During an experiment, a student spins a uniform vertical coin of mass 5.0 g and diameter 2.0 cm about a frictionless horizontal axis passing through a point on the edge of the coin. Initially, the coin was at rest, and the center of gravity of the coin was at the same level as the axis of rotation. Determine the angular speed of the coin when it reaches its lowest position.

A steel cable is connected at one end to a wooden crate that can slide down an inclined ramp. The other end of the cable is wound around a metal solid drum positioned in a groove at the top of the ramp as shown in the diagram. The ramp is inclined at an angle of 30° to the horizontal, and the crate has a mass of 5.0 kg. The solid drum has a mass of 50 kg and a radius of 0.25 m and rotates without slipping as the cable unrolls. Determine the speed of the crate after it has slid 2.0 meters along the ramp, starting from rest, when there is no friction.

A small puck of mass 0.40 kg is tethered to a post by a light string and moves in a circular path on a frictionless tabletop. The puck has an initial speed of 4.0 m/s and revolves with an initial radius of 1.0 m. A physics student carefully pulls the string through the center post, decreasing the radius to 0.60 m and increasing the puck's speed. Determine the work done by the student. Verify that the work-energy theorem is satisfied by this action.