Question: A man of mass m stands on a flat horizontal disc (mass M, radius R) near its edge. The disc is free to rotate without friction about its central axis. At a certain instant the man begins to walk around the disc with a constant velocity v with respect to the ground. 2. A man of of mass m stands on a flat horizontal disk (mass M, radius r) near its edge. The disk is free to rotate without friction about its central axis. At a certain instant the man begins to walk around the disk with a constant velocity v with respect to the ground. The inertia of a disk around its center of mass Icm = Mr2 v
A. If his feet do not slip on the disk, how long will it take him to return to the same point?
B. Once he gets to the starting point, he stops walking. How long after he stops walking will it take the disk to stop turning? Explain.
C. The disk an the man are both stationary. If he walks in toward the center of the disk, what with a velocity u, how fast will the disk turn? Explain.
D. The man again stands at the edge of the disk at rest. A ball of mass m/4 is thrown to him with velocity v tangent to the rim of the disk. He catches the ball. How fast does the disk turn?
(a) If his feet do not slip on the disc, how long will it take him to return to the same point on the disc? Express your answer as a function of R, M, m and v.
(b) Once he gets to the starting point, he stops walking. How long after he stops walking will it take the disc to stop turning? Explain.
(c) The disc and the man are both stationary. If he walks in towards the centre of the disc, with a velocity u, how fast will the disc turn? Explain.
(d) The man again stands at the edge of the disc at rest. A ball of mass m/4 is thrown to him with velocity v tangent to the rim of the disc. He catches the ball. How fast does the disc turn? Express your answer as a function of R, M, m and v.