2. You have a horizontal, disc-shaped platform that rotates around its center.

Its mass is M and radius is R. There is no friction at the axis of rotation. On the platform,

at radius r = R/2, there is a kid with mass m = M/40. They both are initially at rest.

(a) The kid steps forward in such a fashion that her r remains constant, propelled by a force

F due to the friction between the platform and her shoes. As she moves, what is the

ratio of the angular acceleration of the kid to the angular acceleration of the platform?

(b) The kid keeps moving in a manner such that her r is constant. What is the ratio of the

angular velocity of the kid to the angular velocity of the platform at any instant?

(c) What is the ratio of the total angle covered by the kid since she started moving to the

angle rotated through by the platform?