Is there a physical connection between Action and Angular Momentum?

[LarryS]

The Principle of Stationary Action plays a role in Classical Physics (Lagrangians), Quantum Mechanics and QED (phase), GR (geodesics of maximum Proper Time) and apparently even in String Theory. Action and Angular Momentum share the same units. Other than sharing units, is there a real physical connection between Action and Angular Momentum? As always, thanks in advance.

 

[Dr.D]

Not really.

 

[Peeter]

If one can find symmetries in the Lagrangian (changes of variables that leave it unchanged), then the chain rule in a form known as Noether's theorem can be used to find conserved quantities.

For example, a rotation of coordinates for a Lagrangian that has a kinetic energy and central potential (ie: Newtonian gravity) can be used to show that angular momentum is conserved. An example of this can be found in Tong's classical physics notes here:

http://www.damtp.cam.ac.uk/user/tong/dynamics.htm

 

[Cantab Morgan]

Action and Angular Momentum share the same units.

Yeah, that wigs me out a little. What about torque and energy having the same units?

 

[Vanadium 50]

Be careful. They share the same dimensions, not the same units.

 

[Cantab Morgan]

Be careful. They share the same dimensions, not the same units.

Hi Vanadium 50. Could you elaborate a bit please? I've never heard of a distinction.

 

[LarryS]

Hi Vanadium 50. Could you elaborate a bit please? I've never heard of a distinction.

I believe I see Vanadium 50's point. Energy is Force dot Distance whereas Torque is Force cross Distance. Which indirectly answers my original question regarding Action and Angular Momentum sharing the same "units". Action is a pure scalar whereas Angular Momentum is a vector. So, when one takes into account the geometry of the situation, dimensions and units may not be the same thing.