- #1

- 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
- --

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.