Question

A company has asked you to design a new Gravitron ride. They have a motor that will spin the passengers at 28m/s and would like to know how large the machine needs to be in order for the passengers to feel 8g's of acceleration.

Answer 1

Assuming the rotation ishorizontal (so we disregard the natural gravity), the centripetal acceleration is a = v^2 / R, where v is the linear speed of a cabin, and R is the radius of the wheel.
Thus the required radius is R = v^2 / a.
If a = 8*g,
R = (v^2) / (8*g) = ((28 m/s)^2) / (8*9.8 m/s^2) = 10 m.
Answer: the machine needs to be 10 meters in radius.