Ap physics rolling/slipping billiard ball

[Schmoozer3348]

A billiard ball has mass M, radius R and moment of inertia about the center of mass Ic=2/5MR^2. The ball is struck by a cue stick along a horiontal line through the ball's center of mass so that the ball initially slides with a velocity Vo. As the ball moves across the table (which has a coefficient of sliding friction U ), its motion gradually changes from pure translation through slipping to rolling without slipping.

a)Develop an expression for linear velocity v of the center of the ball as a function of time while it is rolling without slipping
b)develop an expression for the angular velocity w of the ball as a function of time while it is rolling without slipping.
c)determine the time at which the ball begins to roll without slipping.
d) when the ball is struck it acquires an angular momentum about a fixed point P on the surface of the table. During the subsequent motion, the angular momentum about P remains constant despite the frictional force. Explain why it is so.


I'm stuck on the first part but am confident i could figure out b,c, and d if i had a little help with a. Is it kinematics V=Vi+at?

 

[Doc Al]

Originally posted by Schmoozer3348

I'm stuck on the first part but am confident i could figure out b,c, and d if i had a little help with a. Is it kinematics V=Vi+at?

Pretend the ball was suspended in mid-air. If it's spinning at a certain angular speed, how fast is its surface moving (linear speed) with respect to the center? Got it? Now if I want to place this spinning ball on the ground so that the surface doesn't slide, how fast had it better be moving?

 

[Doc Al]

This kind of thing should be in the Homework Help forums, but now that we've started...

The purpose of part a is for you to define --mathematically-- the conditions for "rolling without slipping". It's got nothing to do with kinematics (except trivially) since once the ball rolls without slipping, acceleration is zero.

Try this way of thinking. For a rotating ball, what's the speed of surface with respect to the center? Then, of course, the translational speed of the ball is the speed of the center with respect to the ground. Now combine these to find the speed of the ball surface where it touches the ground with respect to the ground. "Rolling without slipping" means that that speed (surface of ball with respect to the ground) is zero.