Question

Future space stations could create an artificial gravity by rotating. Consider a cylindrical space station that rotates with a period of 28 seconds about its axis. Astronauts walk on the inside surface of the space station, and they experience an Earth-like gravitational acceleration of 9.8 m/s2. What is the diameter of the space station?

510m
145m
660m
390m​

Answer 1

P = 2 pi R / v period of space station

F / m = v^2 / R centripetal force per unit of mass

So F / m = 4 pi^2 R^2 / (P^2 * R) = 4 pi^2 R / P^2

Also, F / m = 9.8 m/s^2 earth's gravitational attraction

So 9.8 = 4 pi^2 R / P^2 or R = 9.8 P^2 / 4 * pi^2) = 195 m

Or D = 2 R = 390 m the diameter required