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 298 m. The moment of inertia of the station without people is 1.23 x 109 kg·m2. Suppose 733 people, with an average mass of 74.0 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

we choose our system as the cylinder and the people, since no external angular momentum is exerted to our sys so the product of (moment of inertia)*(angular velocity) remains the same for our syshence : min{moment of inertia} >>>> max{angular velocity}
min{moment of inertia} = (station moment of inertia) + (people moment of inertia)
since station moment of inertia is costant we reach min{moment of inertia} when people are nearest to the axis so they generate minimum inertia hence:
min {moment of inertia} = 1.23*10^9 + 0 = 1.23*10^9
and we reach max{moment of inertia} when people are placed farthest from the axis hence:
max{moment of inertia} = 1.23*10^9 + 733 * 74 * (298 ^ 2) = 6.05*10^9
so
(1.23*10^9) * (max) = (6.05*10^9) * (min)

(max) / (min) = 4.92

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