A rotating space station is said to create \"artificial gravity\"—a loosely-defi

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 230 m in diameter, what angular velocity would produce an "artificial gravity" of 9.80 m/s2 at the rim? rpm

Explanation / Answer

Given diameter d = 230 m

radius r = d/2 = 230/2 = 115 m

radial acceleration a = 9.8 m/s^2

the radial acceleration is given by

a = r * (omega)^2

9.8 = 115 * (omega)^2

omega = 0.29 rad/s = 0.29 * 60 / 2pi rev/min

omega = 2.77 rpm

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