A space station shaped like a giant wheel has a radius 1.06 ✕ 102 m and a moment of inertia of 4.96 ✕ 108 kg · m2. A crew of 150 lives on the rim, and the station is rotating so that the crew experiences an apparent acceleration of 1g. When 100 people move to the center of the station for a union meeting, the angular speed changes. What acceleration is experienced by the managers remaining at the rim? Assume that the average mass of each inhabitant is 65.0 kg.

Question

irishboy123 · Answer

this is about conservation of angular momentum, there's no external force acting on the "system", the system being the space station ad its occupants, so....

$$I_1\omega_1 = I_2\omega_2 $$

$I_1 = 4.96 ✕ 10^8 + \color{green}{150} \times 65 \times 106^2  \quad kg \, m^2$
$I_2 = 4.96 ✕ 10^8 + \color{red}{50}\times 65  \times 106^2    \quad kg \, m^2$ .......cos 100 people are now at the centre of rotation

also, the radial [inward-outward] acceleration at the rim is $\omega^2 r$ so you can also say that $a_1=\omega_1^2 (106) = g \; m/s^2$

put that all together and solve for $\omega_2$ and then for  $a_2=\omega_2^2 (106)$