A cylindrically shaped space station is rotating about the axis of the cylinder
ID: 1502125 • Letter: A
Question
A cylindrically shaped space station is rotating about the axis of the cylinder to create artificial gravity. The radius of the cylinder is 80.6 m. The moment of inertia of the station without people is 2.85 109 kg · m2. Suppose that 450 people, with an average mass of 76.3 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 possible percentage change in the station's angular speed due to the radial movement of the people?
Explanation / Answer
Ii = 2.85*10^9 + 450*76.3*80.6^2
= 3.073*10^9 kg.m^2
If = 2.85*10^9 kg.m^2
let wi and wf are the initial and final angular speeds.
Apply conservation of angular momentum
If*wf = Ii*wi
wf = (Ii/If)*wi
= (3.073/2.85)*wi
= 1.078*wi
the required percentage = (wf - wi)*100/wi
= (1.078*wi - wi)*100/wi
= 7.8 %
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