# What is Centrifugal force?

## Main Question or Discussion Point

I've heard recently that centrifugal "force" doesn't exist. If this is true what is the actual force that creates the centrifugal effect?

Also, do centrifugal and centripetal effects/forces exist in outer space, i.e. on space shuttle.

Thanks

Related Other Physics Topics News on Phys.org
It's the tendency of a mass to continue moving in a straight line, while its environment, it's "frame of reference", is turning.

Sometimes you're a passenger in a car when the car turns suddenly, and your body presses hard against the door. If you visualize the car as being at rest, if your x,y,z axes are drawn on the car, it would seem to you that some force pushed you against the door. Actually all your mass was doing was continue going in a straight line, and the turning of the car made the door hit you.

Yes, it happens in space also.

rcgldr
Homework Helper
Centripital force is the force that accelerates an object inwards, centrifugal force is the equal and opposite reaction force due to the objects inertial resistance to the inwards acceleration from the centrpetal force.

Doc Al
Mentor
I've heard recently that centrifugal "force" doesn't exist. If this is true what is the actual force that creates the centrifugal effect?
A "real" force has an actor, something that exerts the force. Centrifugal force is not a real force as there is no actor creating a force; it's just an artifact of describing things from a non-inertial (rotating) frame of reference. (Often it is extremely useful to describe things from within a non-inertial frame.)

As mikelepore explained, the source of the effect is just inertia (Newton's 1st law).

On the other hand, centripetal force is a real force in every sense of the word. When something moves in a circle, there is a real force (with an actor) pushing it towards the center.

Examples: (a) Tie a string around a ball and whirl it in a circle. The string (the actor) exerts a real centripetal force on the ball. (b) Drive your car around a circular track. The road (the actor) exerts the centripetal force on the car.

Regarding Newton's 3rd law and "action-reaction" pairs: It's true that any real force is part of an equal and opposite 3rd law pair. For example (a), the 3rd law pair of forces is: String pulls ball inward & ball pulls string outward. But that outward force on the string is a real force, not the fictitious centrifugal force. (Centrifugal force would be an outward "force" on the ball.)

I've heard recently that centrifugal "force" doesn't exist. If this is true what is the actual force that creates the centrifugal effect?

Also, do centrifugal and centripetal effects/forces exist in outer space, i.e. on space shuttle.

Thanks
I'm curious as to what you consider to a criteria for existance? It may seem odd but this question goes to the heart of the matter when it comes to things such as the inertial force, of which centrifugal force is one of them.

Definition - Inertial force: When the motion of the reference system generates a force (defined as the time rate of change of momentum, i.e. F = dp/dt), as measured in that system, we call that force an inertial force.

Albert Einstein had the following to say on this topic. That the relation of gravity to inertia was the motivation for general relativity is expressed in an article Einstein wrote which appeared in the February 17, 1921 issue of Nature
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-ordinates? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation.
There is a similar comment in Introducing Einstein's Relativity, by Ray D'Inverno, Oxord/Clarendon Press, (1992) page 122
Notice that all inertial forces have the mass as a constant of proportionality in them. The status of inertial forces is again a controversial one. One school of thought describes them as apparent or fictitious which arise in non-inertial frames of reference (and which can be eliminated mathematically by putting the terms back on the right hand side). We shall adopt the attitude that if you judge them by their effects then they are very real forces. [Author gives examples]
Another opinion on this subject comes from The Variational Principles of Mechanics, by Cornelius Lanczos - The subject of inertial force is also addressed in - 4th Ed., Cornelius Lanczos, Dover Pub., page 98.
Whenever the motion of the reference system generates a force which has to be added to the relative force of inertia I’, measured in that system, we call that force an “apparent force.” The name is well chosen, inasmuch as that force does not exist in the absolute system. The name is misleading, however, if it is interpreted as a force which is not as “real” as any given physical force. In the moving reference system the apparent force is a perfectly real force, which is not distinguishable in its nature from any other impressed force. Let us suppose that the observer is not aware of the fact that his reference system is in accelerated motion. Then purely mechanical observations cannot reveal to him that fact.
To top this off I'll reference one more view on the concept of inertial force. A.P. French - Inertial force is defined as the force on a body that results solely from observing the motion of the body from a non-inertial frame of reference. This in addressed in Newtonian Mechanics, A.P. French, The M.I.T. Introductory Physics Series, W.W. Norton Pub. , (1971) , page 499. After describing the inertial force as seen from an accelerating frame of reference French writes
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.
Pete

Last edited:
Centripital force is the force that accelerates an object inwards, centrifugal force is the equal and opposite reaction force due to the objects inertial resistance to the inwards acceleration from the centrpetal force.
The presence of a centrifugal force does not require the existance of a reaction force. Centrifugal forces are the inertial force on a particle which is only measured by observers in rotating frames of reference and is directed in the outward direction from the center of rotation.

Pete

dst
So in other words, a "fictitious force" in a particular reference frame is one which has no 3rd law pair for that reference frame?

So in other words, a "fictitious force" in a particular reference frame is one which has no 3rd law pair for that reference frame?
No.

Pete

Doc Al
Mentor
So in other words, a "fictitious force" in a particular reference frame is one which has no 3rd law pair for that reference frame?
I'd say yes. (In Newtonian physics, at least.)

dst
So how would you define it? I would have thought that was the case since it works for centrifugal force + coriolis force.

Edit: Oh ok...

Dale
Mentor
Centripital force is the force that accelerates an object inwards, centrifugal force is the equal and opposite reaction force due to the objects inertial resistance to the inwards acceleration from the centrpetal force.

NO! The centrifugal force is not a reaction force. It is a ficticious force and as such it does not obey Newton's 3rd law.

Doc Al
Mentor
NO! The centrifugal force is not a reaction force. It is a ficticious force and as such it does not obey Newton's 3rd law.
Exactly.

Thanks everyone for your replies and references.

Einstein's idea that gravity and inertia could be identical is similar to what I was assuming. However, I was thinking more along the line that either Centrifugal and Centripetal is actually an affect of gravity, and possibly a form of counter gravity. And inertia is a kinetic (stored) energy, which isn't directly related to the inward pulling and outward pulling on an object due to centripetal or centrifugal force.

For example, isn't the centripetal force that keeps an object in orbit, in space (planets, satellite) due to gravity? Why would centripetal force be any different on earth?

With the string and ball analogy. Why does a mass rotating around an axis, rise up against gravity the faster it spins. Could a gravitational force be coming from within the string?

Dale
Mentor
However, I was thinking more along the line that either Centrifugal and Centripetal is actually an affect of gravity, and possibly a form of counter gravity. And inertia is a kinetic (stored) energy, which isn't directly related to the inward pulling and outward pulling on an object due to centripetal or centrifugal force.

For example, isn't the centripetal force that keeps an object in orbit, in space (planets, satellite) due to gravity? Why would centripetal force be any different on earth?

With the string and ball analogy. Why does a mass rotating around an axis, rise up against gravity the faster it spins. Could a gravitational force be coming from within the string?
You are probably aware that there are many descriptions that you can use to accurately describe the same thing, each description capturing a different aspect of the thing.

When you say "gravitational force" you are talking about the mechanism of the force or how the force is exerted. You can also say "electrostatic force" or "tensile force" or "friction force" all refering to the mechanism.

When you say "centripetal force" you are talking about the function of the force, or what it is doing. You can also say "reaction force" or "restoring force" all refering to the function and not the mechanism.

You can always use an infinite amount of words, and equations, to describe or complicate a simple concept.

Centripital force is the force that accelerates an object inwards, centrifugal force is the equal and opposite reaction force due to the objects inertial resistance to the inwards acceleration from the centrpetal force.

NO! The centrifugal force is not a reaction force. It is a ficticious force and as such it does not obey Newton's 3rd law.
I don't understand, it clearly seems to be just like any other reaction force. Any acceleration on an object, regardless of direction, creates a reactionary force. Why change the rules for the one case where the force just happens to be perpendicular to the objects direction of travel? Why should the direction of the force matter at all?

Doc Al
Mentor
I don't understand, it clearly seems to be just like any other reaction force. Any acceleration on an object, regardless of direction, creates a reactionary force. Why change the rules for the one case where the force just happens to be perpendicular to the objects direction of travel? Why should the direction of the force matter at all?
No "rules" are being changed. To accelerate something in a circular path requires a centripetal force; that force, like any other, will be paired with a "reaction" force per Newton's 3rd law. But that "reaction force" is not the centrifugal force. The reaction to a centripetal force is an equal and opposite force on whatever is creating the centripetal force. See my examples in post #3.

Centrifugal force is not a "real" force, but an artifact of describing motion from a noninertial, rotating frame. Newton's 3rd law does not apply.

Dale
Mentor
I don't understand, it clearly seems to be just like any other reaction force. Any acceleration on an object, regardless of direction, creates a reactionary force.
NO! How can you possibly say it seems to be just like any other reaction force? An action-reaction pair act on two different bodies. The centripetal and centrifugal force act on the same body. They cannot possibly form an action-reaction pair.

Let's consider a standard example of a car making a left turn around an unbanked turn of constant radius, and for simplicity let's consider only in the horizontal plane (i.e. ignore gravity and normal forces since they cancel in this problem). We will consider the horizontal forces on the driver and on a cup on the frictionless dashboard and we will analyze their motion in both the frame of the road (inertial) and the frame of the car (rotating).

In the road frame the cup is not accelerating, it moves in a straight line with no horizontal forces acting on it.

In the road frame the driver is accelerating to the left. He experiences a static friction force from the seat which is the centripetal force accelerating him.

In the car frame the cup is accelerating to the right. There are no real forces acting on the cup, so how do we explain its acceleration? We posit a fictional force we call the centrifugal force pointing to the right which explains the acceleration. Since the dashboard is frictionless there is no balancing centripetal force and the cup accelerates in the car's frame.

In the car frame the driver is stationary. There is a real frictional (centripetal) force from the seat, so how do we explain the lack of acceleration? We posit the same centrifugal force pointing to the right as above. This centrifugal force balances the frictional centripetal force and the driver remains stationary.

Now, let's go back and look for action-reaction pairs.

In the road frame the only force is the friction force to the left from the seat acting on the driver. The reaction to that force is a friction force acting to the right on the seat. Note that, as always with action-reaction pairs, they are of the same kind (friction) and act on differen bodies (driver and seat).

In the car frame the friction forces on the driver and on the seat still exist and still form an action-reaction pair of the same kind acting on different bodies. However, the centrifugal forces all act to the right so they are not opposite to each other. They violate Newton's 3rd law.

Last edited:
I disagree. The centrifugal force does obey Newton's third law.

Pete

Thanks everyone for your replies and references.

Einstein's idea that gravity and inertia could be identical is similar to what I was assuming. However, I was thinking more along the line that either Centrifugal and Centripetal is actually an affect of gravity, and possibly a form of counter gravity.
Einstein was motivated by this idea, i.e. that what Newtonians called "fictitious" forces were really, in Einstein's opinion anyway, "real" forces because they behaved like the "real" force of gravity. However others have interpreted this to mean that since inertial forces are identical in nature to "fictitous" forces that it meant that gravity was also to be considered a "fictitous force." This was never Einstein's view though, although it appears to be the view of some physicists today.
And inertia is a kinetic (stored) energy, ..
Inertia and kinetic energy are very different things. First off it is incorrect to think of kinetic energy as being stored anywhere and second it is incorrect to think that because kinetic energy and inertial mass are related that they are the same thing. That would be like saying that velocity and kinetic energy are the same thing and that's obviously wrong.

Gotta go. More later.

Pete

Doc Al
Mentor
I disagree. The centrifugal force does obey Newton's third law.
Give an example of a 3rd law pair with centrifugal force.

Thanks Pete. That makes sense to me.

How about mass moving through space is a form of kinetic "potential"?

Dale
Mentor
I disagree. The centrifugal force does obey Newton's third law.
"I disagree" is insufficient. I just gave a concrete example showing that it did not obey Newton's 3rd law. Please point out the error in my analysis and provide a counter-example.

Dale
Mentor
Einstein was motivated by this idea, i.e. that what Newtonians called "fictitious" forces were really, in Einstein's opinion anyway, "real" forces because they behaved like the "real" force of gravity. However others have interpreted this to mean that since inertial forces are identical in nature to "fictitous" forces that it meant that gravity was also to be considered a "fictitous force." This was never Einstein's view though, although it appears to be the view of some physicists today.
Pete, are you objecting to the word "ficticious"? If so then I am glad to use the term "inertial force" instead of "ficticious force", it is just a label.

Inertial forces cannot be neglected in the non-inertial reference frames where they arise. They accelerate objects, they do work, they cause material stress and strain, etc. When doing an analysis in their frame they are very real in this sense.

However inertial forces have several properties which distinguish them from non-inertial forces (aka real forces):
1) inertial forces are frame dependent while non-inertial forces exist in any frame
2) inertial forces are always proportional to the mass
3) inertial forces cannot be detected by accelerometers while non-inertial forces can
4) inertial forces violate Newton's 3rd law

The centrifugal force is an inertial force and exhibits all 4 of those properties.

PS. Gravity is difficult to categorize. In Newton's approach it has properties 2 and 3, but not 1 and 4. In GR it has all 4 properties. For me, the property 3 is the most important (from an experimental perspective) so that is what I use to draw the line between inertial and non-inertial forces. So I prefer the GR classification.

Give an example of a 3rd law pair with centrifugal force.
I consider all of these to be 3rd law pairs:

While turning, due to slip angle, a car's tires exert an outwards force on the pavement, and the pavement in turn exerts an inwards force onto the tires, which through the tires, wheels and suspension, exert an inwards force on the rest of the car, and the rest of the car's inertia reaction ultimately results in an outwards force on the tires.

A moving object has a force applied to it to cause it to turn. At the point of applicaton of force, the applied force accelerates the object inwards, and the object's inertia reaction results with an equal and opposite outwards reaction force (at the point of application).

A cyclotron generated field results in an inwards force on a moving electron. The electron's inertia reaction results in an outwards force on the cyclotron.

Two objects orbit in a circular path in space. The gravitational force results in an inwards forces on both objects, and the two objects' inertia reactions result in an equal and opposite outwards reaction forces, that maintain their orbits.

Last edited: