Is Angular Momentum Always Conserved with a Rotation-Invariant Lagrangian?

[quasar987]

I have this question here from last year's exam that goes

"Use Noether's theorem to show that the angular momentum is conserved when the lagrangian is invariant under rotations."

I just want to know if this is true in the most general case, or if there are some restrictions somewhere not mentioned in the question.

Thank you.

 

[dextercioby]

Yes, you'd have to check for infinitesimal rotations.