The kinetic energy of a body spinning about an axis — it depends on the moment of inertia and the square of the angular velocity.
Symbols
E
rotational kinetic energy
[J]
I
moment of inertia
[kg·m²]
ω
angular velocity
[rad/s]
Where it comes from
The counterpart of kinetic energy for rotation — the role of mass is played by the moment of inertia I, and that of velocity by the angular velocity ω. A rolling ball has both translational and rotational energy.
When to use it
Spinning rigid bodies: wheels, disks, tops.
Example
A disk with moment of inertia I=0.5 kg·m² spins at ω=4 rad/s. Calculate the energy.