Question

Consider a basketball player spinning a ball on the tip of a finger. If a player performs 1.99 J of work to set the ball spinning from rest, at what angular speed ???? 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 m and a mass of 0.624 kg.

Answer 1

Answer:

25.8 rad/s

Explanation:

C = circumference of the hollow sphere = 0.749 m

r = radius of the sphere

Circumference of the hollow sphere is given as

C = 2π r

0.749 = 2 (3.14) r

r = 0.12 m

m = mass of the basketball = 0.624 kg

Moment of inertia of basketball is given as

$I = \left ( \frac{2}{3} \right )mr^{2}$

$I = \left ( \frac{2}{3} \right )(0.624)(0.12)^{2}$

I = 5.99 x 10⁻³ kg-m²

w = angular speed

KE = Kinetic energy of the ball = 1.99 J

Kinetic energy of the ball is given as

KE = (0.5) I w²

1.99 = (0.5) (5.99 x 10⁻³) w²

w = 25.8 rad/s