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 103 m. The moment of inertia of the station without people is 1.85 x 109 kg

A cylindrically shaped space station is rotating about the axis of the cylinder to create artificial gravity. The radius of the cylinder is 103 m. The moment of inertia of the station without people is 1.85 x 109 kg.m2. Suppose 265 people, with an average mass of 62.0 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

Note that delta(I)max is when

delta(I) max = Imax - Imin

Imax is hwen all people are on the outer surface of the cylinder.

They add I(people) = 265mr^2 = 1.743E8 kg*m^2

Imin is when all people are on the axis itself, hence adding no rotational inertia as r = 0.

Thus, the difference in Imax - Imin is the moment of inertia of the people,

Imax - Imin = Ipeople

= 1.74*10^8 kg*m^2   [ANSWER]

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