Find the Answer to the Ball's Velocity Puzzle

[kamiltartar]

please help me!

I will be so happy if someone gives the answer to this question in a while.
A ping pong ball of radius R and mass M is started with an initial speed Vo and a backward initial angular velocity of wo.The coefficient of kinetic friction between the ball and the table is µk.What should wo be(in terms of R,M,Vo,µk) so that the ball comes back with the same velocity, i.e. the velocity -Vo when rolling without slipping starts?

 

[Meir Achuz]

I get w_o>4 Vo/R.

 

[Meir Achuz]

The time to get back to the original spot is T=2Vo/g*mu.
The angular acceleration of the ball is alpha=(3/2)g*mu/R.
This comes from R*g*mu=I*alpha, using the I for a hollow sphere.
Thus w=w_o-(3/2)g*mu*t/R=w_o-3 Vo/R.
and w must be greater than Vo/R.