User:FyzixFighter/Reactive centrifugal force

In classical mechanics, reactive centrifugal force forms an action-reaction pair with a centripetal force under certain conditions. A mass undergoing circular motion constantly accelerates toward the center of rotation. This centripetal acceleration is caused by a centripetal force exerted on the mass. In accordance with Newton's third law of motion, the rotating mass exerts an equal and opposite force on the source of the centripetal force. When the equal and opposite force is directed away from the center of rotation, it is called "centrifugal", meaning "fleeing the center". However, in some cases the reaction force to the centripetal force is itself also a centripetal force.

The term "reactive centrifugal force", in relation to the reaction force to a centripetal force, is seldom referred to in modern physics and mechanics. The term "centrifugal force" usually refers to the fictitious force in a rotating reference frame that appears due to the rotation of the co-ordinate system. Unlike the fictitious centrifugal force of rotating frames, the reactive centrifugal forces is a real force that appears in all frames, both stationary and accelerating.

Paired forces

A ball in circular motion held by a string tied to a fixed post.

The figure at right shows a ball in uniform circular motion held to its path by a massless string tied to an immovable post. In this system a centripetal force upon the ball provided by the string maintains the circular motion, and the reaction to it, usually called the "reactive centrifugal force" or simply the "centrifugal force", acts upon the string. In this model, the string is assumed massless and the rotational motion frictionless, so no propelling force is needed to keep the ball in circular motion.

Newton's first law requires that any body not moving in a straight line is subject to a force, and the free body diagram shows the force upon the ball (center panel) exerted by the string to maintain the ball in its circular motion.

Newton's third law of action and reaction states that if the string exerts an inward centripetal force on the ball, the ball will exert an equal but outward reaction upon the string, shown in the free body diagram of the string (lower panel) as the reactive centrifugal force.

The string transmits the reactive centrifugal force from the ball to the fixed post, pulling upon the post. Again according to Newton's third law, the post exerts a reaction upon the string, labeled the post reaction, pulling upon the string. The two forces upon the string are equal and opposite, exerting no net force upon the string (assuming that the string is massless), but placing the string under tension.

It should be noted, however, that the reason the post appears to be "immovable" is because it is fixed to the earth. If the rotating ball was tethered to the mast of a boat, for example, the boat mast and ball would both experience rotation about a central point.

Applications

Even though the reactive centrifugal is rarely, if ever, used in physics literature, the concept is applied within some mechanical engineering concepts. An example of this kind of engineering concept is an analysis of the stresses within a rapidly rotating turbine blade. The blade can be treated as a stack of layers going from the axis out to the edge of the blade. Each layer exerts an outward (centrifugal) pull on the immediately adjacent, radially inward layer. At the same time the latter layer exerts an elastic inward (centripetal) pull on the former, resulting in an internal stress. It is the stresses in the blades and their causes that mainly interest mechanical engineers in this situation.

Relation to inertial centrifugal force

There are many distinction between the reactive centrifugal force and the fictitious centrifugal force of rotating frames. The reactive centrifugal force, being one-half of the reaction pair together with centripetal force, is a concept which applies in any reference frame. This distinguishes it from the inertial or fictitious centrifugal force, which appears only in rotating frames. The two forces also act on and originate from different objects. The reactive centrifugal force originates from the object undergoing centripetal acceleration and acts on the source of the centripetal force, while the fictitious force acts on all objects (except those at the center of rotation) in the rotating frame and cannot be said to originate from any object. As noted before, in accordance with Newton's third law of motion the reactive centrifugal force forms an action-reaction pair with the centripetal force, but the fictitious centrifugal force is only an artifact of making observations within a rotating frame and therefore has no corresponding action-reaction force.