In the absence of net external forces, linear momentum is conserved.
In the absence of net external torques, angular momentum is conserved.
Two buckets spin around in a horizontal circle on frictionless bearings. Suddenly, it starts to rain. What happens?
A skater spins up when she brings her arms in toward her rotation axis, reducing her moment of inertia. To conserve angular momentum, her angular speed must increase.
For a particle in circular motion, angular momentum is perpendicular to both the radius and the tangential velocity.
For a system consisting of two masses connected by a massless rod, angular momentum is conserved when the rod expands.
A ring is dropped onto a spinning solid cylinder. Friction causes the ring to match the rotation speed of the cylinder, slowing it down. Use conservation of momentum to find the final angular speed of the system.