Centripetal and Normal ForcesHow many Revolutions per Minute would a 20m Diameter Ferris Wheel have to make in order that the occupants are weightless at the top of the wheel? How much do the occupants weigh at the bottom of the wheel? Describe what happens at the top if the rotation rate is further increased?
If the Ferris Wheel is in constant, uniform, rotational motion the net force on a body on the rim of the wheel must be the correct centripetal force, Fc, always pointed towards the center of the wheel. The actual forces acting on the occupants are gravity (downwards) and some sort of normal force between the body and the structure of the wheel.
Lets assume the occupant is standing in a carriage that is free to rotate so that the ground is always down (at least until it all becomes weightless) - then the normal force between the occupant and the carriage is pointed directly upwards. Thus (taking upwards to be positive):
- T=2 Pi R/v
T=2 Pi Sqrt(R/g)
- N=(60 seconds/minute)/(T seconds/revolution)
- N=9.5 rpm