It has been suggested that rotating cylinders about 12 mi long and 5.4 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth?

Answer 1

R = 2.7 miles = 1.426*10^4 ft
R w^2 = g = 32.2 ft^2/s
Solve for the angular speed, w, in radians/s
w = sqrt (g/R) = sqrt (32.2/1.4264*10^4)
= sqrt 2.259*10^-3 = 4.74*10^-2 rad/s