Formula Rigid body Rotational energy Angular velocity Moment of inertia
$$W_{\text{rot}} ~=~ \frac{1}{2} \, \class{brown}{I} \, \class{red}{\omega}^2$$ $$W_{\text{rot}} ~=~ \frac{1}{2} \, \class{brown}{I} \, \class{red}{\omega}^2$$ $$\class{red}{\omega} ~=~ \sqrt{ \frac{ 2W_{\text{rot}} }{ \class{brown}{I} } }$$ $$\class{brown}{I} ~=~ \frac{ 2 W_{\text{rot}} }{ \class{red}{\omega}^2 }$$
Rotational energy
$$ W_{\text{rot}} $$ Unit $$ \mathrm{J} $$ The rotational energy is the part of the energy that a rigid (non-deformable) body has when it rotates around an axis.
Angular velocity
$$ \class{red}{\omega} $$ Unit $$ \frac{\mathrm{rad}}{\mathrm s} $$ The angular velocity indicates the angle traveled per time.
Moment of inertia
$$ \class{brown}{I} $$ Unit $$ \mathrm{kg} \, \mathrm{m}^2 $$ Moment of inertia depends on the mass and distance from the axis of rotation and acts like a resistance to rotation.