The rotor is an amusement park ride where a person enters the Rotor when it is stationary and stands against the wall with their back against the wall. The rotor then begins to spin around a vertical axis. After reaching cruising speed, the floor drops away and the patron is left suspended against the wall. Assume that the rate of rotation increases according the the expression (alpha)=k(theta)until the floor drops ((alpha)is angular acceleration in rad/s2, theta is angular position in radians). After this point, the rotor spins at a constant speed until the flor rises again. Determine an expression for the number of revolutions the motor should turn before it is safe to drop the floor. The coefficient of friction between the rider and the wall is u_s.

Answer 1

alpha is when the centripetal acceleration is equal to the friction force on the wall.
m w^2/r=mu*mg
solve for w.

This problem is a thinking exercise, not a plug and compute.