potential energy/ momentum

Question

A rotating space station is said to create "artificial gravity"—a loosely-defined term used for an acceleration that would be crudely similar to gravity. The outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. If the space station is 170 m in diameter, what angular velocity would produce an "artificial gravity" of 9.80 m/s² at the rim?

Answer 1

Angular velocity ω relates to centripetal acceleration a as a = v²/r = (ωr)²/r = ω²r. Solve this for ω.