# Does centrifugal force exist?

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

3. Mar 20, 2004

### Chen

When you are in circular motion at a constant velocity, the centripetal force on you is constant and is directed at the center of the circle. For someone looking at you from outside, as an inertial observer, this would be the only force on you. Your acceleration would be centripetal force divided by your mass, usually notated as $$\vec a_r$$, the radial acceleration.

However, when you are in the motion you are feeling things from your own perspective, which is the point of view of an non-inertial observer. And whenever you are a non-inertial observer, there is an extra force on you - it is $$-m\vec a$$, where $$\vec a$$ is your acceleration as perceived by an inertial observer. This force is the centrifugal force that you feel, and its magnitute is exactly the same as the centripetal force but in opposite direction. So while the centripetal force is pulling you in, the centrifugal force is pushing you out.

4. Mar 20, 2004

### aychamo

So this "centrifugal force" is really kinda like Newton's "Every action has an equal an opposite reaction"?

So we feel this force, but it doesn't really exist? Is the "disproof" of centrifugal force that if you were on a carosel and you feel this force pushing you outward, if it existed and you let go of the carosel it would push you away from it, but in reality you would follow the the line tangent to the circle?

5. Mar 20, 2004

### Chen

The centrifugal force isn't unique only to circular motion and carousels... when you drive in your car and step on the gas paddle, aren't you pushed agains the back of your seat? It appears that a force is pushing you back, while in reality you are going forward. (Of course it's not called a centrifugal force there, but it acts on the same principle.)

Why? Because your acceleration, relative to the car / carousel, is zero. And for it to be zero, the sum of forces on you must be zero. The difference is that in your car you only feel it when accelerating/decelerating, because at any other time your velocity is constant, whereas in the carousel you feel it all the time because while your velocity is constant, its direction changes all the time and your acceleration is never zero.

Last edited: Mar 20, 2004
6. Mar 20, 2004

### aychamo

Cool deal :)

What I'm not getting now is how do we say it is fictitious if we can feel it?

7. Mar 20, 2004

### Chen

Here's the definition of a fictitious force:
http://www.bartleby.com/61/7/P0630725.html

That law is that if your velocity is constant, the total force on you must be zero. And relative to the carousel, your velocity is not only constant but also zero. You must "feel" the centrifugal force or else the sum of forces on you would not be zero.

Last edited: Mar 20, 2004
8. Mar 20, 2004

### FZ+

It is said that a measure of a good physicist is how much he/she sniggers at the mention of "centrifugal force".

9. Mar 20, 2004

### aychamo

lol. I was watching the program on Discovery channel, it was something about someone making a 180hp snowmobile. They kept saying centrifugal force OVER AND OVER, and I go "haha, that's bs because the force doesn't even exist." So I go to prove myself and I search on the net and I get like a jillion matches for centrifugal force. I was scared, but not anymore :)

But I'm glad I researched it, because this made me realize that I might have known that the force did not exist, but beyond that I was ignorant.

One question though, may you explain this futher to me?

10. Mar 20, 2004

### aychamo

Last edited by a moderator: May 1, 2017
11. Mar 20, 2004

### aychamo

If I am understanding this correctly, say in a different universe where there wasn't a felt centrifugal force, if you didn't feel the centrifugal force, then the total forces acting on you, relative to the carousel would not be zero, therefore you would fly into the center of the carousel?

So how does this explain rides like the Gravitron (the big spinning thing that sticks you to the walls?) The ride feels like you are sticking to the walls, but since the centrifugal "force" balances out the centripetal force, shouldn't that make you free to walk around inside the ride? Or is the wall stickiness because the ride is spinning so fast that your inertia is keeping you to the wall (cause the you keep trying to move tangent to the circle of the ride)??

12. Mar 20, 2004

### Chen

Sorry but I don't wish to speculate on what would happen in another universe in which Newton's laws don't apply.

In that ride, the walls provide you with the centripetal force that enables you to go in circluar motion. If you were to move away from the walls, would you still move in circular motion? Yes. But the walls would no longer exert a force on you, so what would? The floor of course. But because the floor exerts the force only on your feet, it is a lot harder to stay balanced for a long time. Theoretically, you could walk around during the ride. In fact, if the ride was spinning at lower speeds you will see that you have no difficulties in doing so. But as the velocity increases, so does the centripetal force (which is defined as $$m\frac{v^2}{r}$$) and you will find it more and more difficult to wander about during the ride.

13. Mar 20, 2004

### Chen

Do you understand, that without acceleration your velocity as a vector cannot change? In the carousel, the velocity changes its direction, even though it doesn't change its size, but it is still changing. But of course everything is relative! This is true for someone standing out of the carousel, but for someone inside the carousel, such as yourself, you are not moving at all and your velocity is both constant and zero. This is why for someone standing outside, only the centripetal force exists, while you can also feel the centrifugal force.

Is it just me or are we going around in circles? j/k

Last edited by a moderator: May 1, 2017
14. Mar 20, 2004

### krab

Forces that you can feel are not real? Give me a break.

If this is really what your prof said, then he is incorrect. "Fictitious" is an adjective to denote forces which can be transformed away by choice of reference frame. It is an unfortunate definition. "Inertial" would be better. Because "fictitious" means "unreal" in other contexts, people are led to the incorrect conclusion that such forces are not real. A good example is cookiemonster's inference from the scienceworld.wolfram.com page. That page nowhere says the force is non-real, it shows how to calculate it, introduces the notion of centrifugal acceleration, and takes care to put the words "fictitious forces" in quotation marks.

Since Einstein's principle of equivalence, centrifugal force is an entirely legitimate force. In the Newtonian view, OTOH, it is thought of as an artifact arising from a "non-inertial" frame. However, inertial frames are usually defined as those in which Newton's laws apply. This, if you think about it, is a circular situation. The only way out is to posit "Absolute Space", which Newton did.

FWIW, here are some of Einstein's own words. (From "The Meaning of Relativity", Princeton University Press, 1953)

"The principle of equivalence demands that in dealing with Galilean regions we may equally well make use of non-inertial systems, that is, such coordinate systems as, relatively to inertial systems, are not free from acceleration and rotation... ...let K' be a system of coordinates whose z'-axis coincides with the z-axis of K, and which rotates about the latter axis with constant angular velocity..." [goes on to show that the configuration of rigid bodies at rest in K' are not in accordance with Euclidean geometry] "...according to the principle of equivalence, K' may also be considered as a system at rest, with respect to which there is a gravitational field (field of centrifugal force, and force of Coriolis). We therefore arrive at the result: the gravitational field influences and even determines the metrical laws of the space-time continuum..."

Second, and what really bugs me about the "centrifugal force is unreal" view is that it confuses rather than clarifies the situation for non-physicists. Are you going to tell anyone who feels a force pressing to the wall in the Tilt-a-Whirl ride that what he feels is not real? Similarly, as another example of an inertial force, are you going to tell the person who feels momentarily heavier in an elevator which begins rising, that this extra force is not real? In both these situations, one could take the view that it is the wall (or floor) providing the force and the result is that the person's trajectory is changed. This is beside the point! The guy in the Tilt-a-Whirl really is squashed against the wall, exactly as if he is laying down in an extra strong gravitational field. Spin it fast enough and it is not relevant that he is going in circles. His ribs are breaking!

15. Mar 20, 2004

### mmwave

I think you've got the idea here. My comment is what do physicists mean when they say it is ficticious? It's not that you don't 'feel' it when you are in a rotating frame of reference but rather that in any inertial frame observing the rotation an observer will say there is only centripetal force.

That plus the fact that Newton's laws as commonly taught only hold in inertial frames of ref. is why the centrifugal force is called 'ficticious'. What you feel "pushing you outward" is the action/reaction force from the centripetal force making you go in a circle.

Another complication is that humans are not reliable observers in rotating ref. frames. When you ride in a car that turns & you slide across the back seat you think you are being pushed outward on the turn but an observer through the sun roof will tell you your path was a straight line until you hit the door. Then you go in a circle with the car since you have a source of centripetal acceleration. Try it with a marble & a lazy susan turntable. (i've ignored friction on the seat here.)

16. Mar 21, 2004

### Chi Meson

One point that I always make (and it usually makes the "pro-centrifugalers" go quiet):

consider a rock twirled in a circle. We all usually can agree that there is the centripetal force on the rock from the string. Well, if there is also a centrifugal force on the rock pulling it outward, then these two forces cancel and the rock flies in a straight line.

Promoting the notion of the centrigual effect as a force is more detrimental to the conceptual grasp of Newtonian forces than any other misconception. If we stay inside a rotating reference frame, then fine; but stay in there, because once you step outside of that tilt-a-whirl, it is now "centrifugal farce." You might as well start calling it a force that slams you body into the seat belt when your car stops suddenly.

17. Oct 10, 2008

### sr_philosophy

you people never answer questions -
"Does centrifugal force exists?"

Yes it does. That's all.

18. Oct 10, 2008

### stewartcs

19. Oct 10, 2008

### qspeechc

Ok, here's how I understand it (but I am no physicist), if we speak in Newtonian terms only. To take Chi Meson's example:

Consider the rock being swung around on a string. We all agree there is a centripetal force acting on the rock, which is what causes it to travel in circle. Now this is in an inertial frame so all is legit right? So what about Newton's Third Law? There must be an opposite force (the centrifugal force) in this intertial framework. Of course there is, but it isn't acting on the rock, no! It acts on your hand, which is swinging the rock around. Or, it's acting on the string, which is what keeps the string taut when you swing the rock around. There is no centrifugal force on the rock, it's on the string.

Consider a rock attached to a string, hanging at rest. The gravitational force acts downwards on the rock. The rock acts on the string, and the string produces an opposite force upwards on the rock, which is equal in magnitude to the force the rock exerts on the string. This force the rock exerts on the string is what keeps the string taut. Similarly ,when you swing the rock around, it is the centrifugal force the rock exerts on the string that keeps the string taut.

Consider a man pushing on a wall. He exerts a force on the wall, and the wall exerts an equal but opposite force on the man. (However the force the man exerts is a force that does no work so nothing moves, but this is irrelevant to the discussion here.) It's the same deal with someone swinging a rock attached to a string.

Why then does the rock 'feel' a centrifugal force? While you're swinging the rock there is this centripetal force on the rock (since it's moving in a circle i.e. accelerating). According to Newton's first Law the rock 'wants' to go in a straight line at a constant speed, but there's this pesky centripetal force causing it to mov in a circle. This is what it feels, the centripetal force keeping it going in a circle. Let's not bother tlking about non-inertial frames, namely from the rock's point of view, since we can't discuss that in Newtonian physics anyway.

20. Oct 10, 2008