Kinetic energy is the energy associated with motion. Rotational kinetic energy is associated with rotational motion and is given by: K = ½ Iω2
Notice the similarity with the kinetic energy of linear motion: K = ½ m v2
The expression K = ½ Iω2 for a rotating object follows directly by breaking up the object into infinitesimal subunits and summing the translational kinetic energy of each subunit (see transparency).
The total kinetic energy is: K = ½ m v2 + ½
Iω2.