This question already has an answer here:
Working in 3-dimensions, if we are given a Lagrangian containing $N$ particles. Say, through Noether's theorem, we know that the sum of the linear momentum of all $N$ particles in each direction are constant. We also know that the sum of the angular momentum in each direction are constant.
My question is, if I know that linear momentum is conserved, can I actually automatically say that angular momentum is also conserved?