A circular disk, with a diameter of 0.500 m, is to be rotated through 160 rev, starting from rest, gaining angular speed at the constant rate a, through the first 50.0 rev. Then it continues to rotate at constant angular speed for several rotations and eventually then losing angular speed at the constant rate -5.30 rad/s' until it is again at rest. The magnitude of the centripetal acceleration of the rim of the disk is not to exceed 500 m/s. (a) How many revolutions the disk rotates when its rotating at constant angular speed? (b) What is the least time required for the disk to rotate through 160 rev? (c) What is the magnitude of the tangential acceleration of the rim of the disk as it accelerates towards the maximum angular speed