Quite a few text books separate internal kinetic energy and external kinetic
energy in the following way...
external KE = KE of center of mass = 1/2 M v(cm)^2 where M is the total mass
and v(cm) is the velocity of the center of mass.
internal KE = KE relative to center of mass = sum of (1/2 m v(rel)^2) where
m is the mass of each atom and v(rel) is the velocity of each atom relative
to the center of mass.
Total KE = internal KE plus external KE.
Note, each v(rel) would be assumed to be an instantaneous velocity. If so,
then the internal KE summation will include translational, rotational, and
vibrational KE of atmoms/molecules just like it should. However, the
external KE as defined above would not include any rotational KE of the
overall object. It seems rotational energy of the entire object would be
included in the internal KE calculation.
Then, if thermal energy is then equated to internal KE, as defined
above,(and this is often done), then it seems the flying golf ball could
have additional internal KE because of its flight if the ball is spinning.
But we typically would not want to include rotational energy of the whole
object as part of thermal energy, so it appears to me we have a problem
equating thermal energy with internal KE energy if internal KE is the KE
relative to the center of mass. But I have textbooks on my shelf that do
this.
Another way to approach thermal energy is f/2 k T where f is degrees of
freedom of the consituent atoms/molecules and k is Boltzman's constant and T
is absolute temperature. With this definition the only way the flying golf
ball would have increased thermal energy would be what it got from the
interaction of the golf club with the ball when the ball was hit.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817