Rotational Kinetic Energy

The Kinetic Energy for translational motion is . Translating that to Rotational Motion, we get:

Where is Rotational Inertia or Moment of Inertia.

We can derive this:

For an object experiencing both translational and rotational motion, such as a circle rolling down a slope, the kinetic energy is just the combination of both.

where is the center of mass of the object.

For an object moving about another object moving about an axis, to find the kinetic energy, we would just find the kinetic energy of both, similar to before.