The \"Rotor\" is a ride found at some amusement parks. It is cylinder shaped wit

Question

The "Rotor" is a ride found at some amusement parks. It is cylinder shaped with a diameter of 6 meters. The sides are covered with a rough canvas material. The riders stand up against the side and the ride begins to rotate. When it reaches a certain speed the floor drops away, but the riders do not fall. Explain why the riders do not fall. (A quality free body diagram must be part of your explanation.) Show that the mass of the rider is not a factor in determining the safe linear speed that the wall of the cylinder must reach. A value of mu_s = .4 is typical for the canvas walls and clothes of the rider. Determine the minimal rotation rate that would make the ride work properly.

Explanation / Answer

1.

as there is frictional force on the riders in the upwards direction

which counters the gravity force.

b)

let the safe linear speed is v

frictional force = gravity force

u * m * v^2/r = m * g

v^2 = r * g/u

hence safe speed is not dependent on the mass.

c)

R = 6/2 = 3 m

us = 0.4

us * m * w^2 * r = m * g

0.4 * w^2 * 3 = 9.8

w = 2.86 rad/s

the minimum angular speed of the cycliner is 2.86 rad/s

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