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Oct 2001

Volume 69, Issue 10, pp. 1029-1118

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The great Copernican cliché

Dennis R. Danielson

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1029 | Cited 3 times

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For more than three centuries scientists, historians, and popularizers of science have been repeating the claim that Copernicus “dethroned” earth from its “privileged” central position in the universe. However, a survey of pre-Copernican natural philosophy (which viewed the earth as located in a cosmic sump) and of Copernicans’ own account of the axiological meaning of the new heliocentric astronomy (which exalted earth to the dance of the stars) demonstrates that the cliché about earth’s “demotion” is unwarranted and fit to be discarded. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
95.10.Ce Celestial mechanics (including n-body problems)

An unusual approach to Kepler’s first law

Thomas J. Osler

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1036

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Kepler’s first law of planetary motion states that the orbits of planets are elliptical, with the sun at one focus. We present an unusual verification of this law for use in classes in mechanics. It has the advantages of resembling the simple verification of circular orbits, and stressing the importance of Kepler’s equation. © 2001 American Association of Physics Teachers.
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45.50.Pk Celestial mechanics
95.10.Ce Celestial mechanics (including n-body problems)

The maximal invariance group of Newton’s equations for a free point particle

O. Jahn and V. V. Sreedhar

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1039 | Cited 6 times

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The maximal invariance group of Newton’s equations for a free nonrelativistic point particle is shown to be larger than the Galilei group. It is a semidirect product of the static (nine-parameter) Galilei group and an SL(2,R) group containing time translations, dilations, and a one-parameter group of time-dependent scalings called expansions. This group was first discovered by Niederer in the context of the free Schrödinger equation. We also provide a road map from the free nonrelativistic point particle to the equations of fluid mechanics to which the symmetry carries over. The hitherto unnoticed SL(2,R) part of the symmetry group for fluid mechanics gives a theoretical explanation for an observed similarity between numerical simulations of supernova explosions and numerical simulations of experiments involving laser-induced implosions in inertial confinement plasmas. We also give examples of interacting many-body systems of point particles which have this symmetry group. © 2001 American Association of Physics Teachers.
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45.05.+x General theory of classical mechanics of discrete systems
97.60.Bw Supernovae
52.57.-z Laser inertial confinement
02.20.-a Group theory

The origins of length contraction: I. The FitzGerald–Lorentz deformation hypothesis

Harvey R. Brown

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1044 | Cited 3 times

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“Can there be some point in the theory of Mr. Michelson’s experiment which has yet been overlooked?” H. A. Lorentz, letter to Lord Rayleigh, August 1892.   One of the widespread confusions concerning the history of the 1887 Michelson–Morley experiment has to do with the initial explanation of this celebrated null result due independently to FitzGerald and Lorentz. In neither case was a strict, longitudinal length contraction hypothesis invoked, as is commonly supposed. Lorentz postulated, particularly in 1895, any one of a certain family of possible deformation effects for rigid bodies in motion, including purely transverse alteration, and expansion as well as contraction; FitzGerald may well have had the same family in mind. A careful analysis of the Michelson–Morley experiment (which reveals a number of serious inadequacies in many textbook treatments) indeed shows that strict contraction is not required. © 2001 American Association of Physics Teachers.
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01.65.+g History of science
03.30.+p Special relativity

Photorefractive polymers: Materials science, thin-film fabrication, and experiments in volume holography

David J. McGee and Mark D. Matlin

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1055 | Cited 2 times

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When exposed to low power laser light, photorefractive materials can function as dynamic diffraction gratings, making them attractive for applications in holography and optical image processing. Conventional crystalline photorefractive materials are useful in demonstrations of basic nonlinear optical phenomena at the advanced undergraduate level, although the fabrication of such crystals is beyond the reach of most undergraduate facilities. Within the last five years, however, polymeric photorefractive materials have been developed that can be fabricated by collaborative teams of undergraduate physics and chemistry students. We have found that the study of photorefractive polymers provides an excellent framework to emphasize connections among optics, chemistry, and materials science at a level accessible to undergraduates. We provide an overview of photorefractive polymers, describe the fabrication of a typical photorefractive polymeric system, and discuss experiments in volume holography. © 2001 American Association of Physics Teachers.
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61.41.+e Polymers, elastomers, and plastics
42.40.-i Holography
01.50.Pa Laboratory experiments and apparatus

When do bubbles cause a floating body to sink?

Bruce Denardo, Leonard Pringle, Carl DeGrace, and Michael McGuire

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1064 | Cited 3 times

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The introduction of gas bubbles into a liquid might be expected to cause a relatively large floating body to sink when the average density of the fluid is less than the average density of the body. However, the rising bubbles could entrain the liquid, which would produce an upward drag on the body and thus lower the fluid density required to sink the body. Due to this drag, it is in fact not clear whether any amount of bubbles can cause a floating body to sink. In addition, there are many other effects that could alter the requisite fluid density. We describe qualitative lecture demonstrations which show that bubbles can indeed sink a body, including the case of ice in water. We also describe a quantitative experiment to determine the density of bubbly water required to sink a spherical body. The specific gravity of this body is varied from 0.99 to 0.75, and the results are compared to a simple theory. © 2001 American Association of Physics Teachers.
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01.50.My Demonstration experiments and apparatus
47.55.D- Drops and bubbles
47.55.Hd Stratified flows
47.55.Kf Particle-laden flows

The physics of golf: The convex face of a driver

A. Raymond Penner

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1073 | Cited 4 times

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The impact of the clubhead of a driver with a golf ball is modeled. The effect of the convex clubface of a driver on the flight of the golf ball is considered and the dependence of the optimum curvature of the clubface on the volume, mass, and impact speed of the clubhead is determined. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
01.55.+b General physics
45.40.Gj Ballistics (projectiles; rockets)

Simplified quantum oscillator solution

Thomas F. Jordan

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1082 | Cited 1 time

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To find the eigenvalues and eigenvectors of the quantum oscillator Hamiltonian, it is enough to construct eigenvectors with the raising operator and see that these eigenvectors are complete. The subspace they span must be the entire space of square-integrable functions because it is invariant for the raising and lowering operators and therefore invariant for the position and momentum operators. This shows that the Hamiltonian has no continuous spectrum. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.-w Quantum mechanics

Expectation value analysis of wave packet solutions for the quantum bouncer: Short-term classical and long-term revival behaviors

M. A. Doncheski and R. W. Robinett

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1084 | Cited 12 times

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We discuss the time development of Gaussian wave packet solutions of the “quantum bouncer” (a quantum mechanical particle subject to a uniform downward force, above an impermeable flat surface). We focus on the evaluation and visualization of the expectation values and uncertainties of position and momentum variables during a single quasi-classical period as well as during the long-term collapsed phase and several revivals. This approach complements existing analytic and numerical analyses of this system, as well as being useful for comparison with similar results for the harmonic oscillator and infinite well cases. © 2001 American Association of Physics Teachers.
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03.65.Ge Solutions of wave equations: bound states
03.65.Sq Semiclassical theories and applications
01.50.My Demonstration experiments and apparatus
01.50.Lc Laboratory computer use

Consistent analogs of the Fourier uncertainty relation

G. W. Forbes and M. A. Alonso

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1091 | Cited 5 times

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To resolve an issue that was raised in our earlier paper in this journal [69, 340–347 (2001)], a direct analog of the standard uncertainty relation is derived for the discrete Fourier transform (DFT). This inequality gives a simple lower bound for the degree of localization of the DFT of any sequence in terms of just the localization of the original sequence. It is also shown that the earlier uncertainty relations for the Fourier transform and the Fourier series can be derived from this new relation by taking appropriate limits. Because the same cannot be said of the others, this new relation is arguably the most fundamental of the three. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.Fd Algebraic methods
02.30.Uu Integral transforms

Autoresonant (nonstationary) excitation of pendulums, Plutinos, plasmas, and other nonlinear oscillators

J. Fajans and L. Frièdland

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1096 | Cited 53 times

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A weakly driven pendulum cannot be strongly excited by a fixed frequency drive. The only way to strongly excite the pendulum is to use a drive whose frequency decreases with time. Feedback is often used to control the rate at which the frequency decreases. Feedback need not be employed, however; the drive frequency can simply be swept downwards. With this method, the drive strength must exceed a threshold proportional to the sweep rate raised to the 3/4 power. This threshold has been discovered only recently, and holds for a very broad class of driven nonlinear oscillators. The threshold may explain the abundance of 3:2 resonances and dearth of 2:1 resonances observed between the orbital periods of Neptune and the Plutinos (Pluto and many of the Kuiper Belt objects), and has been extensively investigated in the Diocotron system in pure-electron plasmas. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
07.10.-h Mechanical instruments and equipment
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
96.30.Sn Pluto
95.10.Ce Celestial mechanics (including n-body problems)
45.50.Pk Celestial mechanics
96.30.Rm Neptune

Matter waves in a gravitational field: An index of refraction for massive particles in general relativity

James Evans, Paul M. Alsing, Stefano Giorgetti, and Kamal Kanti Nandi

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1103 | Cited 9 times

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We consider the propagation of massive-particle de Broglie waves in a static, isotropic metric in general relativity. We demonstrate the existence of an index of refraction that governs the waves and that has all the properties of a classical index of refraction. We confirm our interpretation with a Wentzel–Kramers–Brillouin solution of the general-relativistic Klein–Gordon equation. Finally, we make some observations on the significance of the optical action. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
04.20.-q Classical general relativity
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n+1 dimensional Dirac equation and the Klein paradox

Antonio S. de Castro

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1111 | Cited 1 time

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Abstract Unavailable
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01.50.-i Educational aids
03.65.Pm Relativistic wave equations
03.30.+p Special relativity

Erratum: “Field pattern of a magnetic dipole” [Am. J. Phys. 68, 577–578 (2000)]

J. P. McTavish

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1112 | Cited 1 time

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Abstract Unavailable
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99.10.Cd Errata
01.50.-i Educational aids
41.20.Gz Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems
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Demonstration of different bending profiles of a cantilever caused by a torque or a force

Th. Höpfl, D. Sander, and J. Kirschner

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1113 | Cited 3 times

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A simple experiment is described to demonstrate the different deflected shapes assumed by a cantilever due to a torque or a force acting on its end. An optical deflection technique is used to show that different shapes appear in the cantilever even if the torque or force causes an identical displacement of the cantilever end. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
46.32.+x Static buckling and instability
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Scattering of Waves from Large Spheres

Walter T. Grandy, Jr., Author and R. K. Brandt, Reviewer

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1116

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Abstract Unavailable
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03.65.Nk Scattering theory
42.25.Fx Diffraction and scattering
03.50.De Classical electromagnetism, Maxwell equations
01.30.Vv Book reviews
78.35.+c Brillouin and Rayleigh scattering; other light scattering
42.65.Es Stimulated Brillouin and Rayleigh scattering

The Runaway Universe

Donald Goldsmith, Author and Wendy Freedman, Reviewer

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1117

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Abstract Unavailable
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01.30.Vv Book reviews
98.80.-k Cosmology
95.35.+d Dark matter (stellar, interstellar, galactic, and cosmological)
98.70.Vc Background radiations
97.60.Bw Supernovae

The Hole in the Universe: How Scientists Peered over the Edge of Emptiness and Found Everything

K. C. Cole, Author and Wendy Freedman, Reviewer

American Journal of Physics -- -- Volume 69, Issue 10, pp. 1117

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Abstract Unavailable
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01.30.Vv Book reviews
98.80.-k Cosmology
95.35.+d Dark matter (stellar, interstellar, galactic, and cosmological)
98.70.Vc Background radiations
97.60.Bw Supernovae

The Dynamics of Fluidized Particles

Roy Jackson, Author and Mark D. Shattuck, Reviewer

American Journal of Physics -- October 2001 -- Volume 69, Issue 10, pp. 1118

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Abstract Unavailable
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01.30.Vv Book reviews
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