rotational kinetic energy
Anything that spins carries energy purely because it is spinning — that is rotational kinetic energy. A spinning flywheel, a turning grindstone, a rolling bowling ball: each stores real, usable energy in its rotation, quite apart from any energy it has from moving from place to place. It is ordinary kinetic energy, just added up over all the little pieces whizzing around the axis.
Precisely, rotational kinetic energy is K_rot = 1/2 I omega^2, where I is the moment of inertia and omega is the angular velocity. Set it beside the familiar K = 1/2 m v^2 and the parallel is exact: the moment of inertia plays the part of mass, and angular velocity plays the part of speed. The units are joules (J), like all energy. An object that is both moving and spinning — a rolling wheel — carries the sum of both: K = 1/2 m v^2 + 1/2 I omega^2.
This matters whenever spinning things trade energy: a ball rolling down a ramp shares its energy between sliding and spinning, so it reaches the bottom slower than a frictionless block; a flywheel in a bus or a power plant banks energy in its spin to release later. Whenever you use conservation of energy on a rolling or turning object, the rotational term must be in the ledger.
A disk with I = 0.09 kg m^2 spins at omega = 20 rad/s. Its rotational kinetic energy is K_rot = 1/2 I omega^2 = 1/2 x 0.09 x 400 = 18 J — enough to keep it doing useful work as a flywheel.
The same 1/2 (inertia)(speed)^2 recipe as linear kinetic energy, in rotational clothing.
Rotational kinetic energy is not a new kind of energy; it is just kinetic energy, counted piece by piece over a spinning body. A rolling object has both translational and rotational parts.