# Spinning ball dropped on the ground

1. Feb 12, 2009

### vladimir69

1. The problem statement, all variables and given/known data
A solid ball of mass M and radius R is spinning with angular velocity $\omega_0$ about a horizontal axis. It drops vertically onto a surface where the coefficient of kinetic friction with the ball is $\mu_k$. Find an expression for the final angular velocity once it has achieved pure rolling motion. The other part of the question asks for the time taken until its in pure rolling motion. I could solve that part easily enough once I knew the answer to the first part.
2. Relevant equations
$$\tau=I\alpha$$
$$L=I\omega$$
$$RF=i\alpha$$
$$L=RMv$$
3. The attempt at a solution
The answer says
$$\omega=\frac{2}{7}\omega_0$$
I found a way of getting that answer by using
$$I\omega_0=I\omega+RMv=I\omega+MR^2\omega$$
and then solving for omega gives the required result. But I can't understand how using that equation yields the right result, so there must be another way. I dont think you can use conservation of energy for this either.

Thanks,

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