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 164 m. The moment of inertia of the station without people is 2.43 x 109 kg·m2. Suppose 148 people, with an average mass of 60.0 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

Angulr momentum is conservative:

L1 = L2

I1 1 = I2 2

I1 = 2.43*10^9 + 148*(60*(164)2) = 2.43*10^9 + 2.388*10^8 = 2.669*10^9 Kg.m2

M.o.I of people at centre = 0 (as R = 0)>>>> I2 = 2.43*10^9 kg.m² (station only)

I1 1 = I2 2

>>>> 2/1 = I1/I2 = (2.669*10^9)/(2.43*10^9) >>>> 2/1 = 1.098

(Max) fractional change in as people go to centre ..
(2 - 1) / 1 = (2/1) - 1 = 1.098 - 1 = 0.098 >>>>> = 9.8% (increase)

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