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 127 m. The moment of inertia of the station without people is 4.45 x 109 kg·m2. Suppose 591 people, with an average mass of 65.0 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 relative change (/) max in the station's angular speed due to the radial movement of the people?

Explanation / Answer

min I = 4.45e9 kg·m²
max I = 4.45e9kgm² + 591 * 65.0kg * (127m)² = 5.07e9 kg·m²

max change is (5.07/4.45 - 1) * 100% = 13.93%

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