Abilliard ball has mass m, radius r, and moment of inertia about the center of mass i=2mr2/5. the ball is struck by a cue stick along a horizontal line through the ball's center of mass so that the ball initially slides with velocity v0 as shown above. (there's an accompanying diagram. it just shows a cue stick hitting a ball with radius r, not much to see there.) as the ball moves across the rough billiard table (coefficient of sliding friction î¼k), its motion gradually changes from pure translation through rolling with slipping to rolling without slipping.

a. develop an expression for the linear velocity v of the center of the ball as a function of time while it is rolling with slipping.
b. develop an expression for the angular velocity ï of the ball as a function of time while it is rolling with 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 the fixed point p on the surface of the table. during the subsequent motion the angular momentum about point p remains constant despite the frictional force. explain why this is so.