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

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

In combined translation and rotational motion, the total kinetic energy $(K)$ of a rigid body is sum of the translational kinetic energy $\left( {{K_T}} \right)$ and the rotational kinetic energy $\left( {{K_R}} \right)$ $$\begin{equation} \begin{aligned} K = {K_T} + {K_R} \\ K = \frac{1}{2}mv_{com}^2 + \frac{1}{2}I{\omega ^2} \\\end{aligned} \end{equation} $$

where,

${v_{com}}$: Velocity of centre of mass

${I_{com}}$: Moment of inertia about an axis of rotation

$\omega $: Angular velocity about an axis of rotation

In the above case the axis of rotation is at the centre of mass. Therefore, $$K = \frac{1}{2}mv_{com}^2 + \frac{1}{2}{I_{com}}{\omega ^2}$$