A cue ball (a uniform solid sphere of mass m and radius R) is at rest on a level pool table. The ball is positioned at x = 0. A pool cue is used to give the ball a sharp horizontal hit at its midpoint. This results in an initial translational velocity in the +X-direction. The coefficient of kinetic friction between the table and the cue ball is μ k. As the ball slides along the table, it begins to rotate. Eventually, its angular velocity increases to the point where the ball rolls without slipping. In terms of m, R,μk, vo and acceleration of gravity g. Calculate:
a. The translational acceleration of the cue ball while it is sliding.
b. The angular acceleration of the cue ball while it is sliding.
c. The translational and rotational velocities of the ene hall.
d. Determine the torque on the cue ball relative to its center of mass in terms of parameters of the ball and the magnitudes of forces. Express you answer in terms of some or all of the variables m, R, N, fk, and w. Enter positive value if the torque is counterclockwise and negative value if the torques is clockwise.