A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration

angular-acceleration
rest-and-accelerates

#1

A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 4.0 rad/s; 60 radians later, its angular speed is 24 rad/s. Calculate (a) the angular acceleration (rad/s2), (b) the time required to complete the 60 radians, © the time required to reach the 4.0 rad/s angular speed, and (d) the number of radians from rest until the time the disk reaches the 4.0 rad/s angular speed.

Answer:

the average angular speed is … (4.0 rad/s + 24 rad/s) / 2 = 14 rad/s

(b) time = rotation / speed = 60 rad / 14 rad/s = 30/7 s

(a) accel = change in speed / time = (24 rad/s - 4.0 rad/s) / 30/7 s
… = 14/3 rad/s²

© time = speed / accel = 4.0 rad/s / 14/3 rad/s² = 6/7 s

(d) rotation = (average speed) * time = [(0 + 4.0 rad/s) / 2] * 6/7 s
… = 12/7 rad