# Talk:List of second moments of area

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There's something wrong with the displaying of some of the formulas in the table. At least two of them are displaying the code and not the proper formula. Couldn't figure out what the problem was. —Preceding unsigned comment added by 76.65.22.70 (talk) 00:45, 23 November 2008 (UTC)

I couldn't figure out what caused it either, but simplifying the code slightly seems to have worked. Thanks for leaving a note here. Hemmingsen 14:52, 23 November 2008 (UTC)

Rationale for change to circle segment formula: The past formula for the area moment of inertia of a circle segment was incorrect. The derivative versus theta was zero at theta = pi, which is right where it should be a maximum! I did the integration myself by hand, found the problem, then decided to be bold and fixed the formula.--JB Gnome (talk) 11:38, 28 October 2009 (UTC)

This list should be renamed to 2nd moments of area to avoid confusion with mass moments of inertia. — Preceding unsigned comment added by 137.222.212.111 (talkcontribs) 19:56, 28 April 2010

While there are problems with some of the shape displays, this page is important for people (such as myself) studying angular mechanics. There is a note that this page is a candidate for speedy deletion and may disappear at any time. Please allow me to enter a vote for keeping the page. Thank you. —Preceding unsigned comment added by 208.96.82.76 (talk) 19:05, 13 January 2011 (UTC)

## Filled cirlce

Shouldnt the formula for the polar moment of inertia of a filled circle be Ip=pi * R^4/2 instead of r^4/4 ? It's right there in the cited reference. — Preceding unsigned comment added by 77.54.89.249 (talk) 21:18, 30 May 2012 (UTC)

The moment of inertia along the z-axis (perpendicular to the plane) is ${\displaystyle {\frac {\pi }{2}}R^{4}}$, but this article is about the moment of inertia along the x-axis. Ulflund (talk) 06:26, 31 May 2012 (UTC)
Oh okay, but that isn't very useful, at least from an engineering viewpoint. Most of the time we use moments along the z-axis, in shafts and things like that. I'm a student, and that /4 part made me lose half an hour trying to figure it out. I think the axis part should be more explicit, or there should be another article with the moments along the z-axis. — Preceding unsigned comment added by 77.54.89.249 (talk) 01:58, 1 June 2012 (UTC)
Maybe the moments could be listed like here http://www.efunda.com/math/areas/Circle.cfm, with three columns for the different axis. — Preceding unsigned comment added by 77.54.89.249 (talk) 02:01, 1 June 2012 (UTC)

I added the Parallel Axis Theorem. It doesn't quite fit with the rest of the formulas, but it is just so important to the rest that it really needs to be here. I am a practicing engineer and I routinely come to this page in my work. I inevitably have to click through to the parallel axis theorem to continue my work. This bugs the snot out of me.

I added the Parallel Axis Theorem. It doesn't quite fit with the rest of the formulas, but it is just so important to the rest that it really needs to be here. I am a practicing engineer and I routinely come to this page in my work. I inevitably have to click through to the parallel axis theorem to continue my work. This bugs the snot out of me.Marcusyoder (talk) 17:04, 27 February 2013 (UTC)

## filled circular sector

The formula for the filled circular sector seem to be wrong. It gives negative result with some angles value. The correct formula should be the one at http://www.efunda.com/math/areas/CircularSection.cfm If nobody as objection I can modify the formula with the correct one. — Preceding unsigned comment added by 79.2.53.113 (talk) 20:55, 5 May 2013 (UTC)

The formula is correct according to the link you provided. Just note that the formula you provided has ${\displaystyle a}$ as half the angle (the angle from the axis up) whereas the current formula has the full angle. Also note that theta is in radians and I think that it may only work for angle up to ${\displaystyle \theta =pi}$; for the other half you may have to do the method of segment and subtract the segment from the full circle. That need to be verified, though.

BeaumontTaz (talk) 22:04, 9 May 2013 (UTC)

I noted the angle in the formula was halved and made the corresponding substitution. My algebra skill are a bit rusty but I did some check with different angles with both formula and the result were the same. Regarding the limit value of ${\displaystyle \theta }$ I think we should put a note on the formula to warn the reader. — Preceding unsigned comment added by Aracosta (talkcontribs) 20:23, 10 May 2013 (UTC)

I've actually been working on redrawing these images and making the entire thing more uniform in wording and format. Go ahead and edit the page now with that info, and I'll make sure it makes it into the redo of the page. BeaumontTaz (talk) 21:10, 10 May 2013 (UTC)

I think the sector formula is incorrect, both here and in the efunda link. I've done the integration by hand and I get the following results: ${\displaystyle I_{x}=(\theta +\sin \theta ){\frac {r^{4}}{8}}-{\frac {8r^{4}}{9\theta }}\sin ^{2}{\frac {\theta }{2}}}$ which is valid for ${\displaystyle 0<\theta \leq 2\pi }$ For example, if r=10mm, my proposed formula gives:

${\displaystyle \theta }$ (degree) I_x (mm^4)
30.0 142.28677688734979
60.0 269.46278583435833
90.0 384.07419797103739
120.0 517.42677088413666
150.0 729.62923338437258
180.0 1097.5696064646581
210.0 1693.7299192672617
240.0 2561.9065703334863
270.0 3697.3458219733338
300.0 5038.0397586697973
330.0 6471.1002833301964
360.0 7853.981633974483

I have checked the results for theta=30 and 60 and they match the numerical results of TopSolid (CAD program) Dkliu1 (talk) 04:05, 19 May 2016 (UTC)

## Robust references

I am trying to look up some of the references from this page, but the efunda website is just redirecting me to a paywall (it allows approx 5 page views before cutting you off). Does anyone know of a better website to link to? MathWorld has several pages on this topic, e.g. http://mathworld.wolfram.com/MomentofInertia.html — Preceding unsigned comment added by 129.169.141.108 (talk) 12:44, 24 February 2014 (UTC)

Just delete your cookies and you can view it again. Also, any introductory textbook on solid mechanics or engineering statics would have a series of tables that show all of these shapes. Also, the second moment of area page has references not listed on this "list" page. BeaumontTaz (talk) 00:29, 25 February 2014 (UTC)

## Annulus

Is it possible to have more information on the simplification? It's ambiguous why the terms with t^x , x>1 disappear.

This is a common enough practice to ignore higher order terms of small numbers. It's assumes that ${\displaystyle r>>t}$ So think something like ${\displaystyle r=100,t=0.01}$. Now compare the size of the terms ${\displaystyle r^{3}t=10000,r^{2}t^{2}=1,rt^{3}=0.0001,\ldots }$. Clearly ${\displaystyle 10001.0001\approx 10000}$ and we can save a lot of trouble by not calculating the smaller numbers. Now this is an exaggeration in terms of the size difference needed to make the higher order terms negligible. Usually ${\displaystyle r>10t}$ suffices to make it a good enough approximation for most engineering applications. So basically we have ${\displaystyle r^{3}t=1000t^{4},r^{2}t^{2}=100t^{4},rt^{3}=10t^{4},\ldots }$ and clearly the first is an order of magnitude larger than the second which gives about a ${\displaystyle 10\%}$ error. Different authors give different acceptable relationships between ${\displaystyle r}$ and ${\displaystyle t}$. But ${\displaystyle 10}$ is a common one. Personally, this is a common enough practice that these deep details could be spared in the table listing the equations. The details present should be enough to make the point clear without exaggerated example or a relationship limit. BeaumontTaz (talk) 09:21, 7 October 2014 (UTC)

## characters in figures are illegible

e.g. for the annulus, the r's look like lowercase y's. — Preceding unsigned comment added by 24.43.3.130 (talk) 00:34, 10 December 2014 (UTC)

Fixed --IngenieroLoco (talk) 20:17, 16 April 2016 (UTC)

## Formula's not showing

None of the formula's display for me. At first I thought it was vandalism, but the math tags and text are still there, they just aren't rendering. This is the last revision I was able to view them in. Zephalis (talk) 07:27, 2 April 2015 (UTC)

I don't see any problem with the formulas. --IngenieroLoco (talk) 20:18, 16 April 2016 (UTC)