A skater and the moment of inertia

A skater spins at $2.0\ \text{rad/s}$ with her arms out, when her moment of inertia is $3.6\ \text{kg m}^2$. As she pulls her arms in, her angular momentum stays the same. You will make the program find her spin rate and her kinetic energy for every moment of inertia, and the moment of inertia that gives a chosen spin.

The idea. $L = I\omega$ is kept, so $\omega = \dfrac{L}{I}$ and $K = \tfrac12 I\omega^2 = \dfrac{L^2}{2I}$.

Your tasks.

1. Work out her angular momentum.
2. Work out w and K for every I in the list.
3. Find the I in the list closest to giving a spin of $5.0\ \text{rad/s}$.