# Centrifugal Force on a stone tied to a thread

## Main Question or Discussion Point

I am not sure I get the concept of centrifugal force..
If we have a stone tied to a thread and we just spin it in a circle, and while we are spinning it in a circle, the thread breaks and the stone flies off tangentially.
If we watch this motion from an inertial frame, which force will be responsible for making the stone fly of tangentially? Since, when seen from an inertial frame, there is no centrifugal force..

Another case could be :
An object is placed on a frictionless disk and the disk is rotated about its axis with some velocity. When we see the motion of the object from an inertial frame, we will see that stone first slides to the end of the disk and then flies off tangentially ( right? since there is no friction )
Again, which force will be held responsible for this motion? Could it be centrifugal force? I've learnt that centrifugal force is a pseudo force used to validate Newton's equations when we see the motion of an object from a non- inertial frame.
So which force is responsible for this tangential motion?

Related Classical Physics News on Phys.org
Doc Al
Mentor
I am not sure I get the concept of centrifugal force..
If we have a stone tied to a thread and we just spin it in a circle, and while we are spinning it in a circle, the thread breaks and the stone flies off tangentially.
If we watch this motion from an inertial frame, which force will be responsible for making the stone fly of tangentially? Since, when seen from an inertial frame, there is no centrifugal force..
Forces are needed to change the velocity of an object. (That's why you need a centripetal force to keep something moving in a circle.) No force is needed to make something fly off tangentially--it's just inertia in action, Newton's 1st law.

Looked at from an inertial frame there is no need for any centrifugal pseudo force when something moves in a circle.

rcgldr
Homework Helper
So which force is responsible for this tangential motion?
Tangental motion implies a straight line, so no force is required (at least no lateral force) for straight line motion.

As far as the terminology, the string exerts a centripetal force on the rock, and the other part of the newton third law pair is: the rock exerts a reactive outwards force on the string as a reaction to the centripetal acceleration, sometimes called a reactive centrifugal force, which is a real force in a inertial frame. Wiki article:

http://en.wikipedia.org/wiki/Reactive_centrifugal_force

Andrew Mason
Homework Helper
Tangental motion implies a straight line, so no force is required (at least no lateral force) for straight line motion.

As far as the terminology, the string exerts a centripetal force on the rock, and the other part of the newton third law pair is: the rock exerts a reactive outwards force on the string as a reaction to the centripetal acceleration, sometimes called a reactive centrifugal force, which is a real force in a inertial frame. Wiki article:

http://en.wikipedia.org/wiki/Reactive_centrifugal_force
Cromptu: Doc Al is right. There is no centrifugal force acting on the stone. There is no force that accelerates the rope outward either. All forces are toward the centre, including the force on the person causing holding the other end of the rope.

In order to swing that rock you have to lean in the opposite direction - outward from the actual centre of rotation. Both you and the rock rotate about the centre of rotation. Everything accelerates toward the centre. Nothing accelerates away from the centre.

tiny-tim
Homework Helper
An object is placed on a frictionless disk and the disk is rotated about its axis with some velocity. When we see the motion of the object from an inertial frame, we will see that stone first slides to the end of the disk…
No, if it's frictionless, the object will stay where it is. rcgldr
Homework Helper
There is no force that accelerates the rope outward either. All forces are toward the centre, including the force on the person causing holding the other end of the rope.
There are no outwards accelerations, but the rock exerts an outwards reactive force on the string (the outwards reactive force is in response to centripetal acceleration of the rock by the string).

Last edited:
Andrew Mason
Homework Helper
There are no outwards accelerations, but the rock exerts an outwards reactive force on the string (the outwards reactive force is in response to centripetal acceleration of the rock by the string).
There are certainly tensions in the string as there are throughout the stone and the person at the other end of the rope. The tensions are not balanced, however, as there is a net acceleration of every part toward the centre.

AM

Thanks a whole lot! I've finally got it! :D

A.T.
All forces are toward the centre,
Nope. The force by the stone on the string points outwards.

acceleration
Irrelevant, as long you talk about forces in general, not specifically net forces.

Andrew Mason
Homework Helper
Nope. The force by the stone on the string points outwards.
And there are forces on atoms in the stone going sideways, up and down etc. But they don't accelerate anything. We don't care about those forces because they don't do anything. The net forces on all parts of the rope and stone and person are toward the centre of rotation.

Irrelevant, as long you talk about forces in general, not specifically net forces.
I was distinguishing tensions from forces (F=ma). The tension differences on each atom = F = ma. This is what gives each atom its acceleration toward the centre.

AM

A.T.
We don't care about those forces
It's not for you to decide about which forces someone cares. If string and stone are mentioned as separate objects, then there are equal but opposite forces between them in a free body diagram.

The net forces on all parts of the rope and stone and person are toward the centre of rotation.
If you mean 'net forces' then write 'net forces'. Using the more general term 'force' is wrong here.

Andrew Mason
Homework Helper
It's not for you to decide about which forces someone cares. If string and stone are mentioned as separate objects, then there are equal but opposite forces between them in a free body diagram.
If the forces on the rope and the the stone were equal and opposite there would be no acceleration, which is not the case. There are other forces on the rope. You might care about the just the forces of the connecting molecules of the rope and stone. But a student interested in the physics of rotating systems is trying to understand the (net) forces that cause centripetal acceleration. That is why often these kinds of problems treat the rope as "massless": because we care only about the forces between the objects at the ends of the rope.

If you mean 'net forces' then write 'net forces'. Using the more general term 'force' is wrong here.
In the case of bodies, A and B, tethered by a rope of negligible mass and rotating about their centre of mass, we can say that the force of A on B is equal and opposite to the force of B on A and that both forces are directed toward the centre of rotation. There is nothing incorrect about that.

It is true that the tensions within A result in the surface of A pulling on the molecules at one end of the rope and the resulting chain of various tensions between molecules of the rope causes the molecules on the other end of the rope to exert tensile forces on the molecules on the surface of B and through tensile forces throughout B to accelerate all the molecules of B.

It is just easier, and much clearer to the poor student, to say that A and B exert centripetal forces on each other via the rope.

AM

Doc Al
Mentor
If the forces on the rope and the the stone were equal and opposite there would be no acceleration, which is not the case.
Are you saying that the force that the stone exerts on the rope is not equal and opposite to the force that the rope exerts on the stone? (In direct violation of Newton's 3rd law.)

Andrew Mason
Homework Helper
Are you saying that the force that the stone exerts on the rope is not equal and opposite to the force that the rope exerts on the stone? (In direct violation of Newton's 3rd law.)
I am saying that it is correct to say, in my example, that A exerts a force on B by means of the rope, and B exerts an equal and opposite force on A and both forces are directed toward the centre of rotation. If you want to examine the forces between the stone and rope you have to look at what the rope is connected to. If it is connected to nothing, there is no force on the rope and the rope exerts no force on the stone. If it is connected to something, the force on the rope and the rope on the stone depends on what is at the other end of the rope.

In my view, we should not confuse students by introducing a useless and misleading concept of a "real" centrifugal force. This is not a concept taught in many physics texts. When it has been mentioned in a text (eg.Delo E. Mook & Thomas Vargish (1987). Inside relativity) it is wrong (the statement that the earth exerts a centrifugal reaction force on the sun). Even the Wikipedia page (http://en.wikipedia.org/wiki/Reactive_centrifugal_force ) is wrong (eg. centrifugal clutch is an example of the pseudo centrifugal force as it is the inertia of the rotating parts of the clutch that cause the clutch to engage, not an outward accelerating force). Are you aware of a reputable text that even mentions it?

AM

Last edited:
A.T.
If string and stone are mentioned as separate objects, then there are equal but opposite forces between them in a free body diagram.
If the forces on the rope and the the stone were equal and opposite there would be no acceleration
Nonsense. The equal but opposite forces don't cancel, because they act on two different objects: inwards force acts on the stone, outwards force acts on the rope. You have a classic freshman misconception about the 3rd Law, often explained with the horse and cart:
http://www.lhup.edu/~dsimanek/physics/horsecart.htm

...introducing a useless and misleading concept "real" centrifugal force.
Nobody is introducing a new concept here. It is just consequent application of Newtons 3rd Law.

Last edited:
A.T.
Are you saying that the force that the stone exerts on the rope is not equal and opposite to the force that the rope exerts on the stone? (In direct violation of Newton's 3rd law.)
I am saying that it is correct to say, in my example, that A exerts a force on B by means of the rope, and B exerts an equal and opposite force on A and both forces are directed toward the centre of rotation. If you want to examine the forces between the stone and rope you have to look at what the rope is connected to. If it is connected to nothing, there is no force on the rope and the rope exerts no force on the stone. If it is connected to something, the force on the rope and the rope on the stone depends on what is at the other end of the rope.
Doc Al asked you about the 3rd Law force pair between rope and stone. Why do you obfuscate instead of answering his question?

Last edited:
Andrew Mason
Homework Helper
Nonsense. The equal but opposite forces don't cancel, because they act on two different objects: inwards force acts on the stone, outwards force acts on the rope. You have a classic freshman misconception about the 3rd Law, often explained with the horse and cart:
http://www.lhup.edu/~dsimanek/physics/horsecart.htm
You have to read what I said. I said "If the forces on the rope and the stone were equal and opposite there would be no acceleration, which is not the case. There are other forces on the rope.". I am referring to all the forces on the stone and on the rope.

Nobody is introducing a new concept here. It is just consequent application of Newtons 3rd Law.
Ok. But calling it centrifugal suggests it is a force that causes a fleeing from the centre, which is not true. And it makes it difficult to distinguish it from the fictitious centrifugal force, as the examples in Wikipedia and in the text that I quoted demonstrate.

AM

rcgldr
Homework Helper
"If the forces on the rope and the stone were equal and opposite there would be no acceleration, which is not the case. There are other forces on the rope.". I am referring to all the forces on the stone and on the rope.
The forces between the rope and the stone are equal and opposing, a Newton third law pair, but the force the stone exerts on the rope is an (outwards) reaction force to (inwards) acceleration, so it's not a "net" force, but it is a real force (othewise a massless rope would not be under tension).

Last edited:
A.T.
I said "If the forces on the rope and the stone were equal and opposite there would be no acceleration, which is not the case. There are other forces on the rope.". I am referring to all the forces on the stone and on the rope.
If you mean 'net forces' then write 'net forces'. But even when corrected, it is still irrelevant - Newtons 3rd applies in general to individual force interactions, not net forces.

Ok. But calling it centrifugal suggests it is a force that causes a fleeing from the centre, which is not true. And it makes it difficult to distinguish it from the fictitious centrifugal force, as the examples in Wikipedia and in the text that I quoted demonstrate.
The confusion comes from your misguided causation/acceleration reasoning. Newtons Laws don't care about causes. Acceleration is related to net force not just any force.

rcgldr
Homework Helper
"If the forces on the rope and the stone were equal and opposite there would be no acceleration.
Only if those forces act on the same object. In this case, the equal and opposing forces are applied to different objects, the rope exerts an inwards force on the stone, and the stone exerts an outwards force on the rope. The net force on the stone is inwards from the rope (if there's gravity, and the motion is circular at constant speed, the upwards component of tension opposes the downwards force from gravity, so the net force on the stone is still inwards).

Last edited:
WannabeNewton
I don't get what the issue is here? The rope exerts an inward radial force on the stone and the stone exerts an equal and opposite (i.e. radially outward) force on the rope. It is standard to call the inward radial force on the stone from the rope the centripetal force and some sources will call the outward radial force on the rope from the stone as a reactive centrifugal force, not to be confused with the inertial centrifugal force that arises in rotating frames. So, I ask again, what's the issue?

AlephZero
Homework Helper
I don't get what the issue is here?
I suggest some people here stop trying to argue by shouting, and try drawing free body diagrams (including the acceleration!) instead.

If you make this much of a meal of the simplest possible case, circular motion of rigid bodies at constant angular velocity, God help you if you ever try to understand the general motion of flexible bodies!.

If I ever get to be world dictator, my first act will be to execute everybody who has ever used terms like "reactive centrifugal force" as if they actually meant something Andrew Mason
Homework Helper
I don't get what the issue is here? The rope exerts an inward radial force on the stone and the stone exerts an equal and opposite (i.e. radially outward) force on the rope. It is standard to call the inward radial force on the stone from the rope the centripetal force and some sources will call the outward radial force on the rope from the stone as a reactive centrifugal force, not to be confused with the inertial centrifugal force that arises in rotating frames. So, I ask again, what's the issue?
There is really no issue other than choosing to call the third law pair to the centripetal force on the stone "centrifugal".

Centrifugal means fleeing the centre (of rotation). There is no way that the third law pair to the centripetal force on the stone can possibly cause any part of the rope to flee the centre of rotation.

I suggest that "centrifugal" should not be used to describe the 3rd law pair to the force on the stone. In my view, it simply adds confusion and makes it even more difficult for students to understand that centrifugal "forces" (ie. those that cause objects to flee the centre of rotation) are really just inertial effects and not real forces.

AM

WannabeNewton
If I ever get to be world dictator, my first act will be to execute everybody who has ever used terms like "reactive centrifugal force" as if they actually meant something 