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 85.4 m. The moment of inertia of the station without people is 3.27 109 kg · m2. Suppose that 540 people, with an average mass of 65.1 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

r = 85.4 m , Ic = 3.27*10^9 kg.m^2, N = 540

m = 65.1 kg

Moment of inertia of person = N*mr^2

Ip =540*65.1*85.4^2 = 2.56*10^8 kg.m^2

Ir = (3.27*10^9 +2.56*10^8) = 3.526*10^9 kg.m^2

From conservation of angular momentum

angular Momentum with people at rim = angular Momentum with people at center

Ir *wr = Ic *wc

wc/wr = Ir/Ic = 3.526*10^9/(3.27*10^9) = 1.0783

fractional change in w as people go to center

= (wc -wr)/wr = (1.0783-1) = 0.0783

= 7.83 %

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.