# Angular Momentum and Its Conservation

## Angular Momentum and Its Conservation

## Understanding Angular Momentum

- Angular momentum is a
**vector quantity**, measured in kilogram metre squared per second (kg m^2/s). - It represents the
**rotational analogue**to linear momentum, and is determined by an object’s rotational mass (moment of inertia) and rotational velocity. - Calculating angular momentum involves multiplying the object’s
**moment of inertia***(I)*by its**angular velocity***(ω)*. *L = Iω*, where*L*represents angular momentum,*I*the moment of inertia, and*ω*the angular velocity.

## The Principle of Conservation of Angular Momentum

- The principle of conservation of angular momentum states that the
**total angular momentum**of a closed system remains constant unless acted upon by an external torque. - This principle applies whether the system is at
**rest**or in**uniform circular motion**. - It’s important to note that angular momentum is
**conserved**, not constant for each individual component in the system. **Changes in mass distribution or angular velocity**within the system can change the angular momentum of individual components, but the total angular momentum of the system remains constant.

## Angular Momentum and External Torques

- An
**external torque**can change the total angular momentum of a system. - To calculate it, multiply the force causing the rotation (torque) by the time over which it acts.
- The change in angular momentum equals the external torque times time (
**ΔL = T external * Δt**).

## Real World Application of Angular Momentum

- The principle of conservation of angular momentum can be seen in many real-world situations such as spinning ice skaters pulling in their arms to spin faster.
- Other applications include stars shrinking and spinning faster, or planets orbiting more quickly when they are closer to their star due to the moment of inertia decreasing.

## Angular Momentum Practice Problems

- Give yourself time to practice and hone your understanding of mechanics problems involving angular momentum and its conservation.
- This could include examples such as: a disk rotating about its center, two particles rotating about a common point, or a rigid body rotating about a fixed axis.
- Use the formulas and principles discussed to solve these problems.

By consolidating a thorough understanding of angular momentum and its conservation, you can answer complex and intricate physics problems with ease.