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 said:
There is no friction between the pulley and the rope.berkeman said:
So the pulley does not turn, okay. That may not matter if it is just a frictionless turning point for the rope.adjurovich said:
It cannot in this case, but who cares. What is the full problem statement?adjurovich said:
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 said:
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.berkeman said:
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.berkeman said:
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.adjurovich said:
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.adjurovich said:
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.adjurovich said:
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 said:
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?russ_watters said:
All pulley problems state this condition.adjurovich said:
They want you to consider the rotational inertia of the pulley (which implies some tangential force makes it accelerate angularly).adjurovich said:
At the axle (a pulley without peripheral friction is not a pulley).adjurovich said:
Do not confuse rotation with applied moment.adjurovich said:
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 nowjbriggs444 said:
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.adjurovich said:
Thanks for help!jbriggs444 said:
Torque is a measure of the rotational force applied to an object around an axis. In a pulley system, tension in the rope creates torque by exerting a force at a distance from the axis of rotation (the pulley). The torque (τ) can be calculated using the formula τ = r × F, where r is the radius of the pulley and F is the tension in the rope.
The angle of the rope can significantly affect the effective tension that contributes to torque. When the rope is at an angle to the radius of the pulley, only the component of the tension that acts perpendicular to the radius contributes to torque. This means that as the angle changes, the effective force that generates torque also changes, which can alter the overall torque applied to the pulley.
Yes, tension can create torque even if the pulley is stationary. When tension is applied to the rope, it exerts a force on the pulley. If this tension is not balanced by an equal and opposite force, it can create a net torque that can cause the pulley to begin rotating. However, if the system is in equilibrium, the torques will balance out, resulting in no net rotation.
The mass of the object being lifted directly affects the tension in the rope. According to Newton's second law (F = ma), the weight of the object (mass times gravitational acceleration) determines the force exerted on the rope. This increased tension will, in turn, increase the torque applied to the pulley, as torque is dependent on both the tension in the rope and the radius of the pulley.
If the radius of the pulley is increased, the torque generated by the same amount of tension will also increase. This is because torque is the product of the radius and the tension (τ = r × F). Therefore, for a given tension, a larger radius results in a greater torque, making it easier to lift heavier loads or rotate the pulley more efficiently.