An amusement park ride called the Rotor consists of a room in the shape of a ver

Question

An amusement park ride called the Rotor consists of a room in the shape of a vertical cylinder 3.67 m in radius which, once the riders are inside, begins to rotate, forcing them to the wall. When the room reaches the angular speed of 2.6 rad/s, the floor suddenly drops out. It is deemed that this rate of rotation will be sufficient to keep a 400 lbf person pinned against the wall of the cylinder. What is the minimum angular speed required to keep a 200 lbf person pinned against the wall of the cylinder?

Explanation / Answer

friction, f = mg
and Normal reaction, N = mv^2/r
but f = mu*N
so, mu*mv^2/r = mg
mu*mw^2*r = mg
mu = g/w^2*r = 0.395

FOr mass m
mu*v^2/r = g
v = sqroot(rg/mu) = 9.542 m/s
w = v/r = 2.6 rad/s

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