Question

A basketball is rotating at a constant one revolution per second on its way to the rim. Its diameter is 24.26 cm.

a) What is the total angle the ball rotates through if it is in the air for 1.25 seconds?

b) If started from rest in the players hand and it took 0.15 seconds to impart the rotation to the ball during the shot, what is the average angular acceleration?

Answer 1

here,

the angular speed , w = 1 rev/s = 6.28 rad/s

diameter , d = 24.26 cm = 0.2426 m

a)

for t = 1.25 s

the total angle the ball rotates , theta = w * t

theta = 6.28 * 1.25 rad = 7.85 rad

b)

t1 = 0.15 s

let the angular acceleration be alpha

using first equation of motion

w = 0 + alpha * t1

6.28 = 0 + alpha * 0.15

solving for alpha

alpha = 41.9 rad/s^2

the angular acceleration is 41.9 rad/s^2