of a fixed point on the rotating frame relative to the inertial frame, and (2) the motion of the particle in question, relative to that fixed point.

I would take an example to be (i) the location of the origin of the rotating frame relative to the fixed frame and (ii) the vector location of the particle relative to the origin of the rotating frame (which vector location may be time varying, and need not be fixed relative to the rotating frame). I have no objection to that description, which is exactly as shown in Figure 2 at Fictitious force. I do not, however, see how this description leads to any restriction that the particle be co-rotating: the particle can have any trajectory whatsoever. Brews ohare (talk) 19:27, 31 October 2008 (UTC)

Brews, It can't involve the origin of the rotating frame, since that origin doesn't move relative to anything. I don't know where you got that idea from. The relevant issues are (1) Motion relative to a fixed point in the rotating frame, and (2) motion of that fixed point in the the rotating frame relative to the inertial frame. The angular velocity is owned totally by the fixed point in the rotating frame throughout the entire analysis.

But anyhow, we will have to stop arguing about that point. We need to list it as a point of disagreement.

It's now simply a question of how much coverage do you wish to give to non-co-rotating cases of centrifugal force in the main article? Do you wish to dominate the main article with those kind of examples? If not, why not generalize the title back to 'centrifugal force' and generalize the introduction by cutting it short after the first sentence?

David: You say:

It can't involve the origin of the rotating frame, since that origin doesn't move relative to anything.

This statement is (i) Vague, due to vague use of "it". (ii) A non-sequitor.

Please relate your remarks to Figure 2 at Fictitious force and the three variables: (i) the vector x_A (t) between the origin of the inertial frame A and the moving point, (ii) the vector x_B (t) between the origin of the rotating frame B and the moving point, and (iii) the vector joining the origins of the two frames X_AB (t), which may move relative to one another. (The value of X_AB (t) can be chosen to be identically zero throughout the derivation. That is the case of coinciding origins.) Brews ohare (talk) 23:11, 31 October 2008 (UTC)

You ask:

If not, why not generalize the title back to 'centrifugal force' and generalize the introduction by cutting it short after the first sentence?

I'd say I see no reason to do that. The identification of centrifugal force as distinct from real forces is necessary. The treatment of both stationary objects and co-rotating objects seems useful. Brews ohare (talk) 23:15, 31 October 2008 (UTC)

David, I've been working hard to provide some handles you could grab to engage with the issues, but you are ducking them right and left. Brews ohare (talk) 23:30, 31 October 2008 (UTC)

Brews, I don't think it's me that has been ducking anything. There are two separate arguments going on here. I have pointed out to you many times, that no matter what disguise you put the derivation of the rotating frame transformation equations into, when you strip it all down, it will always contain a fundamental core principle. That is the splitting of a vector into two components. One of these components references the object to the rotating frame, and the other references the rotating frame to the inertial frame. We are dealing with two variables r and θ in the limit as they tend to zero. θ is the basis of the angular velocity and it always relates to the fixed point of reference in the rotating frame. Hence in the final result, the angular velocity will always only apply to co-rotating objects. If you don't want to believe that, it up to you. On the other front, we have Dick Lyon blatantly denying the contents of the gold standard book in applied maths university theoretical physics courses. Goldstein clearly treats planetary orbits using plane polar coordinates referenced to the inertial frame. He uses centrifugal force and he doesn't involve rotating frames of reference. Yet we have Dick Lyon trying to tell us all that Goldstein does involve rotating frames of reference and that the centrifugal force is only a reaction. He even managed to bring a radial Coriolis force into his reading of the situation. There is no radial Coriolis force in plane polar coordinates, and I would go further and say that there is never a radial Coriolis force. So I'm not the one that is ducking anything. It is you and Dick that are ducking the plane facts and trying to push a viewpoint in which there exists centrifugal force on non-rotating objects, but that in situations of actual rotation, the centrifugal force is not really there. David Tombe (talk) 11:00, 1 November 2008 (UTC)

Hi David: You take a stance that your viewpoint is so credible that there is no need to answer any of the specific questions I have asked, or engage in any math. Yet it must be clear that verbal statements based upon your own personal authority aren't working with me. So how about digging into some detail? Brews ohare (talk) 11:59, 1 November 2008 (UTC)

To begin, your statement We are dealing with two variables r and θ in the limit as they tend to zero. θ is the basis of the angular velocity and it always relates to the fixed point of reference in the rotating frame. makes no sense to me. It is apparent that the vector derivation in Fictitious force finds no need for these limits. Why is that? Brews ohare (talk) 12:01, 1 November 2008 (UTC)

Brews, It's the vector triangle upon which the entire derivation is based. It means that angular velocity refers to the angular velocity of a fixed point in the rotating frame. David Tombe (talk) 17:44, 1 November 2008 (UTC)