Conservation of angular momentum

Conservation of angular momentum:

Torque and angular momentum are the respective analogous quantities to force and linear momentum in rotational dynamics. With suitable changes this can be transformed into the conservation of angular momentum. Angular momentum of a system is given by L = r x p where r is the position vector from the axis of rotation and p is the linear momentum.

This is the principle of conservation of angular momentum. Examples of conservation of angular momentum: During some shows of ballet dance, acrobat in a circus, sports like ice skating, diving in a swimming pool, etc., the principle of conservation of angular momentum is realized. Thus, if the moment of inertia I is increased, the angular speed and hence the frequency of revolution n decreases. Also, if the moment of inertia is decreased, the frequency increases.

Ballet dancers:

During ice ballet, the dancers have to undertake rounds of smaller and larger radii. The dancers come together while taking the rounds of smaller radius (near the centre). In this case, the MI of their system becomes minimum and the frequency increases, to make it thrilling. While outer rounds, the dancers outstretch their legs and arms. This increases their MI that reduces the angular speed and hence the linear speed. This is essential to prevent slipping.

Diving in a swimming pool (during competition): While on the diving board, the divers stretch their body so as to increase the moment of inertia. Immediately after leaving the board, they fold their body. This reduces the moment inertia considerably. As a result, the frequency increases and they can complete more rounds in air to make the show attractive. Again, while entering into water they stretch their body into a streamline shape. This allows them a smooth entry into the water.