May 2026
Volume 94, Issue No. 5
We describe the fabrication and implementation of a dynamic Kibble balance experiment to enable the measurement of mass without the use of a scale, modifying the experimental design of a recently published approach. In this experiment, the voltage induced by a pellet, consisting of two opposed magnets passing through a coil, is used to determine mass via measurements of the induced voltage, pellet velocity, and the current required to levitate the pellet. In particular, we simplified the electronic timing by the use of two coils separated by a known distance to allow the measurement of velocity without the use of photogates. Thus, the total cost for the equipment fabrication is under $25 USD. For data collection, this equipment is then paired with either an oscilloscope, or a smart pulley system, equipment that is available in most first-year physics laboratories. Finally, we use expressions for the induced electromotive force (EMF) of a magnet falling through a coil to fit the distance dependence of the EMF generated during the velocity mode part of the experiment.
EDITORIAL
Self force on Dirac monopoles by Kirk T. McDonald. DOI: 10.1119/5.0313789
Self-force of a Dirac string: An explicit calculation by Alberto G. Rojo. DOI: 10.1119/5.0332162
LETTERS TO THE EDITOR
Self-force of a Dirac string: An explicit calculation by Alberto G. Rojo. DOI: 10.1119/5.0332162
PAPERS
A dimensional analysis path to h and the Bohr atom structure by Kostas Glampedakis. DOI: 10.1119/5.0292670
Editor's Note: Dimensional analysis provides an essential check on calculations, but it can also show the way to interesting new physics. In this article, the author explores an alternative timeline for atomic physics, in which a classical physicist at the turn of the 20th century uses dimensional analysis to deduce the Bohr energy and Bohr radius of the hydrogen atom—more than a decade before Bohr himself!
This clear and instructive demonstration of techniques of dimensional analysis could easily be incorporated into a modern physics course or a first course in quantum mechanics. The article also paints an interesting historical picture of physics that will appeal to anyone who speculates about how the history of 20th century physics might have played out differently.
A note on the kinematic boundary condition with historical perspective by G. R. Hunt; J. P. Webb. DOI: 10.1119/5.0298780
Editor's Note: One famous result from fluid mechanics is that the normal component of a fluid's velocity must be zero at a boundary. Students and teachers sometimes infer from this statement that no fluid may move to or from a boundary surface. Yet, as the authors show, this is not always the case! Drawing on examples proposed by Kelvin and presenting a striking new demonstration, the authors offer persuasive arguments that there are indeed cases where fluid arrives at or departs from a boundary surface, even though the normal component of fluid velocity remains zero at the boundary surface.
The “Littlewood's” hopping hoop dynamics by Andrey A. Aglaev; Alexander K. Kovaldji. DOI: 10.1119/5.0291968
Editor's Note: John E. Littlewood proposed the notorious problem: “A weight is attached to a point of a rough weightless hoop, which then rolls in a vertical plane, starting near the position of unstable equilibrium. What happens, and is it intuitive?” The variety of answers that have appeared in the literature over the last several decades indicates that, whatever might happen, the result is not intuitive! Here, the authors present a new argument that the hoop will either hop at the instant of release, or not at all.
The ideal gas with a harmonic piston and the constant pressure-to-volume ratio ensemble by Fabrício Q. Potiguar. DOI: 10.1119/5.0208569
Editor's Note: Students sometimes develop a misconception that one of the variables in the ideal gas law (pressure, volume, or temperature) must always remain fixed as these are the most common situations in problems or experiments. Having simple, physically realizable situations where multiple fundamental state variables change simultaneously can help to build deeper intuition for thermodynamic processes. One such simple system is discussed in this article—a container of ideal gas fitted with a movable piston which is coupled to an ideal spring. The system's internal energy and heat capacity are calculated using several complementary methods of increasing complexity, which can be employed in elementary thermodynamics courses or more advanced statistical mechanics courses.
An ideal Fermi gas under uniform gravity by Pattarapon Tanalikhit; Wittaya Kanchanapusakit. DOI: 10.1119/5.0300463
Editor's Note: This paper shows how to find the thermodynamic properties of a Fermi gas in a uniform gravity field. Most of the treatment is within the Thomas–Fermi approximation, in which the gas is assumed to have a uniform local density that varies as a function of height, although the paper presents a short treatment of the fuller quantum mechanical problem. This analysis could form the basis of a challenging problem in a statistical mechanics course.
From discrete states to wavefunctions by Martin Kamela. DOI: 10.1119/5.0255882
Editor's Note: When teaching the spins-first approach to quantum mechanics, it can be challenging to help students make the transition from working with discrete states of spins to working with continuous states of position and momentum. The author shares an approach in which space is discretized, leading to an approximation of the continuous wavefunction, providing a bridge from discrete to continuous states.
From raw data to processed spectra: A step-by-step guide by Erik F. Woering; Richard Hildner. DOI: 10.1119/5.0250104
Editor's Note: A well-known issue in optical spectroscopy is that measurements are typically reported as functions of wavelengths, whereas the physically relevant quantities depend on energy. This paper offers a comprehensive review of how to perform the conversion correctly. As such, it should be extremely useful to both students and educators alike whenever they tackle problems in spectroscopic analysis.
COMPUTATIONAL PHYSICS
Local structure characterization in particle systems by R. S. Skye; E. G. Teich. DOI: 10.1119/5.0323820
Editor's Note: The authors provide an accessible review of how to compute many measures of the local environment of particle-based systems and what can be learned from each of the different measures. The Jupyter notebooks in the supplementary material can be used to reproduce the results discussed in the paper and as an aid to the suggested problems.
INSTRUCTIONAL LABORATORIES AND DEMONSTRATIONS
The Kibble balance: A low-cost implementation as an undergraduate laboratory experiment or demonstration by P. A. Stampe; R. J. Kennedy. DOI: 10.1119/5.0306495
Editor's Note: This paper presents a low-cost realization of a dynamic Kibble balance, an electromagnetic-based setup that enables an object's mass to be determined without the use of balance. Data are gathered in a two-step experiment in which a magnetized “pellet” is first levitated in a coil and then dropped through the coil in order to generate an induced voltage. These data are then compared to relations derived from basic electromagnetic theory yielding the pellet's mass, whose value is shown to compare favorably to that obtained using a standard balance. The authors present a straightforward version of this experiment that is suitable for use in first-year physics laboratories as well as extensions that are appropriate for advanced laboratory students.
Measurement of electromagnetic radiation force using a capacitance bridge interferometer by Devashish Shah; Pradumn Kumar; Pradeep Sarin. DOI: 10.1119/5.0232550
Editor's Note: Radiation pressure can be a difficult concept for students to grasp. One can exhibit the use of radiation pressure to power spacecraft, but, in the end, the concept often remains elusive. This paper proposes an experiment to actually measure the radiation pressure created by a pulsed laser on a metal cantilever, which also serves as one arm of a capacitor. The cantilever then oscillates and the corresponding change in capacitance measured. Your students will be amazed to see that, with a simple setup and a bit of care, they can measure nano-newton-scale forces produced by photons hitting a metal surface. This experiment is appropriate for undergraduate E&M labs, but also for electronics labs, since it uses a capacitance bridge, a home-built amplifier for small-signal detection, and makes use of an electronic simulation platform as well as of FFTs.
Additional Resources
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