This note provides a short guide to dimensional analysis in Lorentzian and general relativity and in differential geometry. It tries to revive Dorgelo and Schouten’s notion of ‘intrinsic’ or ‘absolute’ dimension of a tensorial quantity. The intrinsic dimension is independent of the dimensions of the coordinates and expresses the physical and operational meaning of a tensor. The dimensional analysis

We analyze an example of a totally inelastic interaction between two spinning objects from a didactic perspective. We first describe an interpretative model highlighting why a part of the initial rotational energy needs to be dissipated; this point can be visualized in a diagram of capacitive characteristic curves. Subsequently, we propose and discuss a concrete novel experiment, in which an inductive

We present and discuss a non-expensive mechanical experiment which is very suitable for a classroom demonstration of the fold catastrophe behaviour. The apparatus consists of a bar attached to a pulley, to which a hanging body is connected by means of a thread wrapped around its rim. The system may perform stable oscillations or, else, the body may continuously fall down, while the pulley executes

The journal collection ‘Focus on Physics Competitions’ of the European Journal of Physics (EJP) is an ongoing collection within the European Journal Physics (EJP). In the year 2020, five articles have been submitted within this series. This editorial will briefly sum up the content and ideas of those articles. In addition, the concept of this collection is explained in order to ensure the objectives

We promote the teaching of mass functions as an integral part of an interdisciplinary science education. Mass functions characterize the frequency distributions of objects with different masses on all cosmic scales. We intend to enhance experiential learning of this concept with a creative LEGO brick experiment for a diverse student audience. To our surprise, the LEGO mass function is not only qualitatively

In this paper, we discuss the concept of a reservoir in thermodynamics and its determining role in defining entropy flow, entropy generation, lost work, heat, and work. Also, a relation equivalent to that of Clausius is established, which explains why the statement ‘the entropy generation for an irreversible engine is given by the lost work divided by the lowest temperature reservoir’ is flawed, although

An experimental activity for teaching the origin of some bands of the electromagnetic spectrum using only one substance is presented. The activity is proposed for undergraduate students and focuses on developing their knowledge on the origin and the specific requirements for excitation and detection of three bands of the electromagnetic spectrum, in a comparative way. In this teaching approach, gamma

We investigate the constraint problem of a small ring on non-smooth elliptical orbits. The influence mechanism of the orbital shapes on the motion velocity and constraint force of the small ring are analyzed. Taking circular orbit as an example, the influence of gravity and sliding friction on the orbital motion is given, and the results are verified by kinetic energy theorem. Finally, the characteristics

The Earth’s albedo, as the fraction of sunlight that is directly reflected back into space from the surface or clouds, is a key factor in modeling Earth’s climate. In tasks such as the simplified estimation of the mean temperature, it is usually given as a constant, without mentioning its determination and the associated difficulties. In fact, the albedo can be determined by a basically simple procedure

Quantum electrodynamics was described by Feynman as the ‘jewel of physics’ [1985 QED: The Strange Theory of Light and Matter (Alix G. Mautner Memorial Lectures) (Princeton, NJ: Princeton University Press)] because of its ability to precisely describe the interaction of light and matter. It embodies the key concepts of quantum physics and yetalso describes classical optics. It is normally considered

Comprehending the in-depth functioning of a voltage transformer beyond the trivial voltage ratio, generally deducted from the application of Faraday’s law to an open secondary circuit, can be quite challenging for both students and teachers. In this paper, the authors propose an approach that uses Faraday’s and Ohm’s laws alone to derive an electric equivalent circuit for a transformer, with which

The normal coefficient of restitution (COR) for a sphere that bounces obliquely or at right angles on a horizontal surface usually has an approximately constant value between 0 and 1, which are the limits for a completely inelastic or a perfectly elastic collision respectively. Different results are obtained for the bounce of a non-spherical object. Measurements are presented for a double sphere consisting

This article focuses on the recognition of an important quantity that will be called the Rund–Trautman function. It already plays a central role in Noether’s theorem since its vanishing characterizes a symmetry and leads to a conservation law. The main aim of the paper will be to show how, in the realm of classical mechanics, an ‘almost’ vanishing Rund–Trautman function accompanying an ‘almost’ symmetry

We carried out an experimental study of the floating of a square bar in water and found its equilibrium orientation (tilting angle) as a function of relative density ρ bar/ρ water. Though the theoretical solution of this problem was given in 1963 by Reid, we provided our solution that is more transparent and less cumbersome, enabling an introductory level physics student to follow it. Our experimental

The 32nd International Young Physicists’ Tournament (IYPT), a physics competition for students in schools, settled up a problem for the Moir thread counter. The problem mentioned to design an overlay to measure the thread count of the fabric. In this paper, we made one kind of Moir pattern-based thread counter by printing the designed overlay on the plastic paper. As a contrast, we also constructed

In this paper, we describe easy and cheap optics experiences for teaching undergraduate students the fundamental properties of Fourier transforms on an experimental basis. By exploiting the eye as the Fourier transforming device, a common magnifying lens, and quasi-coherent light from a small white LED, quantitative results can be easily obtained about the fundamental theorems used in Fourier analysis

An experiment is described using double and triple conical pendulums to simulate the behaviour of a rotating chain. The first few rotation modes are calculated theoretically and provide good agreement with experimental results. By contrast, a chain containing many links is difficult to analyse, even though the first few nonlinear modes of a vertically suspended chain are easy to excite and are easily

We performed word frequency analysis of the mechanics portion of an algebra-based introductory physics text. We identified about 400 physics and auxiliary words that constitute the core vocabulary of this subject. We present and discuss our findings especially as they inform physics instruction and communication in English, indigenous, and sign languages. This includes the Hawaiian language, our initial

One of the hurdles in teaching undergraduate thermodynamics is a plethora of complicated partial derivative identities. Students suffer from difficulties in deriving, justifying, or interpreting the identities, misconceptions about partial derivatives, and a lack of in-depth understanding of the meanings of identities. We propose a novel diagrammatic method for the calculus of differentials and partial

We demonstrate how to make the coordinate transformation or change of variables from Cartesian coordinates to curvilinear coordinates by making use of a convolution of a function with Dirac delta functions whose arguments are determined by the transformation functions between the two coordinate systems. By integrating out an original coordinate with a Dirac delta function, we replace the original coordinate

In the preceding paper Ficker (2020 Eur. J. Phys. 41 015101 https://doi.org/10.1088/ 1361-6404/ab4c1e), two alternative methods for measuring emissivity of opaque grey diffuse materials have been presented. In both these methods, the contactless temperature measured by the infrared thermometer has been employed. The thermometer has been set at emissivity ɛ = 1 chosen in the settings menu of the thermometer

We investigate a simple a discrete time random process based on the construction of Platonic solids. As is surprisingly often the case with apparently simple processes, we find some intriguing results, in this case requiring a careful consideration of how the probability distributions describing this process behave. The investigation proceeds by a fruitful combination of geometry, probability and elementary

Images of an explosion can be used to study some of its physical properties. After reviewing the key aspects of the method originally developed to study the first nuclear detonation and analyzing the Trinity blast data, the method is applied to the Beirut explosion of August 2020 by using images from videos posted online. The applicability of the method is discussed and the process of selection, extraction

The fifth edition of the ‘Computing Applications in Particle Physics’ school was held on 3–7 February 2020, at İstanbul University, Turkey. This particular edition focused on the processing of simulated data from the large hadron collider collisions using an analysis description language and its runtime interpreter called CutLang. 24 undergraduate and 6 graduate students were initiated to collider

A relativistic Hamiltonian–Lagrangian formalism for a composite system submitted to conservative and non-conservative forces is developed. A block descending an incline with a frictional force, mechanical energy dissipation process, is described, obtaining an Euler–Lagrange equation including a Rayleigh’s dissipation function. A cannonball rising on an incline, process evolving with mechanical energy

It has been established that the incorporation of active learning experiences in the context of university lectures increases overall student learning. This study contributes to the literature by examining iterations of incorporating interactivity where the ‘intensity’, in terms of the content, structure and time spent on different in-class activities is varied. The study described in this paper deals

Understanding student views about learning physics in the lab context can be invaluable for efforts to improve student learning. In an ethnographic study in which two researchers observed introductory physics labs, we found that many women in mixed gender groups adopted the role of group leader or project manager and ensured that the group stayed on task and completed the lab work as expected throughout

A frequently encountered source of systematic error in quantum computations is imperfections in the control pulses which are the classical fields that control qubit gate operations. From an analysis of the quantum-mechanical time-evolution operator of the spin wavefunction, it has been demonstrated that composite pulses can mitigate certain systematic errors and an appealing geometric interpretation

The planar Landau system which describes the quantum mechanical motion of a charged particle in a plane with a uniform magnetic field perpendicular to the plane, is explored within pedagogical settings aimed at the beginning graduate level. The system is known to possess the Euclidean symmetry in two dimensions with central extension . In this paper, we revisit the well-known energy eigenvalues of

In 1926, Erwin Schrdinger wrote a series of papers that invented wave mechanics and set the foundation for much of the single-particle quantum mechanics that we teach today. In his first paper, he solved the Schrdinger equation using the Laplace method, which is a technique that is quite powerful, but rarely taught. This is unfortunate, because it opens the door to examining quantum mechanics from

We present a simple approach, different from approaches in the literature, for calculating the magnetic field of a finite solenoid with a circular cross section, carrying an ideal surface current with an ordinary azimuthal component and a small axial component due to nonideal winding. The results are given as an infinite series whose terms are elementary functions or simple polynomials rather than

The capacitance technique is one of the simplest methods to determine the dielectric constant of dielectric sheets in the low-frequency band. A new methodology and test procedure which eliminates the effect of the capacitors from the calculations and improves the accuracy of measurement is introduced. The main advantage of the method is that it can be applied for arbitrary-shaped dielectric sheets

For a given total number of identical cells with internal resistance, we inquire the series–parallel combination of the cells that yields the maximum current through a load resistor linked to the combination. The aspect ratio or shape factor (number of parallel strings/number of serial cells in each string) of cell combination for the maximum load current depends on the resistance ratio (internal resistance/load

We describe a method that could have been used by Kepler to determine the shape and dimensions of Mars’ orbit around the Sun, starting from observations of its path across the night sky. Though we use Kepler’s work as a motivation, our approach does not intend to suggest that this method was actually used by him. Rather, it is only intended to show beginning undergraduate students what may be discovered

While riding a motorcycle the rider can find the handlebars along with the motorcycle frame to begin to oscillate at a high frequency. This motorcycle weave can be very dangerous as its frequency can be high at high speeds of the motorcycle. We collect evidence as how to avoid this motorcycle weave by numerically analyzing the eigenvalues of a certain matrix polynomial arising from the linearized model

The aim of this study is to investigate the bouncing dynamics of a small elastic ball on a staircase consisting of rounded edge steps, as an example of a dissipative gravitational billiard, and to determine if its dynamics is chaotic. We derive a nonlinear recursion for the coordinates of the collisions, completed with numerical simulations, which indicate that the bouncing dynamics is chaotic, as

This article describes a curricular innovation designed to help students experience authentic physics inquiry with an emphasis on computational modeling and scientific communication. The educational design centers on a new type of assignment called a computational essay, which was developed and implemented over the course of two semesters of an intermediate electricity and magnetism course at the University

An undergraduate-level student experiment has been designed and implemented to measure the forward–backward asymmetry of the decay of the cosmic-ray muons, offering a pedagogical view to the parity violation in weak interactions. The detector system consists of six plastic scintillators installed vertically in row. The backward–forward asymmetry of the decay e− and e+ with respect to the muon motion

We consider the finite potential well defined by ,where n is an integer. The Schrdinger equation is recast into dimensionless form; the size of the well is characterized by a single parameter . We use three different mathematical techniques to solve for the energy eigenvalues and wave functions. Analytic solutions are given for the triangular well (n = 1), the parabolic well (n = 2), and the square

The electrolysis of water using a DC circuit is a familiar physical science experiment and the empirical details of the process, especially in terms of the chemistry, are well known. There are however, long-standing questions in regard to the specific role played by the circuit itself and the electrolyte. Recent empirical studies of an electrolysis cell as a circuit element have revealed what we see

The forced precession of a symmetrical gyroscope is studied for the particular case in which the axle of a flywheel is pivoted by a hinge joint and follows a horizontal circular path of a given radius. The aforementioned setup appears in the so-called Laithwaite engine, the detailed mechanics of which are still an enigma. Instead of applying Lagrangian equations, Newton’s second law is applied to the

We built a simple structure of seven dipole neodymium magnetic balls, a magnetic spinner that easily rotates around its central ball. This proved to be a very simple magnetic oscillator-rotator with a dipole-like field. After capturing videos of its rotating movements in different magnetic fields, video analysis has provided us with the rotation angle-time function of the motion, either in the case

The Kronig–Penney model is a model used to study properties of electrons confined in a periodic potential. It is a useful model since the electronic properties can be studied analytically with the aid of Bloch’s theorem. An important concept that emerges from the resultant electron band theory is the electron effective mass. Through the use of the Kronig–Penney model we use the so-called ‘effective

Derived in this article is a mathematical model of a cyclist riding over uneven terrain. The model is very general; it is expressed in terms of arbitrary functions that describe how the elevation changes with horizontal distance and how the cyclist’s power output varies, and also accounts for road friction and air resistance. The model was validated by considering special cases such as horizontal and

This paper reviews how a two-state, spin-one-half system transforms under rotations. It then uses that knowledge to explain how momentum-zero, spin-one-half annihilation and creation operators transform under rotations. The paper then explains how a spin-one-half field transforms under rotations. The momentum-zero spinors are found from the way spin-one-half systems transform under rotations and from

A simple experiment is described concerning the vertical bounce of a nonspherical object. The object consisted of two golf balls joined together. The balls were dropped onto a heavy, rigid horizontal surface and were filmed with a video camera to measure the coefficient of restitution (COR). For spherical objects, the COR is usually defined in terms of the vertical speed of the centre of mass and can

We discuss a paradox from the field of relativistic thermodynamics: two heat reservoirs of the same proper temperature move against each other. One is at rest in the inertial reference frame S A, the other in S B. For an observer, no matter in which of the two reference frames he is at rest, the temperatures of the two reservoirs are different. One might, therefore, conclude that a thermal engine can

A goniometer is an instrument which is frequently used in optics and other branches of physics. It enables the study of light scattered in various directions from a solid, liquid or powdered sample. The goniometric instruments that are already available on the market are designed for a specific purpose and are quite costly. Fully-computerized devices—which automatically acquire data and control the

A mechanical resonance phenomenon in the rear wheels of a common shopping trolley is investigated. The trolley examined in this paper has the rear wheels attached to long beams, with no horizontal bar connecting the beams. The beams are thus free to vibrate along their entire lengths. In a resonant mode the beams vibrate with a small amplitude in a direction perpendicular to the general motion of the

This work focuses on exploring the phenomenon of looping pendulum proposed by ‘International Young Physicists’ Tournament in 2019, specifically, the various types of loops observed and the physical conditions for a loop to be successful. Firstly, we establish a theoretical model for three distinct stages of the motion observed in the phenomenon, i.e. slipping, non-slipping, and pulling phenomena. We

An automated system for measuring the energy gap E g of a p–n junction semiconductor diodes was presented in this study. The system, based on temperature–voltage (T–V) measurement, was designed and developed as a teaching tool to support teaching for undergraduate students. The energy gap of diodes was measured by varying the diode temperature from 273 to 343 K and by measuring the voltage drop across

The fact that the nucleus is lighter than its constituents, seems rather strange. How can the whole have a smaller mass than its components? To get some intuition about how this is possible, one can look at a simpler more familiar system exhibiting the same phenomena; the hydrogen atom. It turns out that the same is true here; the hydrogen atom is a little bit lighter than the sum of its constituents

We explore the semi-classical Sommerfeld method of quantization as applied to states with nonzero angular momentum, and show that it leads to qualitatively and quantitatively useful information about systems with spherically symmetric potentials. We begin by reviewing the traditional application of this model to hydrogen, and discuss the way Einstein–Brillouin–Keller (EBK) quantization resolves a mismatch

The uncertainty principle sets a limit to our capacity to predict the outcomes of two incompatible measurements. The Heisenberg uncertainty relation for two arbitrary observables and is usually discussed in textbooks. However, little or no attention is paid to the fact that Schrdinger generalised the Heisenberg relation taking into account the covariance between the observables and . This extended

We study the reflection and refraction of a monochromatic ray of light in a normal or rhomboid-shaped prism with an arbitrary apex angle. In particular, we investigate the conditions for the occurrence of the total internal reflection and propagation of light on the second surface of the prism by varying the incidence angle, apex angle, and refractive index of the prism. The regions within the two-dimensional

Plasmas are indissociable from microwave science. Effectively, the most fundamental properties of any plasma arise from its plasma frequency. However, combining plasma physics with electromagnetic (EM) wave propagation is challenging for physics students. An EM cavity poses an excellent opportunity to understand the behavior of EM standing waves, the issues related to transmitted and reflected power

The fact that repulsive Rutherford scattering casts a paraboloidal shadow is rarely exploited in introductory mechanics textbooks. Another rarely used construction in such textbooks is the Hamilton vector, a cousin of the more famous Laplace–Runge–Lenz vector. We will show how the latter (Hamilton’s vector) can be used to explain and clarify the former (paraboloidal shadow).

Successive Lorentz transformations (SLT) for energy and momentum are derived, and the involved Thomas rotation angle (TRA) is highlighted. In particular, if the axes of the coordinate systems related by SLT are suitably chosen, the SLT for energy and momentum do not depend on the TRA explicitly and take a form analogous to that of the Lorentz transformation for energy and momentum. Then the study of

The result of the only known good quality observations of September 18, 2017 Venus occultation by the Moon is presented in this article. This kind of observation can be done by students using a common camera, and the analysis can be designed as a mathematics and physics exercise. Several observations were carried out in Malang and Jakarta, but high quality data were obtained only in Jakarta. An analysis

Quantum optics plays an important role in many contemporary applications of quantum information processing and quantum metrology. Experimental implementations of these protocols, however, inevitably exhibit loss. This loss has two distinct forms, stochastic loss and deterministic loss, which impact quantum mechanical systems in distinct ways. In this exposition, we offer a straightforward experimental