A cylindrically shaped space station is rotating about the axis of the cylinder

Question

A cylindrically shaped space station is rotating about the axis of the cylinder to create artificial gravity. The radius of the cylinder is 75.8 m. The moment of inertia of the station without people is 2.94 109 kg · m2. Suppose that 550 people, with an average mass of 73.5 kg each, live on this station. As they move radially from the outer surface of the cylinder toward the axis, the angular speed of the station changes. What is the maximum possible percentage change in the station's angular speed due to the radial movement of the people?

Explanation / Answer

The radius of the cylinder r = 75.8 m
The moment of inertia of the station without people I = 2.94 x10 9 kg · m 2 An average mass of each m = 73.5 kg Mass of 550 people M = 550 m                                    = 40425 kg Initial moment of inertia with people I ' = I + Mr 2                                                           = 3.172 x 10 9 kg m 2 Final monent of inertia I " = I Let the initial angular speed be Angular speed after the people move radially from the outer surface of the cylinder toward the axis ' = ? From law of conservation of angular momentum , I = I ' ' From this ' = I / I '                      = 0.9267 The maximum possible percentage change in the station's angular speed due to the radial movement of the people = [( ' - ) / ] x100                                                                                                                                                                            = -7.32 %

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