I am going to ask a question where I am more concerned with the pedagogy than the physics itself. I realize that the scenario proposed has been argued to death in many differeny forums.
Suppose a bright college freshman notices that if two positively charge masses travel through space along parallel paths, that their mutual Coulomb repulsion will cause them to accelerate apart (assume that their velocities are perpendicular to their relative separation vector). The student also notices that the Biot-Savart Law give a mutual attraction between the two charges that reduces the rate at which they accelerate from each other.
The student also notices that in their own center of mass frame the masses have no relative motion so there is only a mutual acceleration from the Coulomb force. Therefore the mutual acceleration in their own frame is larger than in the frame where they are seen to be moving.
How do you respond to the student? Is there a purely classical response that is satisfactory in a general physics course that will not cover relativity until the following semester?
Is it necessary to wave off the question by saying that this will become clearer when relativity is covered? The factor (1-v^2/c^2) naturally comes up when comparing the forces classically. Is this to be noted as a stepping stone to relativity and leave it as a paradox in classical physics?
(If my physics is off here - please feel free to correct it.)
Bob at PC
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From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-bounces@carnot.physics.buffalo.edu] on behalf of LaMontagne, Bob
Sent: Saturday, December 03, 2011 4:40 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Coriolis effect puzzlement
The skater has another advantage - she can pull her arms in and see her rotation rate change relative to her surroundings.
You can also test your absolute rotation even if you cannot see the surroundings. I figure skate and can easily feel the difference when I pull my arms in when I am not spinning and when I pull them in after initiating a rotation. It requires deliberate force to bring them in if there is an initial rotation. It is obvious that I am supplying the energy for the faster rotation.
Bob at PC
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From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-bounces@carnot.physics.buffalo.edu] on behalf of John Denker [jsd@av8n.com]
Sent: Friday, December 02, 2011 6:18 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Coriolis effect puzzlement
snip------------------------
Consider the subsystem consisting of the skater (including
the weights). This subsystem is closed with respect to
momentum. No rocket thrust crossing the boundary. No
applied magnetic fields or anything like that.
Therefore the dL/dt of this system is independent of what
we choose as the axis for defining L.
=====================
Here's another way of looking at it:
Consider the skater's view of the world, including her
view of the spectators, and her view of the fixed stars,
and her view of the gyroscope that hangs from her
necklace. In the initial situation, where she partakes
of the platform motion, it is totally obvious to her
that she is spinning.
If the platform is bowl-shaped in just the right way
("hydrostatic equilibrium") she won't be aware of the
centrifugal force, in which case she won't know or care
where the pivot-point is ... but she will *always* know
that she is spinning. She is spinning relative to any
inertial frame.
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