Re: [Phys-l] energy is well defined

[John Denker <jsd@av8n.com>]

On 02/22/2008 08:08 PM, Jeffrey Schnick wrote:

> I think that KE being energy of a system in the way PE is energy of a
> system and not an individual particle is reasonable model.  In this
> model, what is typically referred to as the kinetic energy of a system
> due to the motion of the center of mass of a system through space in
> reference frame O is always just one part of the energy of a larger
> system whose center of mass is at rest in reference frame O. 

I'm skeptical that such a model is "reasonable".

There are many applications (such as baseball) where it is
quite impossible to restrict attention to "the" system.
Instead, it is necessary to pay attention to various subsystems.
In the frame of the ball, the ball has zero KE.  In the frame
of the bat, the bat has zero KE.  But those zeros do not well
describe the physics of a batted ball.

As a fancier example, consider fluid dynamics.  It is quite 
impossible to restrict attention to "the" system.  Instead, 
it is necessary to pay attention to a great many subsystems 
(such a N different parcels of fluid).  It is necessary that 
the conservation laws apply to each subsystem separately. 
Using N different reference frames for the N different 
subsystems is actually possible, but it is fiendishly
complex, far more complex than the usual formulation that 
allows subsystems to be moving relative to a given reference
frame.

To say the same thing more formally:  The choice of reference
frame is a free choice the *first* time you choose, but 
thereafter it is not free at all.  There is a steep price
to be paid if different subsystems are using different
reference frames.

=============

It is important for students to be able to use models in which
the KE is nonzero.  It is important for students to be able to
handle situations where there are multiple subsystems.

In simple cases it may be convenient to choose a frame where
"the" KE is zero, but this is definitely not the general case.