Conservation of Angular Momentum

From the angular impulse-momentum theorem, the net external torque on a system relates to the change in angular momentum of the entire system. If the net external torque is zero over a time interval, then the angular impulse is zero:

$$\vec{J}_\text{rot} = \vec{\tau}_{\text{net, ext}} \Delta t = \vec{0}$$

This means the change in angular momentum is zero:

$$\Delta \vec{L} = \vec{0}$$

Therefore, angular momentum remains constant:

$$\vec{L}_{\text{initial}} = \vec{L}_{\text{final}}$$

This is the condition for conservation of angular momentum: the net external torque on the system must be zero.

Internal vs. External Torques

Internal torques arise from forces between objects within the system. By Newton's third law, these occur in equal and opposite pairs. They cannot change the system's total angular momentum.

External torques come from agents outside the system boundary. Only these can change the total angular momentum.

Checking Conservation

To determine if angular momentum is conserved:

(1) Define your system boundary.

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