Question

Imagine one such station with a diameter of 129 m, where the apparent gravity is 2.30 m/s2 at the outer rim. How fast is the station rotating in revolutions per minute?

Answer 1

The station is rotating at 1.80 revolution / minute.

Explanation:

For calculating the velocity v,

                      Apparent gravity = v^2 / r

                                          2.30 = v^2/r

                                2.30 $\times$ 64.5 =  v^2

                                                 v = 12.2 m/s .

                 Time for revolution = 2 π r / v

                                                  = (2 $\times$ 3.14 $\times$ 64.5) / 12.2 = 33.2 seconds          

                                                  = 0.553 minutes .  

For converting to revolution per minute, divide one by the value in minutes.

                                    1 / 0.553 = 1.80 revolution / minute.