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Re: [Phys-l] Sharing a problem for students

Dec 24, 2007, at 10:56 AM, Bob Sciamanda wrote:

Ludwik,
It might help to realize that the effective potential U(r) is more
than just a helpful visualization tool for the inertial observer
(helping him to abstract from the angular motion and consider only the
one-dimensional radial motion, It is also the actual view which a
rotating observer would take of the planet. The added term in U(r) is
precisely the potential energy which a rotating observer would ascribe
to the centifugal force which he sees affecting the radial motion of
the planet. The radial motion is all that he sees, since he rotates
along with the angular motion of the planet. The rotating observer
indeed sees one dimensional motion in a potential energy well - no
paradox here.

I would say that there is no paradox for the inertial observer either,
because he realizes that this is not one-dimensional motion. Looking
only at V(r) ignores the important complicating effects of the angular
motion.

Bob Sciamanda
Physics, Edinboro Univ of PA (Emeritus)
www.winbeam.com/~trebor
trebor@winbeam.com
----- Original Message -----
From: "Ludwik Kowalski" <kowalskil@mail.montclair.edu>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Monday, December 24, 2007 10:31 AM
Subject: Re: [Phys-l] Sharing a problem for students


On Dec 24, 2007, at 9:24 AM, Bob Sciamanda wrote:

. . .I still don't appreciate your sense of a "paradox" here.

Dear Bob,
1) What is the better word than paradox?
On one hand we know that the net force must be zero at a potential
minimum, on the other hand we know that the net force, G*M*m/r^2, is
not zero.
. . .

Thanks again, Bob. This was a very useful clarification. For a rotating observer the force directed away from the sun is real. Thus his claim that "a circular orbit is stable when the net force is zero" is justifiable. From his point of view, stability of the orbit radius results from a restoring force, just like in the case of a pendulum at rest. At r>R the restoring force is centripetal, for r<R the restoring force has the opposite direction (because the sign of the second effective potential term is positive).
_______________________________________________________
Ludwik Kowalski, a retired physicist
5 Horizon Road, apt. 2702, Fort Lee, NJ, 07024, USA
Also an amateur journalist at http://csam.montclair.edu/~kowalski/cf/