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 79.8 m. The moment of inertia of the station without people is 2.70 times 10^9 kg middot m^2. Suppose that 505 people, with an average mass of 67.9 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

Momentum of inertia = m R2

Number of people = 505

Total momentum of inertia = 505 x( 67.9 x 79.82) = 2.18x108kgm2

Total momentum of inertia of station + people at the rim = 2.7x109 +2.18x108 = 2.92x109 kgm2

Momentum of inertia of people at centre is zero (R=0) total momentum of inertia = 2.7x109 kgm2

From conservation of angular momentum

Mom with people at rim (Ir x r) = mom with people at centre (Ic x c)

c / r = Ir/ Ic = 2.92x109 / 2.7x109 =1.082

maximum frictional change in as people go to centre = (c-r)/r = c/r-1 = 1.082 -1 = 0.082

= 8.2%

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