Centrifugal Force on a stone tied to a thread

[Cromptu]

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 learned 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?

 

[Doc Al]

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]

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]

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]

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]

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).

 

[Andrew Mason]

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

 

[Cromptu]

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]

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]

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]

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]

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

 

[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.

 

[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?

 

[Andrew Mason]

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]

"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).

 

[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]

"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).

 

[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]

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]

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]

Oh, well then I agree yes it certainly causes confusion. Thankfully it's not a standard term from what I've seen.

 

[D H]

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

My sentiments exactly.

 

[Dale]

All forces are toward the centre, including the force on the person causing holding the other end of the rope.

False. "All net forces" are toward the center in this case, which is not at all the same as "all forces".

I was distinguishing tensions from forces (F=ma).

The F in that equation is the net force.

If the forces on the rope and the the stone were equal and opposite there would be no acceleration, which is not the case.

This is nonsense. A third law pair act on different objects and they are never summed to determine a second law net force or acceleration.

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

You should stick with this objection. Your technical objections are flat out wrong. If you don't like a term then you don't need to use it. If it causes confusion or is redundant or has other semantic problems then explain that. But like it or not the term is well defined and the concept has no technical deficiencies. The only possible objections are semantics and personal preferences.

 

[Andrew Mason]

This is nonsense. A third law pair act on different objects and they are never summed to determine a second law net force or acceleration.

I did not say otherwise. See my response in post #17. My comment was in response to A.T.s statement: "If string and stone are mentioned as separate objects, then there are equal but opposite forces between them in a free body diagram." I was not objecting to that statement. I was just saying it was incomplete. There are other forces on the rope (ie. that you would have to show in a free-body diagram). If there were not, you could not have the (centripetal) acceleration that is observed.

You should stick with this objection. Your technical objections are flat out wrong. If you don't like a term then you don't need to use it. If it causes confusion or is redundant or has other semantic problems then explain that. But like it or not the term is well defined and the concept has no technical deficiencies. The only possible objections are semantics and personal preferences.

I disagree. "Centrifugal" has significant technical deficiencies. There is no possible way that the third law pair to the centripetal force on the stone will ever cause the rope to flee the centre of rotation. You have only to look at the Wikipedia article on "centrifugal reaction force" to see the confusion that surrounds that term.

AM

 

[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." I was not objecting to that statement. I was just saying it was incomplete.

It is complete, as far Newtons 3rd is concerned. Your deflections about accelerations are just conflation of forces and net forces.

"Centrifugal" has significant technical deficiencies. There is no possible way that the third law pair to the centripetal force on the stone will ever cause the rope to flee the centre of rotation.

Irrelevant from the technical standpoint. Newtons Laws don't care about causes. Acceleration is related to net force not just any force. As DaleSpam said, it is just semantics and personal preferences.

 

[A.T.]

So, I ask again, what's the issue?

As far I can say this is the core of the issue:

I was distinguishing tensions from forces (F=ma).

Confusion of "force" and "net force" (as in F=ma). All the other wrong claims follow from that: That there are no outward forces, because there is no outward acceleration. That action & reaction in Newtons 3rd must be actual accelerations. And so on.

 

[Doc Al]

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

 

[A.T.]

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

To me the "reactive"-part is more misleading than the "centrifugal"-part.

 

[technician]

I think someone referred to a free body diagram. It should be the first requirement in discussions of this sort.
I would require my students to produce a free body diagram as part of the explanation of this elementary A level physics, you can tell at a glance whether they understand or not.
Let me offer my diagram.
C is the centripetal force. Can you identify the 3rd law pairings? (hint: they are different colours)

 

[WannabeNewton]

Confusion of "force" and "net force" (as in F=ma). All the other wrong claims follow from that: That there are no outward forces, because there is no outward acceleration. That action & reaction in Newtons 3rd must be actual accelerations. And so on.

Ah ok, thanks for pointing out the issue. Yes as you say it is important to keep a distinction between individual forces and the net force.

 

[Andrew Mason]

I think someone referred to a free body diagram. It should be the first requirement in discussions of this sort.
I would require my students to produce a free body diagram as part of the explanation of this elementary A level physics, you can tell at a glance whether they understand or not.
Let me offer my diagram.
C is the centripetal force. Can you identify the 3rd law pairings? (hint: they are different colours)

It is somewhat arbitrary to speak about third law reaction pairs when what you have is an array of tensions, the existence of each of which depends all the existence of all the others.

We simplify things by treating the person and stone as point masses (located at the respective centres of mass) so we don't have to worry about analysing all the tensions within the person and within the stone. We also assume that the mass of the rope is negligible. If we do that, we can say, quite legitimately I think (although others on this board seem to disagree), that the stone is exerting a force on the person (via the rope) and the person is exerting an equal and opposite force on the stone. These can be considered third law force pairs in our simplified system. Each of those forces is toward the centre of rotation. There is no need to complicate matters by introducing the misleading, and - as far as I can tell - useless, concept of "centrifugal reaction force".

AM

 

[Andrew Mason]

As far I can say this is the core of the issue:Confusion of "force" and "net force" (as in F=ma). All the other wrong claims follow from that: That there are no outward forces, because there is no outward acceleration. That action & reaction in Newtons 3rd must be actual accelerations. And so on.

There is no confusion about net force. I never said that Newton third law pairs must be actual accelerations. A box resting on the Earth's surface undergoes no acceleration but the box and Earth are still exerting equal and opposite forces on each other (a pair of gravitational forces and a pair of mechanical forces).

What I have said (in another thread) is that Newton's third law is really about changes in motion (momentum conservation), not about static forces although I must admit that Newton was not very clear in his writing on this point. If Newton's third law is about changes in motion it becomes a universal law. If it is about equal and opposite tensions it is not universal. A good example of where the latter fails is in electrodynamics: a photon can exert a force on an atom but the atom cannot exert a force on the photon. However, there are always equal and opposite changes in momentum.

AM