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:
[tex]I = I_s + 500I_p = 3*10^9 + 500m_pr_p^2=3*10^9 + 500*70*82.5^2=3.24*10^9[/tex]
When they are at the axis, the total moment of inertia is only the station's, which is [tex]3*10^9[/tex]
By the law of angular momentum conservation:
[tex]I_1\omega_1 = I_2\omega_2[/tex]
[tex]\omega_2/\omega_1 = I_1/I_2 = \frac{3.24*10^9}{3*10^9} = 1.08 [/tex]
So the angular speed changes by 0.08 of itself, or 8%
