Artificial gravity is a must for any space station if humans

Artificial gravity is a must for any space station if humans are to live there for any extended length of time. Without artificial gravity, human growth is stunted and biological functions break down. An effective way to create artificial gravity is through the use of a rotating enclosed cylinder, as shown in the figure. Humans walk on the inside edge of the cylinder, which is sufficiently large (diameter of 2935 meters) that its curvature is not readably noticeable to the inhabitants. (The space station in the figure is not drawn to the scale of the human.) Once the space station is rotating at the necessary speed to create an artificial gravity of 1g, how many minutes would it take the space station to make one revolution?

Solution

Gravitational force = centripetal force

m*g = mw^2*r

g = w^2*r

radius,r = 2935/2 = 1467.5 mt

w = sqrt(g/r) =sqrt(9.81/1467.5) = 0.0817 rad/sec

Time period = 2pi/w = 2pi/0.0817 = 76.90 sec = 1.28 minutes