Meadowlark Lemon, captain of the Harlem Globetrotters, starts spinning a basketb

Question

Meadowlark Lemon, captain of the Harlem Globetrotters, starts spinning a basketball on his fingertip. Initially, the ball is given an angular speed of 8.00 rotations per second. However, there is friction between the ball and Meadowlark's finger, so it gradually slows down. In the 5 s period following the inital spin, the basketball undergoes 38.0 complete rotations. Assuming the torque caused by the friction between the ball and the finger is constant, what is the magnitude of the angular acceleration of the ball in rads2?

Explanation / Answer

Given,

initial speed, w0 = 8 rev/s = 50.24 rad/s

Angle, theta = 38 x 2pi = 238.76 rad

time, t = 5 s

let the magnitude of the angular accelration be alpha

using seccond equation of motion

theta = wo t + 0.5 x alpha x t2

238.76 = 50.24 x 5 + 0.5 x alpha x 52

alpha = - 0.995 rad/s2

So, the magnitude of the angular acceleration is 0.995 rad/s2

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