Here are two versions of the conservation of angular momentum.
- The total angular momentum is constant if there is no external moment on the system
- The total angular momentum of a particle is constant if it is only under the influence of a conservative force with the potential function $V (\mathbf x)$ invariant under rotations. (i.e. $dV/d\theta=0$ in the case of two-dimensional space)
I am perplexed about how different those statements are. Of course "no external force" does not mean all forces are conservative. Are those two versions of angular momentum conservation related, or are they just two independent, unrelated statements?
Also please point out any inaccurate statements there.
What I have noticed is that both statements imply Kepler's 2nd law.