Abstract We investigate the deflection of a uniformly charged cantilever rod under the electrostatic influence of a point charge. The distribution of the electrostatic force along the rod follows Coulomb’s law and therefore depends on the position of the point charge. An exact solution can be obtained for both the deflection and slope of the rod. We further demonstrate that approximate solutions, corresponding to different point charge positions, are in good agreement with the exact solution. This study provides a useful example for understanding calculus-based physics at the university level.

Abstract Everyday experiences help individuals build intuitive understandings of physical phenomena. However, incomplete or incorrect reasoning can lead to persistent alternative conceptions rather than scientifically accurate conclusions. Such misconceptions are particularly common among younger learners and can remain uncorrected unless explicitly addressed in instruction. This study investigates the persistence of misconceptions related to friction among three groups: school students, undergraduate physics students, and physics teachers. An online test consisting of seven yes/no questions was used to identify common alternative conceptions. Three prevalent misconceptions were analyzed in detail, with a focus on their origins and how they might be addressed through targeted instruction. The findings highlight the need for greater emphasis on conceptual understanding in physics education, particularly in teacher preparation programs. This study is intended for undergraduate students, especially those training to become teachers, offering practical insights into how persistent misconceptions about friction can be effectively identified and overcome in the classroom.

Abstract Undergraduate labs teaching solid state physics usually do not encompass experiments that lie in the domain of `soft materials '- materials that have large response functions and dramatic visco-elastic responses. One of the most exciting topics in soft condensed matter is liquid crystals. From calculators to computer screens, liquid crystal (LC) based displays are ubiquitous today. Liquid crystals can flow like a liquid but their molecules show some degree of orientational order like a crystalline solid. They possess special properties like birefringence, and under an applied electric field, liquid crystal molecules develop induced dipole moments and therefore tend to align with the applied field (Fréedericksz transition). Because of these special characteristics, liquid crystals have found use in a wide variety of applications. In this work, we outline a simple undergraduate lab project that brings the exciting world of liquid crystals to the level of physics and chemistry undergraduates. We discuss in detail the fabrication of a liquid crystal-based temperature sensor and a one-pixel liquid crystal display that can be easily made in an undergraduate teaching lab. While the one-pixel display can succinctly illustrate the principles of an LCD screen to an undergraduate student, the LC based temperature sensor can be utilized to develop smart clothing, biomedical devices and flexible sensors. In designing the experiments, special care has been taken to keep the cost within the reach of undergraduate teaching labs in developing countries.

Abstract Many authors in the literature focused on Hamilton's hodograph of the Keplerian motion but none of them developed a vector kinematic analysis of the peculiar velocity shown by the hodograph, so we perform it here. This approach gives an alternative way to teach and learn the Keplerian motion, easier to handle than the classical one based only on Newton's gravitational force. As expected, the analysis predicts the mathematical structure of Newton's acceleration and Kepler's laws, however a kinematic factor replaces Newton's physical factor GM. It also leads to new expressions for the eccentricity and the classical mechanical energy.

Abstract Multimedia learning has always been a topic in physics education—whether through specialized digital data acquisition systems, simulations, or animations. Due to increasing digitalization, more and more media from our everyday lives have also found their way into education in recent decades. This contribution introduces a conceptual framework and illustrative examples for AI-supported experimentation in physics education. It does not yet present empirical data but outlines directions for forthcoming classroom studies evaluating learning outcomes and engagement.

Abstract We derive the exact expression for the resonant frequency of the time-averaged steady-state energy and show that this frequency is excellently approximated by the arithmetic mean of the amplitude and velocity resonant frequencies. In addition, we argue that the frequency of the amplitude resonance can be regarded as the energy resonance frequency, since it provides the maximal peak values of instantaneous energy. We demonstrate our findings experimentally using a simple setup that can be used as a tool in university teaching.

Abstract We show that, under specific conditions, a lighter object can reach a higher terminal velocity than a heavier one when falling through a highly dense and viscous fluid. This counterintuitive result, obtained within the regime where Stokes' law applies, challenges the common assumption that heavier objects fall faster. While it is well known that compact objects fall at similar rates in air regardless of mass, and that heavier objects typically fall faster when lighter ones are more extended, the behavior in denser and more viscous media has been less explored. We analyze spheres with different densities and radii falling in such a medium, considering gravitational, buoyant, and drag forces, and assuming no interaction between them. Depending on the radius ratio, the denser sphere may reach a higher terminal velocity and touch the ground first-whether it is heavier, lighter, or equal in weight to the other. Interestingly, when the less dense sphere has the higher terminal velocity, it is always the heavier one; however, whether it lands first also depends on the initial height. These findings provide new insights into low-Reynolds-number dynamics, with potential applications in education, experimental design, and engineering.

Abstract Polarization singularity beams (PSB) possess specific topological structures and exhibit stability and resistance to interference during propagation. These characteristics bestow vector optical fields (VOFs) with unique physical properties and enhanced degrees of manipulation, offering potential application in optical microfabrication, optical micromanipulation, and optical information processing. Within this study, an experimental generation and detection system for VOFs is introduced. Leveraging the technique of dynamically loading holograms onto a spatial light modulator and using a movable measurement platform, it can achieve the basic generation, manipulation, and detection of PSBs. Specifically tailored for college-level physics education, this system enables undergraduates to understand the fundamental principles of VOF generation. Using PSBs as representatives of VOFs and incorporating hands-on experiments on generating and controlling these beams, students can not only master theoretical concepts but also enhance their practical skills in experimental design, instrument operation, and data analysis.

Abstract The impedance of RC- and RLC-, as well as capacitively and inductively coupled LC-circuits was measured using time-domain and impedance spectroscopy. The results of both methods agree well with regard to the structure of the impedance minima and phase jumps related to the LC series contributions. The frequencies of these mark the eigenfrequencies of the circuits. The agreement of the impedance maxima was less convincing, but overall the two techniques yielded consistent data. The methods developed in this study are employed in a time-domain spectroscopy experiment in an undergraduate physics laboratory course.