Question

2. Suppose you are asked to design a space station that is 1.0 km in diameter, and is spun fast enough so that a resident standing within it at the outer circumference of the station would experience earth normal gravity. How fast (in rotations per minute, rpm) would you have to spin the space station?

Answer 1

The centripetal acceleration on the resident standing within it at the outer circumference of the station

$$a=\omega^2R=g.$$

Hence

$$\omega=\sqrt{\frac{g}{R}}=\sqrt{\frac{9.8}{500}}=0.14\:\rm rad/s=1.34\:\rm rpm.$$