Question

In an old-fashioned amusement ride, passengers stand inside a 3.0 m tall, 5.0 m diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about the vertical axis. The floor on which the passengers are standing suddenly drops away! If all goes well, the passengers will “stick” to the wall and not slide. Clothing has a static coefficient of friction against steel in the range of 0.6 and 1.0 and a kinetic coefficient in the range of 0.4 to 0.7. What is the minimum rotational frequency, in rpm, for which the ride is safe?

Answer 1

The outward “push” experienced by the riders is m⍵²r and the gravitational pull is mg where m is the mass of the riders. Coefficient of friction µ acts at right angles to the push and the frictional force is µm⍵²r opposing mg. If a rider is to remain pinned to the steel wall µm⍵²r>mg so µ⍵²r>g and µ>g/(⍵²r). So ⍵²>g/(µr).

The minimum value of µ is 0.4 and the maximum is 1, covering kinetic and static friction. g=9.8㎨ approx, r=2.5m. Therefore ⍵²>9.8/(0.4×2.5), ⍵²>9.8 and ⍵>3.13 revs per sec or 187.8 rpm.