Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 15

15 A bowler throws a bowling ball of radius \( R = 11 \text{ cm} \) along a lane. The ball (Fig. 11-31) slides on the lane with initial speed \( v_{\text{com},0} = 8.5 \text{ m/s} \) and initial angular speed \( \omega_0 = 0 \). The coefficient of kinetic friction between the ball and the lane is 0.21. The kinetic frictional force \( \vec{f}_k \) acting on the ball causes a linear acceleration of the ball while producing a torque that causes an angular acceleration of the ball. When speed \( v_{\text{com}} \) has decreased enough and angular speed \( \omega \) has increased enough, the ball stops sliding and then rolls smoothly. (a) What then is \( v_{\text{com}} \) in terms of \( \omega \)? During the sliding, what are the ball’s (b) linear acceleration and (c) angular acceleration? (d) How long does the ball slide? (e) How far does the ball slide? (f) What is the linear speed of the ball when smooth rolling begins?