A student sits at rest on apiano stool that can rotate. The moment of inertia of the student-stool system?

Question

A student sits at rest on a piano stool that can rotate. The moment of inertia of the student-stool system is 4.1 kg·m2. A second student tosses a 1.5 kg mass with a speed of 2.2 m/s to the student on the stool, who catches it at a distance of 0.37 m from the axis of rotation. The final angular speed is 0.284 rad/s. Calculate the initial and final kinetic energy of the system.

Answer 1

The initial kinetic energy is easy...provided that the problem intends "initial" to mean "after the mass was tossed, but before it was caught". It's the K of the moving mass alone. The student-chair system is at rest.

For the final KE, calculate the moment of inertia I of the student-chair-mass as the sum I_0 of the chair (given) and I_m of the thrown mass when it was caught at radius 3.7. Then use:
K = (1/2) I * w^2 = (1/2) (I_0 + I_m) * w^2
where "w" (looks like "omega") is the given final angular speed.