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Top 10 Most Read Articles
December 2011
The 10 articles with the most full-text downloads during the month, in descending order.
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Probability, geometry, and dynamics in the toss of a thick coin American Journal of Physics -- December 2011 -- Volume 79, Issue 12, pp. 1195
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When a thick cylindrical coin is tossed in the air and lands without bouncing on an inelastic substrate, it ends up on its face or its side. We account for the rigid body dynamics of spin and precession and calculate the probability distribution of heads, tails, and sides for a thick coin as a function of its dimensions and the distribution of its initial conditions. Our theory yields a simple expression for the aspect ratio of homogeneous coins with a prescribed frequency of heads or tails compared to sides, which we validate using data from the results of tossing coins of different aspect ratios.
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Unraveling a classical mechanics brain twister American Journal of Physics -- December 2011 -- Volume 79, Issue 12, pp. 1250 Online Publication Date: Nov 2011
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We present a comprehensive analysis of an intriguing classical mechanics problem involving the coupled motion of two blocks. The problem illustrates fundamental physics concepts and theoretical techniques. We solve the equations of motion numerically and gain insight into common misconceptions about this system. The problem provides rich opportunities for student investigations using analytical and numerical methods.
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Paradoxical reflection in quantum mechanics American Journal of Physics -- December 2011 -- Volume 79, Issue 12, pp. 1218
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We discuss a phenomenon of elementary quantum mechanics that is counterintuitive, non-classical, and apparently not widely known: the reflection of a particle at a downward potential step. In contrast, classically, particles are reflected only at upward steps. The conditions for this effect are that the wavelength is much greater than the width of the potential step and the kinetic energy of the particle is much smaller than the depth of the potential step. The phenomenon is suggested by non-normalizable solutions to the time-independent Schrödinger equation. We present numerical and mathematical evidence that it is also predicted by the time-dependent Schrödinger equation. The paradoxical reflection effect suggests and we confirm mathematically that a particle can be trapped for a long time (though not indefinitely) in a region surrounded by downward potential steps, that is, on a plateau.
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John S. Bell’s concept of local causality American Journal of Physics -- December 2011 -- Volume 79, Issue 12, pp. 1261
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John Stewart Bell’s famous theorem is widely regarded as one of the most important developments in the foundations of physics. Yet even as we approach the 50th anniversary of Bell’s discovery, its meaning and implications remain controversial. Many workers assert that Bell’s theorem refutes the possibility suggested by Einstein, Podolsky, and Rosen (EPR) of supplementing ordinary quantum theory with “hidden” variables that might restore determinism and/or some notion of an observer-independent reality. But Bell himself interpreted the theorem very differently—as establishing an “essential conflict” between the well-tested empirical predictions of quantum theory and relativistic local causality. Our goal is to make Bell’s own views more widely known and to explain Bell’s little-known formulation of the concept of relativistic local causality on which his theorem rests. We also show precisely how Bell’s formulation of local causality can be used to derive an empirically testable Bell-type inequality and to recapitulate the EPR argument.
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The added mass of a spherical projectile American Journal of Physics -- December 2011 -- Volume 79, Issue 12, pp. 1202
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When a ball moves through the air, the air exerts a force on the ball. For a sphere moving at constant velocity with respect to the air, this force is called the drag force and it has been well measured. If the sphere moves with a nonconstant velocity there are additional forces. These “unsteady” forces depend on the sphere’s acceleration and, in principle, also on higher derivatives of the motion. The force equal to a constant times the acceleration is called the “added mass” because it increases the effective inertia of the sphere moving through the fluid. We measure the unsteady forces on a sphere by observing the one- and two-dimensional projectile motion of light spheres around the highest point. The one-dimensional motion is well described by just the usual buoyant force and the added mass as calculated in the ideal fluid model. This measurement is an excellent experiment for introductory physics students. For spheres in two-dimensional projectile motion the downward vertical acceleration at the highest point increases with the horizontal velocity. This effect can be described by an additional force proportional to the speed times the acceleration.
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Resource Letter EM-1: Electromagnetic Momentum American Journal of Physics -- January 2012 -- Volume 80, Issue 1, pp. 7
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This Resource Letter surveys the literature on momentum in electromagnetic fields, including the general theory, the relation between electromagnetic momentum and vector potential, “hidden” momentum, the 4/3 problem for electromagnetic mass, and the Abraham–Minkowski controversy regarding the field momentum in polarizable and magnetizable media.
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Nonlinear ordinary differential equations in fluid dynamics American Journal of Physics -- December 2011 -- Volume 79, Issue 12, pp. 1255
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The equivalence between nonlinear ordinary differential equations (ODEs) and linear partial differential equations (PDEs) was recently revisited by Smith, who used the equivalence to transform the ODEs of Newtonian dynamics into equivalent PDEs, from which analytical solutions to several simple dynamical problems were derived. We show how this equivalence can be used to derive a variety of exact solutions to the PDEs describing advection in fluid dynamics in terms of solutions to the equivalent ODEs for the trajectories of Lagrangian fluid particles. The PDEs that we consider describe the time evolution of non-diffusive scalars, conserved densities, and Lagrangian surfaces advected by an arbitrary compressible fluid velocity field u(x, t). By virtue of their arbitrary initial conditions, the analytical solutions are asymmetric and three-dimensional even when the velocity field is one-dimensional or symmetrical. Such solutions are useful for verifying multidimensional numerical algorithms and computer codes for simulating advection and interfacial dynamics in fluids. Illustrative examples are discussed.
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Orbits of the Kepler problem via polar reciprocals American Journal of Physics -- December 2011 -- Volume 79, Issue 12, pp. 1246 Online Publication Date: Nov 2011
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Polar reciprocals of trajectories are an elegant alternative to hodographs for motion in a central force field. Their principal advantage is that the transformation from a trajectory to its polar reciprocal is its own inverse. The form of the polar reciprocals of Kepler orbits is established, and a geometrical construction is presented for the orbits of the Kepler problem starting from their polar reciprocals. No obscure knowledge of conics is required to demonstrate the validity of the method. Unlike a graphical procedure suggested by Feynman and extended by Derbes, the method based on polar reciprocals works without changes for elliptical, parabolic, and hyperbolic trajectories.
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Introductory physics going soft American Journal of Physics -- January 2012 -- Volume 80, Issue 1, pp. 51
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We describe an elective course on soft matter at the level of introductory physics. Soft matter physics serves as a context that motivates the presentation of basic ideas in statistical thermodynamics and their applications. It also is an example of a contemporary field that is interdisciplinary and touches on chemistry, biology, and physics. We outline a curriculum that uses the lattice gas model as a quantitative and visual tool, initially to introduce entropy, and later to facilitate the calculation of interactions. We demonstrate how free energy minimization can be used to teach students to understand the properties of soft matter systems such as the phases of fluid mixtures, wetting of interfaces, self-assembly of surfactants, and polymers. We discuss several suggested activities in the form of inquiry projects which allow students to apply the concepts they have learned to experimental systems.
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Eighteenth century treatment of a classical mechanic problem American Journal of Physics -- January 2012 -- Volume 80, Issue 1, pp. 47
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The behavior of a heavy cylinder sliding on the ground is discussed in many introductory mechanics classes. We revisit a solution that was given in the late eighteenth century and compare it with the solution that today’s textbooks usually present.
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