When an object is both translating and rotating, we need to incorporate the kinetic energy of both of these motions, K = ½ mv² + ½ Iω², into energy conservation.

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

1. Define/draw system: Include both objects and coordinates.
2. 0 Choose consistent zero of the potential energy.
3. 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
4. Losses: Incorporate if needed.
   
   E_f = E_i - losses