C Exercise 8.72 « previous | 10 of 13 | ned Part A A billiard ball at rest is st

Question

C Exercise 8.72 « previous | 10 of 13 | ned Part A A billiard ball at rest is struck (bold arrow in the figure (Figure 1) ) by a cue with an average force of 5.40 N lasting for 0.060 s. The cue contacts the ball's surface so that the lever arm is half the radius of the ball, as shown. if the cue ball has a mass of 200 g and a radius of 2.50 cm, determine the angular speed of the ball immediately after the blow. (Neglect friction.) Express your answer using two significant figures rad/s Submit My Answers Give Up Provide Feedback Continue Figure 1 or 1 1.25 cm cation

Explanation / Answer

The torque is T = F*r = 5.40 N * 0.0125m = 0.0675 Nm

The angular momentum imparted to the ball is

p = I*w = T*dt = 0.0675 Nm * 0.06 s = 0.00405 kg.m^2/s

The moment of inertia of a solid sphere, I = 2m*r^2 / 5 = (2*0.2*0.025^2) / 5 = 5*10^-5 kg.m^2

So the angular speed, w = p / I = 0.00405/ 5*10^-5 = 81 rad/s

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