The rotor (the figure below) is an amusement park ride where people stand agains

Question

The rotor (the figure below) is an amusement park ride where people stand against the inside of a cylinder. Once the cylinder is spinning fast enough, the floor drops out.

(a) What force keeps the people from falling out the bottom of the cylinder?

(b) If the coefficient of static friction is 0.42 and the cylinder has a radius of 2.6 m, what is the minimum angular speed of the cylinder so that the people don't fall out? (Normally the operator runs it considerably faster as a safety measure.)

rad/s

Explanation / Answer

1. The gravitational force is balanced by the Static Frictional Force to keep the people from falling down

The answer is 2 ( Static Friction)

2. let f be the frictional force.

We have the following equations:

mg = f

N= m2R

but f=N

mg= m2R

g = 2R

= (g/R)0.5

R = 2.6 m

  =0.42

=(9.8/(0.42x2.6))0.5

= 3 rad/s

Therfore the minimum angular velocity = 3 rad/s

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