Question

In an old-fashioned amusement park ride, passengers stand inside a 5.0 mdiameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about its vertical axis. Then the floor on which the passengers are standing suddenly drops away. If all goes well, the passengers will

Answer 1

There is a normal force, causing the centripetal acceleration toward the vertical axis of rotation. There is a vertical force, W (weight) acting downward. In order to prevent injury (!) there is a friction force, f, acting upward.

The minimum angular speed is that which prevents slipping down the wall (so we can dispense with the kinetic friction!).

Summing the forces in the vertical direction( +ve upward)
f-m*g >0
f > m*g
u*m*(w**2*r) > m*g
u*w**2*r > g
w > sqrt( g/(r*u) ) = sqrt(9.8/( (5.3/2)*.64) )
w > 2.40 1/s

n > 60/pi*w = 45.9 RPM

Thus, the absolute minimum is 46 RPM; to be safe, it should go a bit faster!