# Angular momentum and pulleys

1. Nov 13, 2013

### fogvajarash

1. The problem statement, all variables and given/known data
In the graph shown in the picture, an expression for the acceleration of the pulleys is obtained.

2. Relevant equations

3. The attempt at a solution
The thing i don't understand is, how do we find the angular momentum for the system? In class, I was told that the angular momentum for the system was:

Ltot = MvR + m1vR + m2vR

However, why do we pick the same velocities for the objects? (aren't they accelerating, and thus having different velocities?). As well, why do we choose the radius of the pulley for mass 1 and mass 2 to be that way? (isn't angular momentum calculated for objects in linear motion as the distance from the origin, which in this case is the axle of the pulley?).

Thank you very much.

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2. Nov 13, 2013

### Mentz114

Non-spinning objects travelling in straight lines have no angular momentum (AM). AM is the rotational equivalent of momentum, p = m v, so AM = I ω where I is the moment of inertia and ω is the angular speed ( radians / sec ). I think the only AM in the setup here is in the pulley wheel.

The weights have the same speed because the cord is inelastic.

3. Nov 14, 2013

### fogvajarash

What does it mean by inelastic? So i suppose it's given in the problem? (What i thought was that the accelerations were the same). Moreover, i'm not sure on the angular momentum part. Can someone shed some light on this?

4. Nov 14, 2013

### haruspex

This is not correct. Angular momentum depends on the reference point. An object moving in a straight line also has angular momentum about any reference point not in its line of travel. It's the product of the linear momentum and the orthogonal displacement. In this case, that distance is the radius of the wheel.

5. Nov 15, 2013

### Mentz114

I'm sorry I misled the OP. I'm sufficiently embarassed to withdraw from homework helping for a while, so huruspex won't have to check and correct my attempts.

6. Nov 15, 2013

### fogvajarash

I have been revising this amd came to the conclusion that it's the radius as we are looking for rFsin0 (0 is the angle between r and F) so this is simply R. However, why are the velocities the same? In pulleys, wasn't acceleration the only constrained variable? (Or are we looking at an instant of time?)

7. Nov 15, 2013

### haruspex

If two objects start from rest at the same time and have the same accelerations at all times then they will have the same velocities at all times (and will have the same displacements at all times).