Let us consider a student seated on a stool that can rotate freely about a vertical axis. The student, who is set into rotation at a modest initial angular speed wi, holds two dumbbells in an outstretched hand. His angular momentum lies along the vertical rotation axis, pointing upwards.
Now, if the student pulls his arms towards his chest, his rotational inertia reduces and so the rate of rotation (w) increases markedly. If he stretches his arms, he can slow down. This happens since no external torque acts on the system, consisting of the student, stool and dumbbells. So the angular momentum of the system should remain the same. i.e., Iw = k. So when he reduces the I, w increases.
A ballet dancer can vary her angular speed by outstretching her arms and legs. Suppose the dancer is rotating with her legs and arms stretched outward and if she suddenly folds her arms and brings her stretched legs closer, thereby reducing the moment of inertia, her angular velocity increases due to conservation of angular momentum.
An incredible shrinking of a star takes place when the nuclear fire in the core of a star burns low. The star may eventually collapse, building up pressure in its interior. The collapse may go so far as to reduce the radius of the star from something like that of the sun to the incredibly small value of few kilometres. The star then becomes a neutron star; a very dense star composed mainly of neutrons. During this shrinking process, the star is an isolated system and its angular momentum 
cannot change.
Because its rotational inertia is reduced, its angular speed is correspondingly increased to as much as 600 to 800 revolutions per second. Whereas, the sun, a typical star, rotates at about one revolution per month.
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Spacecraft orientation
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If a spacecraft is mounted with a flywheel, suggesting a scheme for orientation control, the spacecraft and the flywheel form an isolated system. So, if the system's total angular momentum is zero because neither the spacecraft nor the flywheel is turning, it must remain zero. To change the orientation of the spacecraft, the flywheel is made to rotate, say anticlockwise. To maintain the angular momentum at zero, the spacecraft starts rotating in the clockwise direction. The flywheel is brought to rest as and when the required orientation of the spacecraft is obtained, since the spacecraft stops rotating when the flywheel is brought to rest.
a) An idealised spacecraft containing a flywheel. If the flywheel is made to rotate clockwise as shown, the spacecraft itself will rotate counter-clockwise.
b) When the flywheel is brought to a stop, the spacecraft will also stop rotating but will be reoriented by an angle.
Voyager 2, in 1986, as it flew past the planet Uranus, was set into unwanted rotation by this flywheel effect, every time its tape recorder was turned on at high speed. The ground staff at the Jet Propulsion Laboratory had to program the on-board computer to turn on counteracting thruster jets, every time the tape recorder was turned on or off.
