Question

An astronaut in training is seated at the end of a horizontal arm 8 meters long. How many revolutions per second must the arm make for the astronaut to experience a horizontal acceleration of 4.0g

Answer 1

a = v^2 / R where a is the centripetal acceleration and R the radius

v = 2 π R N / t where (N / t) is the revolutions / sec giving distance / time

a = 4 g horizontal acceleration

4 g = (2 π R N / t)^2 / R = 4 π^2 * R * (N / t)^2

(N / t)^2 = g / (π^2 * R)

N / t = 1 / π * (g / R)^1/2 = .318 * (9.80 m / s^2 / 8 m)^1/2 = .352 / sec