State the law of conservation of angular momentum and also describe this law with an appropriate example.

The law of conservation of angular momentum states that the total angular momentum of an isolated system remains constant if no external torque is acting on it. In other words, the angular momentum of a system remains unchanged unless an external force or torque is applied.

Angular momentum (L) is a vector quantity defined as the product of the moment of inertia (I) and the angular velocity (ω) of an object rotating around an axis. Mathematically, it is represented as L = Iω.

An appropriate example to describe the law of conservation of angular momentum is the case of a figure skater. Consider a figure skater spinning on ice. Initially, the skater is spinning with their arms and legs extended outward. Since the moment of inertia is large in this position, the skater's angular velocity is relatively low.

Now, as the skater pulls their arms and legs inward, the moment of inertia decreases. According to the law of conservation of angular momentum, the angular velocity must increase to keep the total angular momentum constant. Consequently, the skater starts spinning faster due to the decrease in the moment of inertia.

This example demonstrates the conservation of angular momentum. By reducing the moment of inertia, the skater increases their angular velocity, maintaining the overall angular momentum of the system. It showcases how changes in the distribution of mass affect rotational motion while preserving the total angular momentum.