Question

A disk is initially spinning at 16 counter-clockwise. After 4 seconds, it is spinning clockwise and a piece of dust located 1 meter from the center of disk is moving at 6 m/s. How many revolutions does the disk make before it stopped spinning?

Answer 1

w_o = initial angular velocity = 16 rad/s

w = final angular velocity = - v/r = - 6/1 = - 6 rad/s

t = time taken = 4 sec

Angular acceleration of disk is given as

= (w - w_o)/t

= (- 6 - 16)/4

= - 5 rad/s²

= angular displacement before stopping

w' = final angular velocity when it comes to a stop = 0 rad/s

Using the equation

w'² = w² + 2

0² = (- 6)² + 2 (- 5)

= 3.6 rad

n = number of revolutions

Number of revolutions are given as

n = /(2)

n = 3.6/(2 x 3.14)

n = 0.573 rev