Angular Impulse ($\vec{J}_{\text{rot}}$, sometimes $\vec{J}_\theta$, $\vec{H}$, or simply 'angular impulse'), is a vector quantity defined as the product of an average torque ($\vec{\tau}_{\text{avg}}$) and the time ($\Delta t$) that the torque is exerted over.

The magnitude of angular impulse, $J_{\text{rot}}$, depends on the strength (magnitude) of the torque $\tau_{\text{avg}}$ and the length of time $\Delta t$.

$$J_{\text{rot}} = \tau_{\text{avg}} \Delta t$$

In real-world scenarios like collisions or explosions, torques often vary rapidly. Instead of tracking the changing torque, we use the average torque $\vec{\tau}_{\text{avg}}$. This constant value makes calculation manageable while representing the same total physical effort delivered over the time $\Delta t$. Often we will drop the average label and just refer to it as torque $\vec{\tau}$.