[Phys-L] Re: conservation of angular momentum question

["John S. Denker" <jsd@AV8N.COM>]

On 03/15/05 13:54, Bob Sciamanda wrote:
> 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)


That's all true ... but it is open to serious misinterpretation
by non-experts.

We should hasten to remind people that while "the" angular
momentum strictly obeys a local conservation law, neither
the spin angular momentum nor the orbital angular momentum
are separately conserved ... so although you can talk spin
AM and orbital AM being properties of the system for the
totality of an *isolated* system, it is risky to talk about
them for subsystems.

To illustrate what I mean, consider a disk with a popgun
mounted on its rim, aimed tangentially.  The system is
floating in free space, initially rotating, with zero
CoOM velocity in the lab frame.  Here CoOM stands for
"Center of its Own Mass".

Now the popgun is fired.  The cork goes flying away.  The
cork, considered as a subsystem unto itself, has zero
spin angular momentum.  Also, we have adjusted the popgun
so that firing the cork provides just enough impulse
to exactly arrest the rotation of the wheel.  The wheel,
which was spinning but not moving, is now moving but
not spinning.  The CoOM of the wheel (considered as a
subsystem unto itself) moves in a direction antiparallel
(but not colinear) with the motion of the cork.

The overall system has the same AM, and the same spin
AM as before, but the wheel (considered as a subsystem)
has lost its spin AM, and this did not show up as
spin AM in the cork (considered as a subsystem).

"The" angular momentum is one of the central ideas, one
of the pillars of physics.  In contrast, the partition
into "spin" and "orbital" AM is more in the nature of
a convenience.
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