How can tension apply torque on a simple pulley?

[adjurovich]

Let’s say we have a pulley with some box attached to it, mass of the box is $m$. We consider rope to be massless and inextensible and pulley to have mass but be frictionless. How can tension apply torque on pulley?

 

[Baluncore]

A rope has two ends, where is the other?
Is the pulley free to rotate on the shaft?

There must be friction between the rope and the pulley, or there can be no torque applied by the rope.

A pulley has a finite radius and the rope passes a number of turns around the pulley. The rope tension must be summed as a torque about the centre of the pulley. If there is no pulley friction, the tension in the rope will be the same at each end. Otherwise, you have a capstan.
https://en.wikipedia.org/wiki/Capstan_equation

 

[berkeman]

pulley to have mass but be frictionless

What part is frictionless? There is no axle friction for the pulley, or there is no friction between the rope and the pulley circumference surface? Do you see why that distinction makes a difference?

 

[adjurovich]

What part is frictionless? There is no axle friction for the pulley, or there is no friction between the rope and the pulley circumference surface? Do you see why that distinction makes a difference?

There is no friction between the pulley and the rope.

 

[berkeman]

There is no friction between the pulley and the rope.

So the pulley does not turn, okay. That may not matter if it is just a frictionless turning point for the rope.

How can tension apply torque on pulley?

It cannot in this case, but who cares. What is the full problem statement?

 

[adjurovich]

So the pulley does not turn, okay. That may not matter if it is just a frictionless turning point for the rope.


It cannot in this case, but who cares. What is the full problem statement?

In high school textbook I’m using (and also the other high school textbooks), it’s said that tension applies torque. Take for an example this diagram I found on the internet:

 

[berkeman]

T is tension in that diagram. If the pulley is frictionless (in either of the ways that I asked you about), then any torque on the pulley is zero and can be neglected in the problem to be solved.

 

[berkeman]

T is tension in that diagram. If the pulley is frictionless (in either of the ways that I asked you about), then any torque on the pulley is zero and can be neglected in the problem to be solved.

Well, full disclosure -- if the friction of the rope on the pulley circumference surface is not zero and the axle friction is zero, but the moment of inertia (MOI) of the pulley is not zero, then there can be some energy invested in accelerating the pulley. But so far it does not sound like that is what you are asking about.

 

[adjurovich]

T is tension in that diagram. If the pulley is frictionless (in either of the ways that I asked you about), then any torque on the pulley is zero and can be neglected in the problem to be solved.

This is what seems logical to me but when dealing with high school problems, I am constantly hitting my head against the wall. Things seem to make no sense to me quite often, like in this example. I don’t know if it’s just me but I feel like the only way to learn this level of physics is just to memorize until you reach college to be able to actually understand it.

I am wondering how can something like this I found in textbook be true?

 

[berkeman]

I don’t know if it’s just me but I feel like the only way to learn this level of physics is just to memorize until you reach college to be able to actually understand it.

No, memorizing is not the best/only strategy. There are some things to memorize, but many more things to understand intuitively in order to be able to solve problems.

I am wondering how can something like this I found in textbook be true?

You still have not posted the whole problem statement so we can try to help you with your misunderstandings. Please post the whole problem statement and show your best efforts to start working on the problem. That's how things work here at PF, and how you should always approach your schoolwork problems. Thank you.

 

[russ_watters]

This is what seems logical to me but when dealing with high school problems, I am constantly hitting my head against the wall. Things seem to make no sense to me quite often, like in this example. I don’t know if it’s just me but I feel like the only way to learn this level of physics is just to memorize until you reach college to be able to actually understand it.

I am wondering how can something like this I found in textbook be true?

The situation described comes close to real life, so maybe you can just try to apply it to real life? In real life, the friction between a pulley and rope is much more than the friction between the pulley and shaft. So the pulley rotates at the same rate as the rope pulls it.

 

[hutchphd]

We consider rope to be massless and inextensible and pulley to have mass but be frictionless.

Usually pulleys have good bearings at the axle and the rope (or belt) rolls without slipping along the groove. We don't know exactly what the book says (and what is surmise on your part ) but I bet they talk about pulleys somewhere. The fact that you have different understanding is regretable for you, so please check and be aware of the "usual"notion of a pulley mentioned above . This is really not hard duty: consider it educational, We can agree that calling a pulley "frictionless" is fraught unless further specified.

 

[adjurovich]

The situation described comes close to real life, so maybe you can just try to apply it to real life? In real life, the friction between a pulley and rope is much more than the friction between the pulley and shaft. So the pulley rotates at the same rate as the rope pulls it.

Yes according to solution there’s no slipping. But friction isn’t mentioned anywhere so it confuses me. In real life, friction between pulley and the rope must result in net torque. But if the pulley and rope were somehow frictionless, wouldn’t the rope just slide even though pulley isn’t massless?

 

[Lnewqban]

We consider rope to be massless and inextensible

All pulley problems state this condition.

... and pulley to have mass

They want you to consider the rotational inertia of the pulley (which implies some tangential force makes it accelerate angularly).

... but be frictionless.

At the axle (a pulley without peripheral friction is not a pulley).

How can tension apply torque on pulley?

Do not confuse rotation with applied moment.
We can only talk about applied moment when another moment resists it.

 

[adjurovich]

 

[jbriggs444]

The key words in the problem posted above are "frictionless axis" and "does not slip". As @Lnewqban suspected, the pulley is frictionless at its axle. But not where the rope rides over it.

 

[adjurovich]

The key words in the problem posted above are "frictionless axis" and "does not slip". As @Lnewqban suspected, the pulley is frictionless at its axle. But not where the rope rides over it.

This is quite intuitive to be honest, but why is friction not taken into account in equations then? That’s exactly what I’m trying to figure out right now

 

[jbriggs444]

This is quite intuitive to be honest, but why is friction not taken into account in equations then? That’s exactly what I’m trying to figure out right now

It is static friction without slipping. That means that the force of friction will be whatever it has to be so that the rope does not slip. That is a constraint. A constraint that allows us to write down an equation relating the acceleration of the pulley to the acceleration of the falling weight.

It is a massless rope. That means that Newton's second law tells us that the force from tension in one direction must match the force from friction in the other. There is no need to even mention the force of friction since it will obviously be equal to the force from tension. One can plug the tension directly into the equations and solve.

 

[adjurovich]

It is static friction without slipping. That means that the force of friction will be whatever it has to be so that the rope does not slip. That is a constraint. A constraint that allows us to write down an equation relating the acceleration of the pulley to the acceleration of the falling weight.

It is a massless rope. That means that Newton's second law tells us that the force from tension in one direction must match the force from friction in the other. There is no need to even mention the force of friction since it will obviously be equal to the force from tension. One can plug the tension directly into the equations and solve.

Thanks for help!