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.
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.