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I've been struggling with an AP physics free resposne problem. I have what I hope to be the right answer, but I'm not sure.

Heres the question:

A billiard ball has mass M, radius R, and moment of inertia about the center of mass Ic = 2/5 * M * R^2

The ball is struck by a cue stick along a horizontal line through the ball's center of mass so that hte ball initially slides with a velocity v0. As the ball moves across the rough billard table (coefficient of sliding friction u), its motion gradually changes from pure translation through rolling with slipping to rolling without slipping.

a) develop an expression for hte linear velocity v of the center of the ball as a function of time while it is rolling with slipping.

What I got for this part was v = v0 - u * g * t

What I don't know is if the rotation of the ball needs to be factored into the acceleration. If so, please advice.

b) Develop an expression for the angular velocity w of the ball as a function of time while it is rolling with slipping.

I got w = (5*g*u*t)/(2R)

This part I am more sure about... However, if that's the answer, isn't the limit as t goes to infinity infinity, which clearly cannot be? Help me out, please :)

c) determine the time at which the ball begins to roll without slipping.

v=wr

v0 - (u*g*t) = (5*g*u*t)/(2)

solve for t: t = (2*v0)/(7*g*u)

d) when the ball is struck it acquires an angular momentum about the fixed point P on the surface of the table. During the subsequent motion the angular momentum about point P remains constant despite the friction. Explain why this is so.

I'm not so sure about this, but I was thinking because the point is on the table, and the ball is on the table, as the ball loses momentum it loses it to the table, which makes the angular momentum about point P constant.

No more for now guys... Thanks a lot, and any help on any of it is appreciated (assuming what you say is correct, as I'm sure it will be :tongue2:) I am kind of in a rush with this, so get back to me asap

Thanks again,

UnSaniTiZ

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# Homework Help: Rotational motion - billiard ball problem

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