# Angular Momentum, and its Conservation

I am confused as to how to reconcile the conservation laws of linear and angular momentum. Are they independent (and how can this be, if $$L = r$$ x $$p$$?) Does one supersede the other? In short: how are they related?

Moreover, the notion of conserving angular momentum seems a bit arbitrary to me, for $$L$$ itself seems to 'appear' upon us specifying a reference point. In other words, if I have a body moving in a straight line, then it has linear momentum, for it has both mass and velocity... this is a given. But, it will not have angular momentum, lest I specify a reference point. This seems a bit at odds with the theory that angular momentum cannot be created nor destroyed.

Lastly, if I wish to quantify the total momentum of a system $$S$$, how can this be done (maybe, $$S$$ = $$L_{body}$$ + $$p_{body}$$)? And will this value not change in accordance as to whether I have specified a reference point (paragraph 2)?

• note $\vec L + \vec p \rightarrow \vec L - \vec p$ under a parity transformation, so that would cause more problems than it would solve.
– JEB
Feb 5 '19 at 2:03

Linear momentum and angular momentum are independent conserved quantities for a closed system. The fact that $$\mathbf{p}$$ happens to appear in the definition of $$\mathbf{L}$$ does not matter.
You cannot add $$\mathbf{p}$$ and $$\mathbf{L}$$ together; they don’t even have the same units!