Oooops, an obvious typo!
SUM(Ri x Vi) should be: SUM {Mi(Ri x Vi)}
-Bob Sciamanda
----- Original Message -----
From: "Bob Sciamanda" <trebor@WINBEAM.COM>
To: <PHYS-L@LISTS.NAU.EDU>
Sent: Tuesday, March 15, 2005 1:54 PM
Subject: Re: conservation of angular momentum question
|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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