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Re: PHYS-L Digest - 1 Feb 2004 to 3 Feb 2004 (#2004-34)

Even if you lift out of the air the conservation of gratuitously defined
energy (K + P) and momentum, how do you arrive at the existence of an
orbital trajectory without (gratuitously) adding the stipulation that the
momentum exchange is central? This is tantamount to introducing the central
force concept.

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
----- Original Message -----
From: "Bob Sciamanda" <trebor@VELOCITY.NET>
To: <>
Sent: Tuesday, February 03, 2004 9:40 AM
Subject: Re: PHYS-L Digest - 1 Feb 2004 to 3 Feb 2004 (#2004-34)

I would comment that this is an instance of the weakness (incompleteness?)
of attempts to bypass the force concept and begin with (and be confined
energy/momentum concepts (lifted out of the air). To me, the force
(embodied in all three N laws) is the indispensible root basis of

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
----- Original Message -----
From: "Brian Blais" <bblais@BRYANT.EDU>
To: <>
Sent: Tuesday, February 03, 2004 9:26 AM
Subject: Re: PHYS-L Digest - 1 Feb 2004 to 3 Feb 2004 (#2004-34)

On Tue, 3 Feb 2004, Automatic digest processor wrote:

Quoting Brian Blais <bblais@BRYANT.EDU>:

I was wondering if anyone knew of a calculation showing that the
energy of an object in a circular orbit is equal to half of the
energy, where the calculation does *not* use acceleration or force
Is there an argument for this based purely on energy concepts?

0) Be careful, the result as stated only applies to objects
orbiting in a 1/r potential (although generalizations are
possible to other power laws).

I was assuming a gravitational situation, and wasn't clear in my

1) Certainly it is possible to derive the viral theorem
without mentioning acceleration. The standard derivations
don't mention it. Indeed you don't need to know the masses
of the particles involved.

Look at
about halfway down, in the section called "the proof".

Actually, this derivation refers to force. Perhaps I should have asked,
the simple case of a 1/r potential, one small mass orbitting a much
one, is there a simple way of obtaining the KE=1/2 PE relationship?

3) Why do you care, anyway? If you know the potential,
you implicitly know the force, and conversely if you know
the conservative force you implicitly know the potential,
plus or minus an arbitrary gauge term.

Good question! I teach an algebra-based, 1-semester intro physics
This course has no prerequisites, is not followed by further physics
and may be (perhaps) the last science class the students will ever take.
such, it doesn't fit into the mold that most textbooks use. Because of
limited time, I have to be very selective in the topics that I can
Others would perhaps disagree with my choices, but I am certainly open
considering other options. I found that covering energy and momentum,
much in 1-D, was a way that I could link classical physics, relativity
quantum mechanics without introducing a huge number of new concepts each
time. I found that vectors took too long to cover well, so I don't
force at all: everything is in terms of energy. I do cover
I am trying to see if there is any way I can get away without that to.
example, I can cover near-surface gravitational potential energy,
denoted U=mgh, without mentioning that "g" is an acceleration by writing
it in
units of J/(m*kg), and describing it as the energy needed to lift 1 kg 1
high. Accleration can also be covered in terms of changes in momentum
time, which of course is equivalent to the standard kinematic way of
describing acceleration.

I feel that if there are only a few rules, conservation of
energy/momentum/etc., used in many different circumstances, then the
will gain an appreciation for the *simplification* that physics

Kepler's law, which is high on my list of priorities to teach, is
derived from acceleration and force, and not with energy. If I had a
derivation of the KE=1/2 PE relationship, then Kepler's law follows
straightforwardly. Lacking this, I could decide not to teach Kepler's
cover enough of the other concepts (acceleration due to gravity, and
force) to
come up with Kepler's law, or assert the KE = 1/2 PE relation is either
empirical or "has a derivation beyond the scope of the class".


Brian Blais