Define angular acceleration and torque. Establish the relation between angular acceleration and torque.

Angular acceleration: The rate of change of angular velocity is called angular acceleration.
$\therefore \mathrm{\alpha }=\frac{\mathrm{dw}}{\mathrm{dt}}$
Torque : The rate of change of angular momentum is called torque.
$\therefore \mathrm{\tau }=\frac{\mathrm{dL}}{\mathrm{dt}}\left(\text{ or }\right)\mathrm{\tau }=\overline{\mathrm{r}}\times \overline{\mathrm{F}}$
Relation between $\mathrm{\alpha }$ and $\mathrm{\tau }$ :
Consider a rigid body of mass m rotating in a circular path of radius ‘r’ with angular velocity ’w’ about fixed axis by definition $\begin{array}{c}\mathrm{\tau }=\frac{\mathrm{dL}}{\mathrm{dt}}\\ (\because \mathrm{L}=\mathrm{Iw})\end{array}$
$\begin{array}{l}\Rightarrow \mathrm{\tau }=\frac{\mathrm{d}\left(\mathrm{Iw}\right)}{\mathrm{dt}}(\because \text{ where I }=\text{ moment of inertia) }\\ \Rightarrow \mathrm{\tau }=\mathrm{I}\frac{\mathrm{dw}}{\mathrm{dt}}\left(\because \frac{\mathrm{dw}}{\mathrm{dt}}=\mathrm{\alpha }\right)\Rightarrow \mathrm{\tau }=\mathrm{I\alpha }\end{array}$