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Three-line derivation of the Thomas precession
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| Pengarang | : | Pawe? Lewulis |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 8) |
| Halaman | : | 674 |
| Abstrak | : | Recently,1 a half-page derivation of the Thomas precession effect2 has been presented (see also all the references in Ref. 1 for the history and prehistory of the problem). In this short note, we provide a much simpler, three-line derivation of that effect which, to our knowledge, is the simplest in the literature. Consider Bob B moving relative to Alice's frame A with a relativistic velocity v, as shown in Fig. 1. If Bob's velocity changes by an infinitesimal value relative to his initial reference frame B, Alice will observe his new velocity to be some ?. The new Bob's frame is now rotated relative to Alice's frame by a Thomas–Wigner angle ?. In the non-relativistic theory, we have and the rotation is absent. Therefore, the Thomas–Wigner... |
Why physical understanding should precede the mathematical formalism—Conditional quantum probabilities as a case-study
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 8) |
| Halaman | : | 668-673 |
| Abstrak | : | Conditional probabilities in quantum systems which have both initial and final boundary conditions are commonly evaluated using the Aharonov–Bergmann–Lebowitz rule. In this short note, we present a seemingly disturbing paradox that appears when applying the rule to systems with slightly broken degeneracies. In these cases, we encounter a singular limit—the probability “jumps” when going from perfect degeneracy to negligibly broken one. We trace the origin of the paradox and solve it from both traditional and modern perspectives in order to highlight the physics behind it: the necessity to take into account the finite resolution of the measuring device. As a practical example, we study the application of the rule to the Zeeman effect. The analysis presented here may stress the general need to first consider the governing physical principles before heading to the mathematical formalism, in particular, when exploring puzzling quantum phenomena. |
Electric field lines: The implications of students' interpretation on their understanding of the concept of electric field and of the superposition principle
| Pengarang | : | Esmeralda Campos |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 8) |
| Halaman | : | 660-667 |
| Abstrak | : | A common way to represent an electric field in a course on electricity and magnetism is with the electric field line diagram. Some literature claims that students have difficulties understanding this representation and relating it to their understanding of the electric field concept. We conducted a study at the introductory level that aims to understand the effect of students' interpretation of electric field line diagrams on their application of the superposition principle for the electric field. The results give some evidence that an incorrect interpretation of the electric field line diagram may hinder the understanding of the superposition principle. Students who understand a vector representation of a field at a position tend to answer a superposition principle question better. We question whether teaching the electric field line representation is productive at the introductory level, and we discuss the need to have a representation that helps students reach a better understanding of the electric field concept and of the superposition principle. |
Data-driven decision making in an introductory physics lab
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 8) |
| Halaman | : | 654-659 |
| Abstrak | : | A new lab activity for first-year introductory physics teaches students to use data to drive decision-making in science and engineering processes. Using the popular PDCA (plan-do-check-act) cycle, students manufacture a small sample of ball bearings out of modeling clay. By statistically analyzing their sample, they determine whether a larger shipment will meet tolerance levels specified by the lab TA. They then make decisions on ways to change their manufacturing process to improve results, employing another round of data analysis to confirm whether the change improved their process. Judging by student comments, such an activity reinforces the conceptual basis for numerous statistical properties, helps distinguish many commonly confused statistical concepts, and reinforces the use of data in process management. This activity can be incorporated into either algebra-based or calculus-based physics labs and, because it does not rely on background knowledge of physics concepts, should prove ideal for the early weeks of lab instruction. |
Free fall through the rotating and inhomogeneous Earth
| Pengarang | : | Stefan Isermann |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 8) |
| Halaman | : | |
| Abstrak | : | Analytical solutions of the motion through the Earth and suitably shaped gravity tunnels are derived so that inertial forces caused by the Earth's rotation are eliminated and the journey takes place in complete weightlessness. The inhomogeneity of the Earth is represented by the one-dimensional Preliminary Reference Earth Model (PREM). A piecewise linear approximation of the model is used to obtain an analytical solution that corresponds very well to the solution obtained numerically for the PREM. |
Note on the history effect in fluid mechanics
| Pengarang | : | Humphrey J. Maris |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 8) |
| Halaman | : | 643-645 |
| Abstrak | : | A freshman mechanics course often includes a theoretical discussion or demonstration of the motion of solid particles through fluids. The effect of viscosity is typically considered to provide a drag force on the particle which at each instant is proportional to the particle velocity. We present a brief discussion of the limitations of this approach and the importance of the so-called history effect first considered by Boussinesq and Basset in the late 19th century. |
Maximal angular correlation in ? – ? coincidences: A quantitative study
| Pengarang | : | Filipe Moura |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 8) |
| Halaman | : | 638-642 |
| Abstrak | : | The measurement of the angular distribution of maximally correlated annihilation gamma rays radiated in coincidence, like those emitted from a 22Na source, is a classic experiment that is nowadays ordinarily performed in nuclear physics laboratory classes. For the first time, we present an analytic expression for such angular distributions, which can be easily tested and compared with the laboratory measurements. |
The delicate dance of orbital rendezvous
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 8) |
| Halaman | : | 627-637 |
| Abstrak | : | The meeting of two spacecraft in orbit around a planet or moon involves a delicate dance that must carefully balance the gravitational, Coriolis, and centrifugal forces acting on the spacecraft. The intricacy of the relative motion between the two spacecraft caused problems for the Gemini missions in the mid-1960s. Although now mastered, the problem of how to bring two orbiting objects together continues to be misrepresented in popular movies and books. In this article, I will consider the case when the two spacecraft are in close proximity (compared with the radii of their orbits), and examine the counter-intuitive trajectories that are needed to bring them together. I will examine how a stranded astronaut might use an impulsive force to return to her ship in Earth orbit, how and when line-of-sight targeting may be used for a rendezvous, and how the Apollo 11 lunar module executed a Terminal Phase Initiation maneuver to rendezvous with the command/service module as they both circled the Moon. |
Low-entropy expressions
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 87 (No. 8) |
| Halaman | : | 613-615 |
| Abstrak | : | Last time, I described how the quadratic formula often creates an unholy mess. In the example there, a stone started falling freely down a well at time zero and made a splash heard at time T. The well's depth h was the horrible1 (1) Sadly, the quadratic formula is only one of many ways to go wrong; the cubic or quartic formulas make bigger messes (fortunately, there's no quintic formula). But what exactly has gone wrong? And what would going right mean? These issues can be quantified approximately using a seemingly strange quantity that I learned from R. David Middlebrook (1929–2010): the entropy of an expression.2 In a high-entropy expression, “the arrangement of the terms and the symbols conveys no information in itself.... |
A flexible positron spectrometer for the undergraduate laboratory
| Pengarang | : | Jason Engbrecht |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 86 (No. 7) |
| Halaman | : | 549–558 |
| Abstrak | : | Positron physics touches on a wide-ranging variety of fields from materials science to medical imaging to high energy physics. In this paper, we present the development of a flexible positron annihilation spectrometer appropriate for the undergraduate laboratory. Four NaI gamma-ray (γ-ray) detectors are connected to an oscilloscope-based data acquisition system. Coupled with the software we developed, these detectors allow students to explore a variety of positron and γ-ray phenomena. These include γ-ray energy spectroscopy, Compton scattering, PET scanning fundamentals, speed of light measurements with γ-rays, historically important polarimetry of annihilation radiation, 3-γ annihilation radiation observations, and positron lifetime spectroscopy of materials. We present the developed apparatus and examples of experiments it can perform here. A website, https://wp.stolaf.edu/physics/positron-laboratory-for-undergraduates/, has also been developed to present supplementary materials including apparatus drawings, laboratory write-ups, developed software, and an instructors' manual. |