To me, it seems pretty obvious that a hoop should roll down a ramp slower than a bowling ball, and this clarity comes not so much from knowledge that rotational inertia is proportional to r^2, as from mundane experience showing that it takes longer to bring to rotation a larger disk than a smaller one with the same mass.
But if I am just a rare exception (which I doubt), this would only mean that paradoxes or "conflicts" occupy a much broader domain than I had outlined in my previous message and accordingly they should be addressed in all Physics courses rather than in SR or QM alone. Which is OK, I think. In this respect, I agree that, when it comes to a gyroscope, or any rotational motion with precession, it is hardly "conflict free". I recall now (it was pretty long ago!) demonstrating to students some experiments with a rapidly spinning wheel, especially one when the wheel is suspended on the end of its long axle, and instead of falling down it starts precessing around the rope. This is, indeed, quite counter-intuitive and may at first seem paradoxical to some students even familiar with the concept of angular velocity and angular momentum.
Generally, "paradoxes" come in many different varieties (see, e.g., "Quantum Paradoxes" by Aharonov & Rohrlich), and even the excellent axiomatic presentation of the subject does not automatically elucidate all of them. Such presentation is necessary but not sufficient. Ignoring paradoxes in wishful belief that showing the elegant mathematical structure of the theory eliminates them only prevents the students (and sometimes the teachers) from gaining a deeper insight into the subject.
As to "bizarre examples that no one will ever encounter", they are precisely the "real life examples like particle accelerators etc." There are many effects depending on length contraction and observed in particle accelerators. For example, the amount and angular distribution of particles born in high-energy collision of two nuclei can be correctly estimated only by taking into account the Lorentz contraction of both nuclei in their center of mass, producing a fleeting disk-shaped compound nucleus, so that the Lorentz-contracted length is the PROPER LENGTH of this nucleus (L. Landau, Reports of the Acad. of Sci. of USSR (1953)). The results are confirmed by observations. So is the Lorentz contraction unreal? Another example: an atomic excitation or ionization by a high-energy charged particle can be described correctly only by taking account of the particle's field as being Lorentz-contracted (E. Fermi, Zeitschrift fur Physik, 29, 315-327 (1924)).
Moses Fayngold
NJIT
________________________________
From: "LaMontagne, Bob" <RLAMONT@providence.edu>
To: Moses Fayngold <moshfarlan@yahoo.com>; Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Sent: Friday, October 14, 2011 8:02 AM
Subject: RE: [Phys-l] three central misconceptions about relativity
I would not consider the motion of a top or gyroscope as "conflict free". The idea that a hoop rolls down a ramp more slowly than a bowling ball is hardly "conflict free" either. We certainly wouldn't start a mechanics course with the study of rotating bodies.
The undue emphasis on Twin Paradox and the like leaves the students with the impression that the sizzle is more important than the steak. There are enough real life examples like particle accelerators, questions about superluminal neutrinos, GPS coordination, etc., that can be used as validations of relativity after the foundation is laid that we hardly need to go into bizarre examples that no one will ever encounter.