Formula Rigid body Rotational energy Angular velocity Moment of inertia
$$W_{\text{rot}} ~=~ \frac{1}{2} \, I \, \class{red}{\omega}^2$$ $$W_{\text{rot}} ~=~ \frac{1}{2} \, I \, \class{red}{\omega}^2$$ $$\class{red}{\omega} ~=~ \sqrt{ \frac{ 2W_{\text{rot}} }{ I } }$$ $$I ~=~ \frac{ 2 W_{\text{rot}} }{ \class{red}{\omega}^2 }$$
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
\( I \) 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.