Question

Consider a basketball player spinning a ball on the tip of a finger. If a player performs 1.99 J1.99 J of work to set the ball spinning from rest, at what angular speed ωω will the ball rotate? Model a basketball as a thin-walled hollow sphere. For a men's basketball, the ball has a circumference of 0.749 m0.749 m and a mass of 0.624 kg0.624 kg.

Answer 1

Mass of the basketball = M = 0.624 kg

Circumference of the basketball = C = 0.749 m

Radius of the basketball = R

C = 2R

0.749 = 2R

R = 0.1192 m

The basketball is modeled as a thin walled hollow sphere.

Moment of inertia of the basketball = I

I = 2MR²/3

I = 2(0.624)(0.1192)²/3

I = 5.91 x 10^-3 kg.m²

Work done by the player on the ball = W = 1.99 J

Angular speed of the ball =

The work done by the player is equal to the kinetic energy gained by the ball and since the ball is initially at rest,

W = I²/2

1.99 = (5.91x10^-3)²/2

= 25.95 rad/s

Angular speed at which the ball rotates = 25.95 rad/s