What is the Angular Momentum of a System with Pulleys and Blocks?

In summary, the student is trying to solve a problem involving the angular momentum of a system, but is having difficulty with the calculation. They are helped by posting the image of the problem.
  • #1
postfan
259
0

Homework Statement



A block of mass m1 is attached to a block of mass m2 by an ideal rope passing over a pulley of mass M and radius R as shown. The pulley is assumed to be a uniform disc rotating freely about an axis passing through its center of mass (cm in the figure). There is no friction between block 2 and the surface. Assume that the pulley rotates counterclockwise as shown with an angular speed ω and that the rope does not slip relative to the pulley, and that the blocks move accordingly and do not topple or rotate.

Consider the system to be formed by the pulley, block 1, block 2 and the rope.

Calculate the magnitude of the angular momentum of the system about the center of mass of the pulley. Express your answer in terms of some or all of the variables m1, m2, M, R, ω and g. Type omega for ω


Homework Equations





The Attempt at a Solution



Used formula L=Iw I=.25MR^2 then multiply by w so L=1/4*(M*R^2)*w. What am I doing wrong?
 

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  • #2
Is there any way you can post the figure?

Note that they are asking for the angular momentum of the system, not just the pulley.

I don't think the 1/4 factor for the moment of inertia of the pulley is correct.
 
  • #3
I attached the image. If so don't we need to know the distances between the blocks and the pulley?
 
  • #4
You don't need those distances. Treat each block as a point particle located at the center of each block. Think about how to calculate the angular momentum of each block relative to the center of the pulley. You can use the definition of the angular momentum of a point particle relative to an origin.
 
  • #5
The formula is mr^2, right, so you still need the distances?
 
  • #6
postfan said:
The formula is mr^2, right, so you still need the distances?

That's not the formula for angular momentum. That's the moment of inertia of a single particle moving in a circle of radius r. The blocks are moving along straight lines. You should have covered the formula for the angular momentum of a point particle. It was probably at the very beginning of your study of angular momentum.
 
  • #7
The 2 formula I know are m*r*v and I*w, we don't know both r and w, so how do we do it?
 
  • #8
OK, the m*r*v formula can be used for a particle moving along a straight line with speed v. r is then the perpendicular distance from the origin to the straight line.

The speed v of one of the blocks is related to the angular speed of ω of the pulley. So in the formula m*r*v you can express v in terms of ω.
 

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  • #9
Ok so the formula is m*r*(w*r)=m*r^2*w, right?
 
  • #10
Yes. That's it.
 
  • #11
OK so the total angular momentum for the system is (M+m1+m2)*r^2*w, right?
 
  • #12
postfan said:
OK so the total angular momentum for the system is (M+m1+m2)*r^2*w, right?

No, the part that deals with the pulley is not correct. You had the right approach for the pulley in your first post, but you didn't quite have the right expression for the moment of inertia, I.
 
  • #13
Ok, so the angular momentum is M*r^2*w, right?
 
  • #14
No, look at a table of moments of inertia.
 

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  • #15
i met this problem once... but still cannot figure out the final formula of the angular momentum!
 
  • #16
i think the final formula for the angular momentum is (m1+m2)*v*R+M*omega*R^2, right?
 
  • #17
OK, so according to the diagram the answer is .5*M*r^2*w, right?
 
  • #18
postfan said:
OK, so according to the diagram the answer is .5*M*r^2*w, right?

Yes, for the pulley.
 
  • #19
Do we need to add anything for the blocks?
 
  • #20
postfan said:
Do we need to add anything for the blocks?

Yes. See post #9 for the angular momentum of each block.
 
  • #21
OK, I got it. Thanks for your help!
 

1. What is angular momentum?

Angular momentum is a measure of the rotational motion of an object. It is calculated by multiplying the object's moment of inertia by its angular velocity. In simpler terms, it is the tendency of an object to continue rotating at a constant rate.

2. How is angular momentum related to pulleys?

In a pulley system, angular momentum is conserved. This means that the total angular momentum before and after the pulley system remains the same. The angular momentum of the pulley and the objects attached to it may change, but the total remains constant.

3. Can angular momentum be increased or decreased in a pulley system?

Yes, angular momentum can be increased or decreased in a pulley system. This can be achieved by changing the moment of inertia of the rotating object or by changing the angular velocity of the object.

4. How does the number of pulleys affect the angular momentum in a system?

The number of pulleys in a system does not affect the total angular momentum, as long as the direction and magnitude of the forces remain the same. However, using more pulleys can make it easier to lift heavier objects by distributing the force over multiple ropes or belts.

5. Can pulleys change the direction of angular momentum?

Yes, pulleys can change the direction of angular momentum. In a single pulley system, the direction of the angular momentum will be reversed. In a multiple pulley system, the direction may change multiple times depending on the arrangement of the pulleys.

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