The law of conservation of angular momentum states that if no external torque acts on a system, the total angular momentum of the system remains constant. 

law of conservation- equation-01

The law of conservation of angular momentum is one of the fundamental principles of physics. It has been verified from the cosmological to the submicroscopic level. The effect of the law of conservation of angular momentum is readily apparent if a single isolated spinning body alters its moment of inertia. This is illustrated by the diver in Fig. 5.13.


Fig. 5.13: A man diving from a diving board.

The diver pushes off the board with a small angular velocity about a horizontal axis through his centre of gravity. Upon lifting off from the board, the diver’s legs and arms are fully extended which means that the diver has a large moment of inertia I1, about this axis. The moment of inertia is considerably reduced to a new value I2, when the legs and arms are drawn in to the closed tuck position. As the angular momentum is conserved, so 

law of conservation- equation-02

Hence, the diver must spin faster when moment of inertia becomes smaller to conserve angular momentum. This enables the diver to take extra somersaults.

Point to ponder

water-drips-into-the-beakerWhy does the coasting rotating system slow down as water drips into the beaker?

 The angular momentum is a vector quantity with direction along the axis of rotation. In the above example, we discussed the conservation of magnitude of angular momentum. The direction of angular momentum along the axis of rotation also remain fixed. This is illustrated by the fact given below

The axis of rotation of an object will not change its orientation unless an external torque causes it to do so.

Do You Know?

The law of conservation of angular momentum is important in many sports, particularly in diving. Gymnastics and ice-skating.

This fact is of great importance for the earth as it moves around the Sun. No other sizeable torque is experienced by the earth, because the major force acting on it is the pull of the Sun. the Earth’s axis of rotation, therefore, remains fixed in one direction with reference to the universe around us.