All (classical) Perpetual Motion machines are IMPOSSIBLE. Angular momentum, linear momentum, and energy are SEPARATELY conserved. There is a more general way of seeing this.

All the laws of classical mechanics are implied by Lagrange's Equations. [Look it up.]
Noether's famous theorem states that:
1. If a system is a system is translation invariant, then all three components of linear momentum are conserved;
2. If a system is time invariant, then energy is conserved;
3. If a system is rotation invariant, then all three components of angular momentum are conserved.
#2 above implies that energy is conserved and cannot be extracted from any system, so long as the system is time invariant.