**Conservation of Angular Momentum:**

When no external torque acts on a system, the angular momentum of the system is conserved. Angular momentum is a property of rotating objects and is defined as the product of the moment of inertia and angular velocity. It is a vector quantity and its direction is perpendicular to the plane of rotation.

**Explanation:**

To understand why angular momentum is conserved when no external torque acts on a system, let's consider the principle of conservation of angular momentum.

- **Angular Momentum:** Angular momentum is given by the equation L = Iω, where L represents the angular momentum, I represents the moment of inertia, and ω represents the angular velocity.
- **Moment of Inertia:** The moment of inertia depends on the mass distribution of an object and its rotation axis. It is a measure of an object's resistance to changes in its rotational motion.
- **Angular Velocity:** Angular velocity is the rate at which an object rotates about an axis. It is the change in angular displacement per unit time.

When no external torque acts on a system, it implies that the net external torque is zero. In other words, the sum of all the torques acting on the system is zero.

- **Torque:** Torque is the rotational analogue of force. It causes objects to rotate about an axis. The torque acting on an object is given by the equation τ = Iα, where τ represents the torque, I represents the moment of inertia, and α represents the angular acceleration.

If the net external torque is zero, it means that there are no external forces or torques causing any change in the system's rotational motion. Therefore, the angular momentum of the system remains constant.

- **Conservation of Angular Momentum:** The principle of conservation of angular momentum states that if no external torque acts on a system, the total angular momentum of the system remains constant.

This conservation principle is observed in various situations, such as when a figure skater pulls their arms inward during a spin, causing their moment of inertia to decrease and their angular velocity to increase. As a result, their angular momentum remains constant.

In conclusion, when no external torque acts on a system, the angular momentum of the system is conserved. This conservation principle is a fundamental concept in physics and is applicable in various rotational motion scenarios.