Question

A space crafter shaped like a hoop with a radius of 100m is revolving at 3 RPM. It’s rotational inertia is 8.8 * 105 kgm2. It then extends out a set of solar panels from all sides effectively moving 20kg from a radius of 100m to 120m. After deploying, what will be the rotational speed of the station?

Answer 1

From the conservation of momentum:

$$I_1\omega _1=I_2\omega _2$$

$$I \omega _1=(I+0.5M(a^2+b^2))\omega _2$$

$$\omega _2=\omega _1 \frac{I}{I+0.5M(a^2+b^2)}$$

$$\omega _2=3 \frac{ 8.8 \cdot 10^5}{ 8.8 \cdot 10^5+0.5(20)(100^2+120^2)}=2.35\ RPM$$