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 117 m, where the apparent gravity is 3.10 m/s2 at the outer rim. How fast is the station rotating in revolutions per minute

Explanation:

The apparent gravity decreases because of centrifugal force that is acting on the astronaut .

centrifugal  acceleration = ω²r , ω is angular velocity and r is radius of circular path .

Given

r = 117/2 = 58.5 m .

centrifugal  acceleration = (2πn)²r , where n is revolution per minute.

= 4 π² n² r

Given g - 4 π² n² r  = 3.10

9.8 - 39.43 x n² x 58.5 = 3.10

6.7 = 2306.65 n²

n² = .0029

n = .05385 rev /s

= 3.23  rev per minute .

unlike poles attract

increases it