3.0 Relation between torque and angular momentum

3.1 Conservation of angular momentum

As we know, $$\overrightarrow \tau = I\overrightarrow \alpha $$ or $$\begin{equation} \begin{aligned} \overrightarrow \tau = I\frac{{d\overrightarrow \omega }}{{dt}} \\ \overrightarrow \tau = \frac{{dI\overrightarrow \omega }}{{dt}} \\\end{aligned} \end{equation} $$ As we know, $I\overrightarrow \omega = \overrightarrow L $ $$\overrightarrow \tau = \frac{{d\overrightarrow L }}{{dt}}$$

So, the rate of change of angular momentum of a body is equal to the external torque acting upon the body.