1.4 Torque equation

1.1 Torque or moment of a force
1.2 Relation between torque and moment of inertia
1.3 Pseudo torque
1.4 Torque equation
1.5 Principal of moments

2.1 For better understanding angular momentum is classified as following four types,

3.1 Conservation of angular momentum

5.1 Total kinetic energy of a rigid body in a combined translational and rotational motion

8.1 Geometrical method
8.2 Relative velocity method

Torque equation is the vector sum of all the torques due to every force about an axis of rotation.

Let us consider a rigid body which is subjected to $n$ number of forces. These forces produces torque $\left( {{{\overrightarrow \tau }_1},{{\overrightarrow \tau }_2}...,{{\overrightarrow \tau }_n}} \right)$ about an axis of rotation as shown in the figure.

Mathematically, $${\overrightarrow \tau _{net}} = {\overrightarrow \tau _1} + {\overrightarrow \tau _2} + ... + {\overrightarrow \tau _n}$$

The net torque $\left( {{{\overrightarrow \tau }_{net}}} \right)$ produces an angular acceleration $\left( {\overrightarrow \alpha } \right)$ about an axis of rotation whose moment of inertia is $I$.

So, $${\overrightarrow \tau _{net}} = I\overrightarrow \alpha $$ or $$I\overrightarrow \alpha = {\overrightarrow \tau _1} + {\overrightarrow \tau _2} + ... + {\overrightarrow \tau _n}$$