An untrained bowler doesn’t put any spin on the ball – he just throws the ball d

Question

An untrained bowler doesn’t put any spin on the ball – he just throws the ball down the lane. Suppose that the ball (moment of inertia 2mr2) begins its motion moving at 5 speed v, but with 0 = 0. Gradually, friction will make the ball start rotating. If the coefficient of kinetic friction between the ball and the lane is k, how long does it take for the ball to begin rolling without slipping? In order to get credit for these problems, you must include text describing your reasoning. All of these problems are difficult; discuss briefly what the difficulty is with each one, and how you overcame it. All solutions must be well-reasoned and show all steps.

Explanation / Answer

from eqn of motion we know that,

I(ball) = 2/5 mr^2

Torque = frictional force x radius

T = uk m g r

we know that, Torque = I alpha

alpha = torque/I

alpha = uk m g r/(2/5 m r^2) = 5 uk g/2 r

v = v0 + at

but due to friction, a = -uk g

V = v - uk g t

w = alpha t = 5 uk g t/ 2 r

Ball begins to roll when, V = r w

v - uk g t = 5 uk g t /2 r x r = 5 uk g t/ 2

solving for t, t = 2 v/7 uk g

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