The acceleration due to gravity

Question

One method of creating artificial gravity in space is to make a circular space station that spins and creates a centripetal force that points towards the center of the space station
to simulate the normal force that astronauts would feel on Earth. If an engineer created
a space station with a radius of 30 kilometers, how fast would the space station have to
spin in order to simulate the acceleration due to gravity on Earth?

Answer 1

Did you really mean a radius of 30 kilometers?  That is unrealistically large.  Anyway, the tangential speed v at a distance r from the rotation axis must satisfy

 

g = v²/r

 

v = √(rg)

 

Plug in the correct radius r and g in appropriate units and get v.  If you want the angular speed ω, then

 

g = rω²

 

ω = √(g/r)