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Re: [Phys-l] teaching energy +- reference frames



I think the answer depends on what level of models you wish to use. If you
are restricted to Newtonian mechanics, then E_k will not be independent of
the frame of reference. But E_g is also not independent of the reference
frame. E_k depends on the origin of the velocity frame, and E_g depends on
the origin of the position frame. But conservation of energy still applies
in all frames, so the energy transferred is the same.

Of course these are not questions that should be tackled at the beginning
level of physics. They should only be tackled after the student has
acquired a clear view of what goes on in a single inertial frame, namely the
lab frame. Then the idea of using other frames such as the CM frame... can
be readily tackled.

The centrifugal force problem needs to be approached carefully. If students
are introduced to interactions and the idea that forces are ONLY exerted by
other objects, then there is no centrifugal force as commonly invoked. It
has to be called something else such as a pseudoforce, imaginary force, ...
My favorite is virtual force because students relate to the term. This is
one area where Modeling is weak and Minds on Physics is strong. MOP hits
interactions very hard. There is evidence that introducing NTN3 and
interactions first improves understanding of NTN3.

Of course what is frame independent is the process of energy or momentum
transfer. Understanding this is a very tall order for students. In
Newtonian mechanics forces and acceleration are also frame independent. The
impulse and the working are also independent. Of course all of this changes
when you go to relativistic mechanics, as JD already pointed out. But your
question was about Newtonian mechanics, so again it depends on what level of
sophistication of model you are using.

BTW when asking for a response John could be more than one person. JD and
JC have now both responded. If the other JC at U. Mass Amherst joins things
could really be confusing.

John M. Clement (JMC)
Houston, TX


KE requires a frame of reference ... but the frame doesn't matter.

Students should understand that the laws of physics are independent
of the choice of reference frame. This is important ... arguably
about as important as the idea of energy itself.

I like to say that if you get an answer that is frame-dependent, you
were asking the wrong question ... or at best a not-very-fundamental
question. There must be a frame-independent way of restating the
important part of the question.

To piggyback off of this response (which is kind of where I thought Dan
MacIsaac would go next), I'm interested in this whole idea of choice of
frame and the results that derive from the choice:

If I'm reading this correctly, John (or whoever wants to jump in), should
we
expect answers to be frame independent as a general rule for Newtonian
physics? Should the calculation of KE be consistent regardless of frame?
If so, of course, this would pretty much require energy to "reside" in a
system of particles (since performing the calculation on an object could
yield a different answer - Dan's example). But DO we require that? And
what of the previous LONG discussion regarding centrifugal force wherein
this force only appears in SOME frames and not in others? Wouldn't a
demand
that answers be the same in any frame be tantamount to asking what is the
answer "really"; much as my asking which are "real" forces? If answers
should/must be frame independent, what characteristics are we talking
about?
Forces? Momentum? Energy?




This is a tricky pedagogical problem, because it arises only at
_intermediate_ levels of sophistication. The most unsophisticated
students will just pick a frame -- the lab frame -- and will not be
concerned with the possibility that "KE requires a frame". At the
other extreme, sophisticated students will know how to talk about
energy in terms that are manifestly invariant w.r.t the choice of
frame (four vectors and all that). We can discuss the details if
anyone is interested.

========

One very common way to generate frame-dependent and therefore non-
fundamental questions is to ask for the _components_ of a vector
in a particular frame.

In my mind, it is very important to distinguish between a vector
and the components that represent that vector in a particular
frame. Similarly it is important to distinguish between an
operator (e.g. tensor) and the matrix elements that represent
that operator in a particular basis.

I know this is a sophisticated distinction. I remember reading
about it as a youngster and not appreciating it until years later.

The terminology on this point is messed up, which creates further
barriers to understanding. For more discussion of this, see
http://www.av8n.com/physics/two-vector.pdf

There exist vectors that have geometric and physical reality
*independent* of the choice of basis ... vectors with tip and
tail, vectors with direction and magnitude.

It is important to be able to switch back and forth between
the geometric viewpoint and the component viewpoint. Neither
should be allowed to ride roughshod over the other.

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l