On 15-Mar-05, at 1:00 AM, John Denker wrote (out of context):
I say angular momentum always obeys a local conservation
law. No exceptions.
Let's beat that one to death with a stick. It would be a great mistake
to think that angular momentum is, like electric charge, a locally
conserved quantity. It is not.
Let's put aside considerations of electrodynamics and intrinsic angular
momentum. Consider only the mechanical angular momentum of a system of
particles. If the sum of external torques *with respect to a point in
space* acting on a system is zero, the angular momentum of the system
*with respect to that same point* is conserved. Angular momentum is a
canonical quantity which has a useful meaning only when calculated
according to rule. The rule is simple, but it does require the
selection of a specific point in space as a center. One should probably
not call this the "origin" because it frequently happens that a more
convenient center can be chosen if one already has chosen an origin of
coordinates. This can be a useful tool when insufficient information is
available about some force. One can simply recenter the canonical
angular momenta and torques about a point through which that force
acts(*). We have all seen this done in static ladder problems, for
example.
I tell my students that their symbols for torque and angular momentum
in classical mechanics problems should always be subscripted to
emphasize this canonical nature. It is also a good idea to get away
from defining angular momentum with respect to an axis (or axle) as
soon as it is possible to do so. While this small white lie is
applicable in many problems, the really interesting ones are rendered
mysterious by it.
Of course since angular momentum is a canonical quantity (i.e.
calculated according to a conventional rule) it has no absolute meaning
and thus no local meaning.
Leigh
* For an extreme example of multiple "recentering" of canonical
angular momentum see Tad McGeer and Leigh Hunt Palmer, Wobbling,
toppling, and forces of contact, AJP 57, 1089-1098 (1989).
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