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 117 m. The moment of inertia of the station without people is 1.36 x 109 kg·m2. Suppose 770 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

The of the station with out people(I1)=1.36*10^9 kg.m^2 the corresponding angular speed=(W1) when the people live on this station, total mass(M)=770*62 kg =47740 kg radios of the cylinder(R)=117m now, the moment of inertia of cylinder with people=12=M R^2 I2=47740(117)^2 I2=6.53*10^9 kg .m^2 the corresponding angular velocity =(W2) as, there is no torque acting on the entire system angular momentum should be constant. L= CONSTANT or L= IW = constant or I1W1=I2W2= constant W1/W2=I2/I1 =6.53*10^9/1.36.*10^9 =4.80 the maximum relative change of angular momentum (W1/W2) -1 =4.8-1 (W1-W2)/W2 =3.8 so, the maximum relative change of angular momentum=3.8

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