Angular momentum is conserved when there is no net external torque acting on a system. This means that the total angular momentum of a system remains constant if no outside forces cause it to twist or rotate. In other words, angular momentum is conserved in a closed system where the net torque is zero. This principle is analogous to the conservation of linear momentum, which holds when there is no net external force. For angular momentum conservation, the formula is expressed as:
- L=IωL=I\omega L=Iω, where LLL is angular momentum, III is the moment of inertia, and ω\omega ω is the angular velocity.
- Conservation means L=constantL=\text{constant}L=constant or L=L′L=L'L=L′ when the net external torque τ\tau τ is zero.
Therefore, if no external torque acts on an object or system, its angular momentum does not change. Examples include an ice skater spinning with arms pulled in to spin faster (moment of inertia decreases, so angular velocity increases to keep angular momentum constant), a gyroscope maintaining stability, or Earth's rotation changing very slowly due to minimal external torque like tidal forces.
