A disk, with a radius of 0.25 m, is to be rotated like a merry-go-round through 800 rad, starting from rest, gaining angular speed at the constant rate through the first 400 rad and then losing angular speed at the constant rate - until it is again at rest. The magnitude of the centripetal acceleration of any portion of the disk is not to exceed 100 m/s2. (a) What is the least time required for the rotation

a)

Explanation:

a) Let consider that disk accelerates and decelerates at constant rate. The expression for angular acceleration and deceleration are, respectively:

Acceleration

Deceleration

Since angular acceleration and deceleration have same magnitude but opposite sign. Let is find the maximum allowed angular speed from maximum allowed centripetal acceleration:

Maximum magnitude of acceleration/deceleration is:

The least time require for rotation is:

15.3 cos 65 degrees trig