Law of conservation of angular momentum

Definition

The law 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 principle is crucial in understanding rotational dynamics.

5 Must Know Facts For Your Next Test

1. Angular momentum is given by the product of the moment of inertia and angular velocity: $L = I \omega$.
2. In an isolated system with no external torques, the initial angular momentum equals the final angular momentum: $L_{initial} = L_{final}$.
3. This law can be observed in various phenomena such as a spinning figure skater pulling in their arms to spin faster.
4. External torques can change the angular momentum of a system; internal forces cannot.
5. Conservation of angular momentum explains why planets continue to orbit stars without needing an external force.

Review Questions

• What is the mathematical expression for angular momentum?
• How does an external torque affect a system's angular momentum?
• Give an example where conservation of angular momentum is clearly observed.

Related terms

Torque: A measure of how much a force acting on an object causes that object to rotate. It is given by $\tau = r \times F$.

Moment of Inertia: A measure of an object's resistance to changes in its rotation rate, dependent on mass distribution relative to the axis of rotation.

Angular Velocity: The rate at which an object rotates or revolves around another point, expressed in radians per second ($\omega$).