An amusement park ride consists of a large vertical cylinder that spins about it

Question

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 .
Given g = 9.8 m/s2, the coefficient µ = 0.605 of static friction between a person and the wall, and the radius of the cylinder R = 5.4 m. For simplicity, neglect the person’s depth and assume he or she is just a physical point on the wall. The person’s speed is
v = 2pR T
where T is the rotation period of the cylinder (the time to complete a full circle).
Find the maximum rotation period T of the cylinder which would prevent a 69 kg person from falling down.
Answer in units of s

Explanation / Answer

mg = f mg = u x mw^2 x R g = u x w^2 x R w = 1.732 rad/s Time period = w/2pi = 0.276 seconds

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