Centrifugal Force: Facts & Equations

Hello guys!

Back in my first physics class in college, a few years ago, my prof said that centrifugal force does not exist, and something about there is something called the centrifugal force effect that we seem to think we feel, but it really is centripetal force.

I took this as physics dogma, and today I spouted my mouth off while watching a TV show, and everyone thought I was lying so I looked it up in my physics book, and centrifugal force was no where to be found, which was good for me. Then I looked on the net, and found tons of mentions of it.

I found definitions of centrifugal force ranging from a group of gay men that practice beating drums to the definition that blew me (no pun intended) out of the water. One paper I read on centrifugal force said that it is not the fictitious force that people think it is, and that it does exist. It just doesn't exist in inertial frames, but in accelerated frames, it does. I'm assuming this is a SR connection.

So my question is what is centrifugal force, does it exist, and what equation do you use to "measure" it?

Thank you kindly,
AYCHAMO

Centrifugal force has nothing to do with relativity. It is simply a manifestation of the law of inertia (things like to go in straight lines at constant speed). When you whirl something around on a string, you are exerting a force (centripetal) to keep it from flying off. The tendency to fly off is centrifugal force, i.e. it wants to go in a straight line and you are keeping it in a circular path.

Originally posted by aychamo
Hello guys!

Back in my first physics class in college, a few years ago, my prof said that centrifugal force does not exist, and something about there is something called the centrifugal force effect that we seem to think we feel, but it really is centripetal force.

I took this as physics dogma, and today I spouted my mouth off while watching a TV show, and everyone thought I was lying so I looked it up in my physics book, and centrifugal force was no where to be found, which was good for me. Then I looked on the net, and found tons of mentions of it.

I found definitions of centrifugal force ranging from a group of gay men that practice beating drums to the definition that blew me (no pun intended) out of the water. One paper I read on centrifugal force said that it is not the fictitious force that people think it is, and that it does exist. It just doesn't exist in inertial frames, but in accelerated frames, it does. I'm assuming this is a SR connection.

So my question is what is centrifugal force, does it exist, and what equation do you use to "measure" it?

Thank you kindly,
AYCHAMO

The centrifugal force is a fictitious force which means that it does not correspond to a force four vector. One can have a zero force four vector and still have frame dependent forces of affine connection or fictitious forces such as Centrifugal, Corriolis, and gravitational forces. Whether a four vector is zero does not depend on whether frame is accelerated or inertial. So it is the force four vector and not these fictitious forces that are thought of as real in the paradigm of modern relativity. Where the centrifugal force and other fictitious forces are manifested in general relativity as forces of affine connection corresponding to a zero force four-vector is exactly derived as equations 6.3.33 on page 80 at
http://www.geocities.com/zcphysicsms/chap6.htm#BM80

Originally posted by aychamo

Back in my first physics class in college, a few years ago, my prof said that centrifugal force does not exist,..

He was wrong or at a minimum very misleading

Then I looked on the net, and found tons of mentions of it.

The best resource you're apt to find on this is A Coriolis Tutorial, James F. Price, Woods Hole Oceanographic Institution

http://www.whoi.edu/science/PO/people/jprice/class/aCt.pdf

One paper I read on centrifugal force said that it is not the fictitious force that people think it is, and that it does exist.

That depends on one's definition of "exists". But I agree with him

It just doesn't exist in inertial frames, but in accelerated frames, it does.

That is quite true. According to Einstein's General Theory of Relativity the centrifugal force is a gravitational force. These forces are frame dependent. Such frame dependent forces are called inertial forces

I'm assuming this is a SR connection.

It's related to GR. As mentioned above is an inertial force. The coriolis force is an inertial force too. In fact Einstein commented on both of these.

From A Brief Outline of the Development of the Development of the Theory or Relativity, Albert Einstein, Nature, February 17, 1921

Can gravitation and inertia be identical? This question leads directly to the General Theory of Relativity. Is it not possible for me to regard the Earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordiantes? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation.

As you've noticed there are several opinions on this subject. The whole debate hinges on the definition of "force" and on "exists". You'll notice phrases like "psuedo-force" or "fictitious force" tossed around. That is something left over from Newtonian mechanics where mechanical concepts were based on absolute time and absolute space. The laws of physics, in Newtonian mechanics, were said to be held only in "inertial" frames of reference. Even then there wa much debate on this topic. For example

From Newtonian Mechanics, A.P. French, The M.I.T. Introductory Physics Series, W.W. Norton Pub. , (1971) , page 499.

From the standpoint of an observer in the accelerating frame, the inertial force is actually present. If one took steps to keep an object "at rest" in S', by tying it down with springs, these springs would be observed to elongate or contract in such a way as to provide a counteracting force to balance the inertial force. To describe such force as "fictitious" is therefore somewhat misleading. One would like to have some convenient label that distinguishes inertial forces from forces that arise from true physical interactions, and the term "psuedo-force" is often used. Even this, however, does not do justice to such forces experienced by someone who is actually in the accelerating frame of reference. Probably the original, strictly technical name, "inertial force," which is free of any questionable overtones, remains the best description.

However this "frame dependance" is no longer true in GR since in GR the laws of physics are the same in all frames of reference and not simply in inertial frames. Recall that force is defined as the time rate of change of momentum. In relativity there are two kinds of forces. There is force in the normal sense and there are 4-forces, the former being part of the later just as momentum is part of 4-momentum. The vanishing of inertial forces is frame dependent while the vanishing of 4-forces is not frame dependent. If you're in an inertial frame of reference and a particle is moving in a straight line a constant velocity then the momentum is constant and thus the force is zero, i.e. both the force and the 4-force are zero. Now change to an accelerating frame of reference. The same particle now has a spatial acceleration relative to your, accelerating, frame of reference. There is now a force on it. This is an inertial force and as such it is a gravitational force according to Einstein's general relativity. However whether the 4-force vanishes does not depend on the frame of reference (i.e. the coordinate system). Therefore the 4-force is zero.

See also Cosmological Physics, John A. Peacock, page 6-7

http://assets.cambridge.org/0521422701/sample/0521422701WS.pdf

To answer your question: The centrifugal force is an inertial force. If you want too know if it exists or not then you need to ask a philosopher.

For more on gravitational forces in GR please see
http://www.geocities.com/physics_world/gr/grav_force.htm

If you are in a rotating cylinder - and didn't know it, you would find a mysterious pseudo force pressing you against the wall of the cylinder - your body wants to go in a straignt line, but can't because its being forced to move in a circle by the walls of the rotating cylinder. So you could consider yourself as being centrifuged - but from the standpoint of there being an independent force other than centripetal, there is none in the usual context of mechanical physics.

Feynman in his first volume suggested that gravity might be a pseudo force - these forces are always proportional to mass just as is gravity and inertia. Feynman then muses that perhaps we experience gravity because in some way we may not exist in an inertial frame.