When an object is both translating and
rotating, we need to incorporate the kinetic
energy of both of these motions, K = ½ mv^{2} + ½
Iω^{2}, into energy conservation.

With this more complete form of kinetic energy, we can still apply: DOEL for solving energy conservation problems.

- Define/draw system: Include both objects and coordinates.
- 0 Choose consistent zero of the potential energy.
- Energy conservation
statement:

E_{f}= E_{i}

K_{f}+ U_{f}= K_{i}+ U_{i}

U_{i}- U_{f}= K_{f}- K_{i}

- Δ U = Δ K - Losses: Incorporate
if needed.

E_{f}= E_{i}- losses