Editing Kinetic energy (section)

===Rotating bodies===
If a rigid body Q is rotating about any line through the center of mass then it has [[rotational energy|''rotational kinetic energy'']] (<math>E_\text{r}\,</math>) which is simply the sum of the kinetic energies of its moving parts, and is thus given by:

<math display="block">E_\text{r} = \int_Q \frac{v^2 dm}{2} = \int_Q \frac{(r \omega)^2 dm}{2} = \frac{\omega^2}{2} \int_Q {r^2}dm = \frac{\omega^2}{2} I = \frac{1}{2} I \omega^2</math>

where:
* ω is the body's [[angular velocity]]
* ''r'' is the distance of any mass ''dm'' from that line
* <math>I</math> is the body's [[moment of inertia]], equal to <math display="inline">\int_Q {r^2} dm</math>.

(In this equation the moment of [[inertia]] must be taken about an axis through the center of mass and the rotation measured by ω must be around that axis; more general equations exist for systems where the object is subject to wobble due to its eccentric shape).