A space station shaped like a giant wheel is located far from anything else in s

Question

A space station shaped like a giant wheel is located far from anything else in space, and has a radius of 100.0 m. When unoccupied, it has a moment of inertia I = 5.000 times 10^8 kg m^2. A crew of 150 is living on the rim, and the space station's rotation causes the crew to experience an apparent "gravity" (in reality, their centripetal acceleration, as seen by an inertial observer) of 1 g. When 100 people move to the center of the station for a union meeting, the angular speed changes. Assume the average inertia of each inhabitant is 65 kg. It is also very safe to assume that the average person is very short, compared to 100m. What apparent "gravity" (centripetal acceleration) is experienced by the managers remaining at the rim?

Explanation / Answer

Initial moment of inertia, I1 = (5 * 108) + [150 * (65 * 1002)] = 5.975 * 108 kg-m2

Final moment of inertia, I2 = (5 * 108) + [50 * (65 * 1002)] = 5.325 * 108 kg-m2

Also, initial centripetal acceleration, a1 = 12R = g

Angular momentum of the system is conserved.

=> I11 = I22

=> 2 = I11/I2

New apparent gravity, a2 = 22R = (I1/I2)(12R) = (5.975 / 5.325) * 9.81 = 11 m/s2

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