Rotational Kinetic Energy

The kinetic energy of rotation of a rigid body is obtained by first dividing it up into a collection of smaller masses, and then summing up the kinetic energies due to the tangential velocities of the individual masses making up that rigid body:

$$\sum {1\over 2}$$ KE_r =

$$\sum {1\over 2} \omega^{2}_{} {1\over 2} \omega^{2}_{} \sum$$ =

$${1\over 2} \omega^{2}_{}$$ = (12)

Note: The units of rotational kinetic energy are Joules (J).

When considering the total mechanical energy of a rigid body, this kinetic energy must be added to the kinetic energy of translation:

$${1\over 2}$$ (13)

where v_cm is the velocity of the center of mass.