# Centrifugal force

1. Mar 20, 2004

### 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

2. Mar 20, 2004

### mathman

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.

3. Mar 23, 2004

### DW

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

4. Mar 23, 2004

### pmb_phy

He was wrong or at a minimum very misleading

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

That depends on one's definition of "exists". But I agree with him
That is quite true. According to Einstein's General Theory of Relativity the centrifugal force is a gravitational force. These forces are frame dependant. Such frame dependant forces are called inertial forces
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
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.
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 dependant while the vanishing of 4-forces is not frame dependant. 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.

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

5. Mar 24, 2004

### yogi

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 centripital, 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.