Re: vibration vs. oscillation

[John Denker <jsd@AV8N.COM>]

Todd Pedlar wrote:
> A quibble on this statement, Carl.  Rotational energy is definitely
> not internal. Just as translational kinetic energy is not internal,
> because it is a BULK motion, so is rotational kinetic energy.

This is at best a quagmire.  Different people use the term
"internal" energy in different ways.  They should be allowed
to do so, without quibbles, as long as they clearly say
what they mean by the term.

1) In thermodynamics, as taught in the typical "physical
chemistry" class, the particles of interest are molecules
and the term "internal energy" conventionally refers to
the *entire* energy of the particles, and is denoted E
or U.  It includes rotational, vibrational, translational,
and other forms of energy.  I personally prefer to entirely
avoid the word  "internal" in this context, and just call
this quantity "the energy" ... or if emphasis is required,
"the plain old energy".

2) There is a theorem that says the energy of a system
of particles can be expressed as the sum of the KE of
the motion of the center-of-mass (relative to your chosen
reference frame) plus the KE of the particles relative
to the center-of-mass.

In this context, some authors choose to define the notion
of "internal" energy to be the energy measured in the frame
comoving with the CM.  It includes rotation and vibrational
energy, plus other contributions ... but not the bulk
motion of the CM relative to the lab frame.

> Internal energies must involve motion of constituents relative to
> other constituents, and can never involve common motion of the bulk
> body, as both translational and rotational motions do.
.               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The last bit is almost never true.  A very common and important
situation involves bulk translation, moving the CM without any
relative motion of the constituents.  Another very common and
important situation involves rotation, without any motion of
the CM.
 *) For molecules (with consitutuent atoms) the rotational
and vibrational modes conventionally are analyzed in the CM
frame.
 *) The same goes for a macroscopic object (with constituent
parcels of material) such as a bell.  Pick one:
  -- If you define "bulk" motion so that rotation of the bell
is considered bulk motion, then vibration is bulk motion also.
  -- Alternatively, if you define "bulk" motion so that
vibration is not bulk motion (perhaps because it leaves the
CM unaffected) then rotation is not bulk motion either.


As far as I can see, the only self-consistent way to put
vibration in one category and rotation in the other would
be to switch to a _rotating_ frame of reference, comoving
with the CM and corotating with the "bulk" of the system.
That's not necessarily unreasonable, but it requires an
unusual degree of sophistication, well beyond the scope
of intro physics courses ... so anybody who wants to do
that should give the readers a few words of warning or
explanation.

I'm certainly not going to quibble with anybody who puts
rotation and vibration in the same category.