Question

A cylindrically shaped space station is rotating about the axis of the cylinder to create artificial gravity. The radius of the cylinder is 82.5 m. The moment of inertia of the station without people is 3.00 ???? 10 9 kg ???? m2. Suppose that 500 people, with an average mass of 70.0 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 possible percentage change in the station’s angular speed due to the radial movement of the people?

Answer 1

Answer:

8%

Step-by-step explanation:

The maximum change happens when all 500 people moves form outer surface to the station center. When all of them are at the surface, the total moment of inertia is:

$I = I_s + 500I_p = 3*10^9 + 500m_pr_p^2=3*10^9 + 500*70*82.5^2=3.24*10^9$

When they are at the axis, the total moment of inertia is only the station's, which is $3*10^9$

By the law of angular momentum conservation:

$I_1\omega_1 = I_2\omega_2$

$\omega_2/\omega_1 = I_1/I_2 = \frac{3.24*10^9}{3*10^9} = 1.08$

So the angular speed changes by 0.08 of itself, or 8%