# 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.