I would point out that the (mechanical) angular momentum of a system can
always be written as an "orbital " plus a "spin" term. The spin term is
truly a property of the system, since it is defined relative to the center
of mass as "origin". Further, one need not use the CM for the origin of
both positions (Ri) and velocities (Vi) in calculating
L(spin) = L(cm) = SUM(Ri x Vi).
In fact if one chooses one space point A for the origin of position vectors
and a second space point B for the origin of velocity vectors (ie the origin
for position vectors whose time derivatives are the velocity vectors), one
can show that the spin angular momentum is independent of the choices for A
and B, so long as one (or both) of them is chosen to be the system center of
mass. (IE, either the CM is the origin of the Ri and/or the Vi are
calculated relative to the CM frame.)
Bob Sciamanda
Physics, Edinboro Univ of PA (Em) http://www.winbeam.com/~trebor/
trebor@winbeam.com
----- Original Message -----
From: "Leigh Palmer" <palmer@SFU.CA>
To: <PHYS-L@LISTS.NAU.EDU>
Sent: Tuesday, March 15, 2005 11:34 AM
Subject: Re: conservation of angular momentum question
| . . .
| 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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