An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough that a person inside is stuck to the wall and does not slide down when the floor drops away. The acceleration of gravity is 9.8 m/s2. The static coefficient between a person and the wall is 0.52 and the radius of the cylinder is R= 3.8 meter. For ease, ignore the person's depth and suppose she or he is just a physical point on the wall. The person's speed is v=2πR/T, where T is the rotation period of the cylinder (the time to complete a full circle).
Obtain the maximum rotation period of the cylinder which would prevent a 50 kg person from falling down.
Answer in units of s.