An amusement park ride consists of a large vertical cylinder of radius R. When it spins fast enough the floor drops and the people remain stuck to the wall. Assume the the coefficient of static friction is µs and kinetic friction is µk.
a) Find an expression for the maximum safe period of rotation, T, in terms of the variables given above, and the gravitational acceleration, g.
b) If the rotation period, T, becomes a bit larger than your answer in a), and the mass of the person is m, what is the magnitude the normal force (in terms of the above variables, T , and m )? What is the magnitude of the acceleration?
c) If the rotation period becomes smaller that your answer in a), what is the magnitude of the normal force? and the force of friction? (again, in terms of the variables given)