(a) What is the angular speed of the ball when its motion becomes a pure rolling

Question

(a) What is the angular speed of the ball when its motion becomes a pure rolling motion?

(b) How far down the bowling lane does the ball travel before this happens?

A bowling ball of mass M and radius R is released onto the surface of a bowling lane with a forward velocity center of mass translational speed Vi and a backspin rotation, angular speed Wi. (A backspin means that the rotation is against the direction of motion.) There is a coefficient of kinetic friction of Muk between the ball and the surface. (a) What is the angular speed of the ball when its motion becomes a pure rolling motion? (b) How far down the bowling lane does the ball travel before this happens?

Explanation / Answer

condition for a body to Roll With out slipping is V = RW

here angular speed of the Ball = W = V/R

Wi = Vi/R

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Apply the kinematic equation V^2 = 2aS

S = Vi^2 R^2/(2* a)

S = R^2 Vi^2/(2g)

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