State the principle of conservation of angular momentum. Give two examples.

Explanation

Law of conservation of angular momentum : When no external torque is acting on a body then the angular momentum of that rota-ting body is constant
` I_1 omega_1 = I_2omega_2 ("when" tau =0)`
Example-1: A boy stands over the centre of a horizontal platform which is rotating freely with a speed `omega_1` (`n_1` revolutions/sec.) about a vertical axis passing through the centre of the platform and straight up through the boy. He holds two bricks in each of his hands close to his body. The combined moment of inertia of the system is say `I_1` . Let the boy stretches his arms to hold the masses far away from his body. In this position the moment of inertia increases to( `l_2 " and let " omega_2` ), is his angular speed.
Here omega_2 lt omega_1` because moment of inertia increases.
`becuase I_1 omega_1 = I_2 omega_2 rArr I_1 (2pi)/(T_1) = l_2 (2pi)/(T_2) rArr I_1 n_1 = I_2 n_2`
Example - 2 : An athlete diving off a high spring board can bring his legs and hands close to the body and performs Somersault about a horizontal axis passing through his body in the air before reaching the water below it. During the fall his angular momentum remains constant.