The Drum of Discomfort is an amusement park ride which consists of a large vertical hollow cylinder which turns on its axis. A person of mass M enters the drum (inside-radius R) while the drum is still and stands against the wall. The drum begins to turn, until it achieves uniform rotation with period T and the rider feels as if some force is pushing him against the wall (see figure). Then the floor drops down, so there is nothing touching the bottoms of the rider's shoes.
Assume the coefficient of friction between the rider's clothes and the surface of the drum is µ.
What values of µ assure that the rider will not slide down when the floor drops?