A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 7 rev/s. 55 revolutions later, its angular speed is 21 rev/s.

Question

A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 7 rev/s. 55 revolutions later, its angular speed is 21 rev/s. 
(a) Calculate the angular acceleration. 
(b) Calculate the time required to complete the 55 revolutions mentioned. 
(c) Calculate the time required to attain the 7 rev/s angular speed. 
(d) Calculate the number of revolutions from rest until the time the disk attained the 7 rev/s angular speed.

(a) Divide the change in angular rotation rate by the time required for the acceleration to occur. 
alpha = (14 rev/s)*(2 pi rad/rev)/Time 
Since 55 revolutions were required and the average rotation rate was 14 rev/s, the time required was 55/14 = 3.93 s. 
alpha = 22.4 rad/s^2 
(b) already determined above 
(c) It will take 1/2 as long to go from 0 to 7 rev/s as it takes to go from 7 ro 21 rev/s 
(d) In radians, the answer is 
(angle) = (1/2) alpha t^2, where t is the time you get in part (c). Divide by 2 pi for he number of revolutions