Why Is Angular Momentum Not Conserved When a Cylinder Moves on a Stopping Board?

In summary, the conversation is about solving a physics problem involving conservation of momentum and angular momentum. The person has tried solving it by taking the center of the cylinder as the axis, but there is friction between the cylinder and the board which causes a change in angular momentum. They suggest taking moments about the point of contact as an alternative solution.
  • #1
Mark128
4
1
Homework Statement
On the flat surface lays a flat board with mass M, and on the board - a cylinder with mass m and radius r. Initially, board moves with velocity v, and cylinder rotates with such angular velocity, that it's stationary relative to the ground. Because of friciton between the board and surface, the board stops after some time. What is velocity of cylinder after that happens?
Relevant Equations
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cylinder.PNG

I've been trying to solve it mainly through conservation of momentum and angular momentum, appareantly it's not correct. My idea was:
I, Moment of inertia = 0.5*m*r^2
L1, initial angular momentum = I * v/r

After a board stops, the change in it's momentum is M*v, so the impulse of torque on the cylinder will be M*v*r.

So the change in angular momentum is M*v*r.

So L2-0.5*m*r^2 = M*v*r

L2 = 0.5*m*r*v_final

So v_final = v*(0.5*m + M)/(0.5*m)

But as mentioned earlier, it's incorrect and I'm also not entirely sure which part is wrong.
 
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  • #2
You can only take angular momentum about some chosen axis to be conserved in a system if there are no external forces that have a torque about that axis. You appear to be taking the centre of the cylinder as axis, but there is friction (rolling contact) between the cylinder and the board.
What axis could you use to avoid this difficulty?
 
  • #3
haruspex said:
You can only take angular momentum about some chosen axis to be conserved in a system if there are no external forces that have a torque about that axis. You appear to be taking the centre of the cylinder as axis, but there is friction (rolling contact) between the cylinder and the board.
What axis could you use to avoid this difficulty?

Yes, I was taking a center of the cylinder keeping in mind, that there is friction acting on it, and that's why change in angular momentum (L2-L1) is non-zero.

If I choose point of contact as center, the angular momentum is in fact conserved, but I don't know, how this could help.
 
  • #4
Mark128 said:
Yes, I was taking a center of the cylinder keeping in mind, that there is friction acting on it, and that's why change in angular momentum (L2-L1) is non-zero.

If I choose point of contact as center, the angular momentum is in fact conserved, but I don't know, how this could help.
There are two ways you can solve it:
1. Take moments about the cylinder’s centre, but include the torque from friction with the board and write a linear momentum equation also involving the friction. (You will have terms like ##\int F.dt##.)
2. Take moments about a point at the surface of the board. (Better not to think of it as a point fixed to the board or the point of contact over time since in principle that gets you into noninertial frames.) Since angular momentum of the cylinder is conserved about such a point you can get the answer in one equation.
 

Related to Why Is Angular Momentum Not Conserved When a Cylinder Moves on a Stopping Board?

1. What is a "cylinder on a moving board" experiment?

The "cylinder on a moving board" experiment is a classic physics experiment that involves a cylinder placed on a board that is free to move in a horizontal direction. The aim of the experiment is to observe the behavior of the cylinder as the board is moved at different speeds and in different directions.

2. What is the purpose of this experiment?

The purpose of this experiment is to study the effects of friction and inertia on the motion of a cylinder on a moving board. It also helps to illustrate concepts such as Newton's laws of motion and the relationship between force, mass, and acceleration.

3. How is this experiment set up?

The experiment requires a board, a cylinder, and a smooth surface to reduce friction. The board is placed on the smooth surface and the cylinder is placed on top of the board. The board is then moved in a horizontal direction at different speeds and in different directions.

4. What are the variables in this experiment?

The variables in this experiment are the speed and direction of the board's movement, the mass and shape of the cylinder, and the surface on which the experiment is conducted. These variables can be manipulated to observe their effects on the motion of the cylinder.

5. What can be learned from this experiment?

This experiment can help us understand the principles of motion and how different variables affect the behavior of objects. It also demonstrates the importance of friction and inertia in determining the motion of objects. This experiment is also a good way to practice data collection and analysis skills.

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