16. Angular Momentum

You stand on a stool that is free to rotate about an axis perpendicular to itself and through its center. The stool's moment of inertia around its central axis is 1.50 kg m² . Suppose you can model your body as a vertical solid cylinder (height = 1.80 m, radius = 20 cm, mass = 80 kg) with two horizontal thin rods as your arms (each:length = 80 cm, mass = 3 kg) that rotate at their ends, about the same axis, as shown. Suppose that your arms' contribution to the total moment of inertia is negligible if you have them pressed against your body, but significant if you have them wide open.

If you initially spin at 5 rad/s with your arms against your body, how fast will you spin once you stretch them wide open? (Note: The system has 4 objects (stool + body + 2 arms), but initially only stool + body contribute to its moment of inertia)

A professor sits on a rotating stool that is spinning at an initial angular velocity of ${\omega }_i$. If the professor pulls her arms inward, reducing her moment of inertia from $I_i$ to $I_f$, what happens to her angular velocity $\omega$?