Re: vibration vs. oscillation

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 11:44 AM -0500 6/25/04, Todd Pedlar wrote:

> 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.  All parts of the object have the
> same angular
> velocity \omega.  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.
I'm not sure I agree with that characterization of rotational KE. A
rotating object will generate internal stresses that can be measured
without reference to any external indicators (this is extensive
objects only, not particles--I don't want to get into the quantum
mechanical aspects of spin). Thus it would be possible for us to
measure the rotational energy of the earth even if we couldn't see
the sun or any other external body. But without external references
we cannot measure our translational energy, which is always relative
to some other body (not strictly true because the earth's
translational motion includes a significant curvilinear component,
which could, in principle, be measured, but I suspect is well beyond
our earth-based capability).

Although I agree that rotational energy can be thought of as a bulk
property (but even though all parts of a rotating object may have the
same angular velocity they do not have the same moment of inertia,
and so the energy is not uniformly distributed throughout the
object), I still think of it as part of its internal energy because
it is intrinsic to a property which is independent of external
references. Consider the following example: a spherical shell, filled
with liquid is observed to be spinning. If you stop the spinning of
the shell, it will appear to have no rotational KE, even though the
liquid inside is still spinning for some time (depending on its
viscosity), as can readily be demonstrated by releasing the
constraint on the shell, as in the egg demo that Herb talked about a
couple of days ago in another context.

I agree that it's probably a close call, but I think I have to come
down on the side of considering rotational KE as an "internal"
property; I hesitate to call it an "internal degree of freedom" but
that may be a reasonable way to put it.

Hugh
--

Hugh Haskell
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<mailto:hhaskell@mindspring.com>

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