Question

A cylindrically shaped space station is rotating about the axis of the cylinder to create artificial gravity. The radius of the cylinder is 157 m. The moment of inertia of the station without people is 5.92 x 10⁹ kg·m². Suppose 320 people, with an average mass of 54.0 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?

Answer 1

Given,

R = 157 m

I = 5.92*10⁹ kg-m²

Total mass of people, M = 320*54 = 17280 kg

total moment of inertia of the system when the people are at the radius, I_t = I + MR² = 5.92*10⁹ + 17280*157² = 6.345*10⁹ kg-m²

Conservation of momentum,

I_tw₁ = Iw₂

I_t/I = w₂/w₁

w₂/w₁ = (6.345*10⁹)/(5.92*10⁹ ) = r(say)

r = 1.071

Relative change in angular speed is given, i = (w₂-w₁)/(w₁) = (w₂/w₁) - 1

i = 1.071 - 1

i = 0.071