Question

A uniform, spherical bowling ball of mass m and radius R is projected horizontally along the floor at an initial velocity v0 = 6.00 m/s. The ball is not rotating initially, so ω0 = 0. It picks up rotation due to (kinetic) friction as it initially slips along the floor. The coeffcient of
kinetic friction between the ball and the floor is µk . After a time ts , the ball stops slipping and
makes a transition to rolling without slipping at angular speed ωs and translational velocity vs .
Thereafter, it rolls without slipping at constant velocity.

(b) Find an equation for the linear acceleration a of the ball during this time. The acceleration
should be negative, since the ball is slowing down.
(c) Find an equation for the angular acceleration α of the ball while it is slipping. It will be
simpler if you use the sign convention that clockwise rotations are positive, so α > 0.
(d) What constraint on ω and v must take effect at time t = ts , the moment when the ball
stops slipping and begins rolling without slipping?

Answer 1

b) Energy is not conserved do to friction. So you know initial veloicty, and final velocity.
linearacceleartion=(finalveloicyt-initialvelocity)/time
= (vs-vo)/ts

c) alpha= acceleration above/ radius

d) v=w*r at ts