February 2026
Volume 94, Issue No. 2
A bent straw as a tool for an affordable student-safe experiment in vortex ring dynamics
Vortex dynamics are an important topic in fluid dynamics, explaining phenomena like drag and lift generation, jet propulsion, and corner flows. It is also often excluded from introductory or undergraduate fluid dynamics courses on account of its complexity and the inaccessibility of practical and engaging experiments. We present an affordable student-safe experiment to generate vortex rings and study their dynamics using a bent straw and dyed water that allows students to control key parameters, can be imaged using a smartphone camera, and explains the complex physics with simple and easily measured parameters. Vortex rings are produced that parallel seminal experiments, demonstrating secondary structures and the mirroring effect. Meanwhile, nonplanar and triangular jet exits are used to demonstrate asymmetric vortex rings and vortex ring inversion.
EDITORIAL
In this issue: February 2026 by John Essick; Jesse Kinder; Claire A. Marrache-Kikuchi; Beth Parks; Daniel Schumayer; Keith Zengel. DOI: 10.1119/5.0318569
AWARDS
2026 AAPT award citations at the winter meeting in Las Vegas, NV. DOI: 10.1119/5.0319698
PAPERS
Motivating separation of variables by Douglas A. Kurtze. DOI: 10.1119/5.0286500
Editor's Note: Separation of variables is essential in theoretical physics, but instructors often introduce it as an unmotivated ansatz, justified only because it works. Students gain no intuition for when or why the method succeeds—or when it might fail. This article offers an alternative. Starting from basis vectors in three dimensions, the author introduces function spaces and eigenvalue problems at a level accessible to sophomore physics students. Separation of variables emerges naturally rather than as a clever trick, and students gain early exposure to mathematical structures they will encounter later.
Shaping softness from hard elements by Holger Götz; Thorsten Pöschel. DOI: 10.1119/5.0293811
Editor's Note: When a ball collides with a wall, we know that it will reverse direction and travel away with a fraction of its original speed given by the coefficient of restitution. What happens when there is a second ball with a smaller mass between the larger ball and the wall? The authors show that in a certain limit, the large ball accelerates as it would in a repulsive potential. Other fun treats include a clear geometric picture of the system and a welcome reminder of a novel way to calculate pi.
From pinhole imaging to planetary orbit: A year-long solar angular measurement with a pinhole camera by Johannes Grebe-Ellis; Thomas Quick. DOI: 10.1119/5.0289306
Editor's Note: Involve your students in solar observations using the low-cost experiment described in this paper. The authors show how you can follow in Kepler's footsteps to measure the eccentricity of Earth's orbit while also observing sunspots and mesmerizing effects due to atmospheric turbulence. They also work out the details of the optics and show that—contrary to my expectations—an optimal “pinhole” might have a diameter on the order of centimeters.
Numerical modeling of the magnetic vector potential and the associated electromagnetic momenta by John Adams; Christopher Duston. DOI: 10.1119/5.0246553
Editor's Note: Using Mathematica-based simulations of charges interacting with finite solenoids, this paper explores the relationship between the magnetic vector potential and the stored linear and angular electromagnetic momenta. This approach turns the vector potential, often regarded by students and educators alike as an abstract quantity, into a tangible teaching tool, connected to momentum and motion. Appropriate for undergraduate level E&M or computational physics classes.
The exact solution of magnetic resonance for arbitrary spin using an operator-based formalism by Sanya Bharti; J. K. Freericks. DOI: 10.1119/5.0248238
Editor's Note: This article revisits a well-known quantum mechanical problem: the temporal evolution of spin precession in a magnetic field. Its educational value lies in two key aspects: (a) it extends the model beyond the commonly studied spin-1/2 case, and (b) it presents a solution for arbitrary spin using an operator-based approach. By employing tools including the Trotter product formula, the Baker–Campbell–Hausdorff identity, and the exponential disentangling identity, the work offers a clear and structured analytic method that can benefit educators and students tackling similar systems. While the analytic solution is elegant—especially given the rarity of exactly solvable dynamical problems in quantum mechanics—the main strength of the work lies in its pedagogical and didactic development. Some aspects of this work can also be used to motivate numerical approaches when an analytic path is not available.
Effect of depolarization on the CHSH inequality: A hands-on approach by Jörg Hettel. DOI: 10.1119/5.0295675
Editor's Note: Interactions with the environment cause noise in quantum technologies. Understanding this effect is an important part of an education in quantum information. This paper shows how to model depolarization using quantum channels, specifically applied to the violation of the CHSH inequality. It will be useful to instructors of courses in quantum information and quantum computing.
Is the law of optical reflection true? by Tom A. Kuusela. DOI: 10.1119/5.0270188
Editor's Note: When light reflects from a surface, small deviations from specular reflection occur, including the Goos–Hänchen shift and the Imbert–Fedorov shift. These shifts are normally challenging to understand and to measure. This paper shares compact derivations and also guidance for how they can be measured in an upper-level undergraduate optics laboratory course.
INSTRUCTIONAL LABORATORIES AND DEMONSTRATIONS
A bent straw as a tool for an affordable student-safe experiment in vortex ring dynamics by Elijah James; Yukun Sun; Yicong Fu; Jena Shields; Cade Sbrocco; Christopher Dougherty; Chris Roh. DOI: 10.1119/5.0287782
Editor's Note: The authors present an affordable and accessible experiment for exploring the complex physics underlying vortex ring dynamics. Unlike many classroom demonstrations that spark curiosity and excitement but lack quantitative depth, the experiments in this paper allow for the control of simple, well-controlled parameters. These experiments allow students to gain a deeper understanding of vortex ring formation, parameter influence, and related phenomena such as mirroring, entrainment, and vortex ring inversion. This work will be of interest to the undergraduate physics community and is well-suited for use as a laboratory exercise or student project.
Raspberry Pi multispectral imaging camera system (PiMICS): A low-cost, skills-based physics educational tool by John C. Howell; Brian Flores; Juan Javier Naranjo; Angel Mendez; César Costa-Vera; Chris Koumriqian; Nathan Taormina; Juliana Jordan; Pieter H. Neethling; Calvin Groenewald; Michael A. C. Lovemore; Patrick A. T. Kinsey; Tjaart P. J. Krüger. DOI: 10.1119/5.0254097
Editor's Note: This paper describes an affordable Raspberry Pi-based camera system that students can build to perform multispectral imaging, an analysis tool relevant to many fields. The authors promote an open-ended approach to the design, construction, and use of the system, pointing to several possible multispectral imaging applications that students can undertake; a study of banana ripening is presented. This project originated in a course taught to students in developing countries, but its low-cost, undergraduate-accessible demonstration of an advanced imaging technique will be of interest to all advanced instructional laboratory professors.
3D-printed microscope with illumination for undergraduate wave-optics laboratory by Sergey G. Martanov; Valery A. Prudkoglyad; Arslan A. Galiullin; Georgy A. Shmakov; Aleksandr Yu. Kuntsevich. DOI: 10.1119/5.0294867
Editor's Note: The authors present a low-cost video-camera-equipped microscope that can be constructed from off-the-shelf and 3D-printed mechanical and optical components. Developed for instructional laboratory use, the instrument allows students to quantitatively investigate foundational topics from an undergraduate optics course, including refraction, interference, Fresnel diffraction, and Fraunhofer diffraction. Advanced optics-related topics can be explored as independent projects with additional optical elements. A detailed parts list with cost estimates and links to example commercial components, along with the STL files required for the 3D-printed components, are included.
Additional Resources
 |