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?

Due to the rotation of the space station the astronauts experience a centripetal acceleration towards the centre of the space station. If '[tex]\large{a_{c}}[/tex]', 'ω' and 'R' represent the centripetal acceleration, angular velocity of the space station and the radius of the space station respectively, then

[tex]a_{c} = \omega^{2}.R[/tex]

As according to the problem the space station has to rotate in such an angular velocity that it produces the same "artificial gravity" as Earth's surface, we can write

[tex]a_{c} = g = 9.8 ms^{-2}[/tex]

Also given [tex]R = \dfrac{diameter~of~the~space~station}{2} = \dfrac{200 m}{2} = 100 m[/tex]

Therefore we can write,

[tex]&& a_{c} = g = \omega^{2}.R\\&or,& \omega = \sqrt{\dfrac{g}{R}} = \sqrt{\dfrac{9.8 ms^{-1}}{100 m}} = 0.313~rads^{-1}[/tex]