일반물리학 1 — Rotation: Problem 31

31 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 \(\alpha_1\) through the first 400 rad and then losing angular speed at the constant rate \(-\alpha_1\) until it is again at rest. The magnitude of the centripetal acceleration of any portion of the disk is not to exceed 400 m/s². (a) What is the least time required for the rotation? (b) What is the corresponding value of \(\alpha_1\)?