As an illustration, if a physical system behaves the same regardless of how it is oriented in space (that is, it's invariant), its Lagrangian is symmetric under continuous rotation: from this symmetry, Noether's theorem dictates that the angular momentum of the system be conserved, as a consequence of its laws of motion. The physical system itself need not be symmetric; a jagged asteroid tumbling in space conserves angular momentum despite its asymmetry. It is the laws of its motion that are symmetric.