A 1.0-m-long massless rod is pivoted at one end and swings around in a circle on a frictionless table. A block with a hole through the center can slide in and out along the rod. Initially, a small piece of wax holds the block 60 cm from the pivot. The block is spun at 30 rpm , then the temperature of the rod is slowly increased. When the wax melts, the block slides out to the end of the rod. What is the final angular velocity?

A kid's merry-go-round in a park is a thin 150 kg disk (I = ½ MR2) with a radius of 3 m mounted to rotate freely about a central axis. On the edge of %3D the disk is an essentially massless bar. A 25 kg child jumps onto the bar (tangentially to the outer rim of the disk) at a speed of 12 m/s and a distance of 3 m from the rotation axis. If we think of the child as being essentially a point mass, what is the angular velocity of the system after the collision?

A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass md = 2.7 kg and radius R = 0.25 m. The rods each have mass m, = 1.2 kg and length L = 0.86 m.

A 10 kg wheel with a 0.4 meter radius is rotating at 4 rad/s. A 8 Nm torque is applied to the wheel. The rotational inertia of the wheel is 0.48 kgm2. The angular momentum of the wheel changes by 4 kg*m2/s. How long was the torque applied to the wheel.

A solid disk rotates in the horizontal plane at an angular velocity of 4.50 x 10-2 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.13 kg.m?. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.40 m from the axis. The sand in the ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of the disk?

A 26 g block sits at the center of a turntable that rotates at 50 rpm.  A compressed spring shoots the block radially outward from the center along a frictionless groove in the surface of the turntable.  Calculate the turntable's angular speed when the block reaches the outer edge.  Treat the turntable as a solid disk with mass with mass 200 g and diameter 30.0 cm.  Express your answer in revolutions per minute.

Trucks can be run on energy stored in a rotating flywheel, with an electric motor getting the flywheel up to its top speed of 683 rad/s. One such flywheel is a solid, uniform cylinder with a mass of 535 kg and a radius of 1.2 m that rotates about its central axis. What is the kinetic energy of the flywheel after charging?  If the truck uses an average power of 8.4 kW, for how many minutes can it operate between chargings?

A playground merry-go-round rotates like a large solid turntable about a fixed vertical axis, rotating at a rate of 0.65 rad/s. The moment of inertia of the turntable about this axis is 850 . A child of mass 40.0 k, initially standing at the center of the turntable, moves outward to a position 1.2 meters from the axis of rotation.  Modeling the child as a particle, what is the new rotation rate of the merry-go-round?