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

• From: Leigh Palmer <palmer@SFU.CA>
• Date: Thu, 17 Mar 2005 08:53:21 -0800

(I'm sorry for the subject line screwup. I've changed it back. I get
the digest version of phys-l and I'm not as careful as I should be.)

On 17-Mar-05, at 1:00 AM, Bob Sciamanda wrote:

Leigh wrote:

I am confused by this. The general definition of the angular momentum
of a system of particles with respect to *any* point is given by your
expression. It is only necessary that all the Ri be relative to that
same point. The Vi are merely time derivatives of the Ri; they are
not
usually thought of as being related to an origin.

The rotational form of Newton's second law (Torque = dL/dt) is
applicable to
some few special circumstances in addition to that which uses a single
inertial "origin" for the calculation of torques and the particle
positions
and velocities in L (the angular momentum of the many particle
sysytem).

In particular, one can use an accelerating origin, A, for the
calculation of
torques, and the position vectors in L, if the velocities in L are
calculated relative to an inertial frame AND the velocity of A is
parallel/antiparallel to the velocity of the CM of the system.

Of course the rotational form of the second law to which you refer can
always be used with an accelerating origin provided one accounts for
torques due to so-called "frame forces"*. In those special choices of
origin for which frame forces produce zero net torque one may apply the
law thoughtlessly without suffering an error in the answer. However,
would it not be better to apply the law thoughtfully and recognize that
the frame force forces contribute zero net torque with proper choice of
origin? Is this so different from choosing any other origin because it
simplifies calculation?

Leigh further wrote:

I dislike this use of "spin" and "orbital" nomenclature. Consider the
example of two solar systems bound in orbit with one another (a
binary
stellar system) and you will see that the distinction is next to
useless.

You can easily show the many situations where this distinction is
useless.
I don't know where it started, but it is not uncommon and, of course,
has
found widespresd use in atomic system descriptions. I also recall an
astronomy book ascribing our night and day experience to the earth's
spin
angular momentum and the seasonal experience to the earth's orbital AM.

I'm going to reserve "spin" and "orbital" as nomenclature in atomic
physics**. In astronomy we use the terms "rotational" and "orbital"
angular momentum, and one could even be perverse and change the latter
to "revolutionary"! Rotation and revolution are distinct in our
lexicon. We would say (most incompletely) that night and day are
consequences of Earth's rotation and the seasons are due to the annual
revolution of Earth in a plane tilted with respect to its rotational
axis***.

As an astrophysicist, astronomy teacher, and indefatigable nit picker,
I am no longer shocked by deficiencies in textbooks. I have not run
across that one, but it doesn't surprise me. There exist worse examples

It is my feeling that the introduction of "spin" and "orbital"
designations for these two terms in the calculation is gratuitous. It
does not help the student to understand. Rather, from the student's
frame of reference, these are simply two more things he must remember.

Leigh

* As Einstein pointed out, these forces are no less real than gravity -
please do not refer to them as "fictitious" forces.

** I can still recall the first instance when a Brit seminar speaker
spoke without clarification of "RS coupling", which I had never heard
of. Had he said "LS coupling" or "spin-orbit coupling" I would have
known what he was talking about. Gratuitous variation in nomenclature
obstructs the transmission of information. (RS coupling is the same
thing as the others, but eponymously recognizes Russell and Saunders,
whom I have always assumed were two Brits.)

*** I'm not going to clean that up more. It's hard to state the
mechanism of the seasons in a sentence. One needs a physical globe, a
lamp to represent the Sun, and a spacious lecture platform.
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