Engineers and science fiction writers have proposed designing space stations in the shape of a rotating wheel or ring, which would allow astronauts to experience a sort of artificial gravity when walking along the inner wall of the station's outer rim. (a) Imagine one such station with a diameter of 104 m, where the apparent gravity is 2.20 m/s2 at the outer rim. How fast is the station rotating in revolutions per minute

f = 1.96 revolutions per minute

Explanation:

The formula for the the frequency of revolution of a satellite, to develop an artificial gravity, with the help of centripetal acceleration is given as follows:

f = (1/2π)√(ac/r)

where,

f = frequency of rotation = ?

ac = centripetal acceleration= apparent gravity or artificial gravity = 2.2 m/s²

r = radius of station or satellite = diameter/2 = 104 m/2 = 52 m

Therefore,

f = (1/2π)√[(2.2 m/s²)/(52 m)]

f = (0.032 rev/s)(60 s/min)

f = 1.96 revolutions per minute