Posted by **Samantha** on Wednesday, November 19, 2008 at 7:20pm.

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?

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