Jumping Into/Out of Moving Disc Practice Problems

A potter is spinning a pottery wheel that has a moment of inertia equal to 500 kg·m² and a radius of 2.0 m. It rotates at 2.50 rad/s and faces insignificant friction. Aiming toward the center of the spinning wheel, about which it rotates, the potter pushes some clay onto the edge of the wheel. This changes the wheel speed to 1.75 rad/s. Calculate the mass of the clay.

One end of a stationary rod is connected to a pivot on a smooth horizontal surface. The rod can rotate freely without friction. On the other end, a 15.0-g squirrel stands still. Given that the rod has a mass of 75.0 g and it is 120 cm long, calculate the angular speed of the rod if the squirrel jumps off in the horizontal direction, perpendicular to the rod, with a speed of 25.0 cm/s relative to the surface, just after the squirrel jumps. Assume that the rod has a uniform mass distribution.

A roundabout in a park has a diameter of 3.4 m and is rotating freely at an angular speed of 0.90 radians per second. The roundabout's total moment of inertia is calculated to be about 1540 kg·m². If three children initially on the ground, each weighing about 55 kg, decide to hop onto its edge, what would be its new angular speed?