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

Centripetal acceleration:  a_c = v²/r, where

a_c = g = 9.8 m/s²;

v = speed = ?;

r = 30 km = 3×10⁴ m

 

v = sqrt(a_cr) = sqrt[(9.8 m/s²)(3×10⁴ m)] = 542.2 m/s