Artificial gravity is a must for any space station if humans are to live there f

Question

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 (radius L) 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 long would it take the space station to make one revolution? Express this time t in terms of g and L.

Explanation / Answer

Here the centripetal acceleration is equal to weight then

FC =mg

mw2r =mg

g =w2*r

Given that radius (r) =L

Then w =Sqrt(g/L)

The time period for one revolution is given by

T =2pi/w =2pi/Sqrt(g/L) =2pi*Sqrt(L/g)

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