Angular momentum is defined with respect to a certain origin, right? Well, what's stopping me from changing my origin ever so slightly, so that the angular momentum changes ever so slightly?
Oh fair enough ... though if I measure angular momentum, then use identical apparatus in a different position (i.e. translated, but not rotated) on the same particles, doesn't that just give the same measurement? In fact, would we normally expect a mere translation of axis to change the projections of a vector? Wouldn't a rotation, instead, be more illustrative for OPs question? Or maybe I have the wrong question?We're not talking about a rotation, the question posed was, what happens to L under a translation?