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

Answer 1

0.221 rad/s

Step-by-step explanation:

The formula for centripetal acceleration is ...

a = ω²r

Solving for ω gives ...

ω = √(a/r) = √(9.8 m/s²)/(200 m) = √(0.049)/s ≈ 0.221 radians/s

The required angular velocity is about 0.221 radians per second, or about 2.1 RPM.