Bounded by the statements of Feynman and Galileo, I describe certain tricks that can be useful for the teaching of physics. In particular, I describe the calculation of the center of mass (centroid) of an arc of circumference and a circular sector. For this purpose, I also use Pappus's theorems. An Appendix is available with Archimedes' method to…

Keto-enol tautomerization is paramount to understanding the mechanisms involved in many organic reactions and biochemical transformations. Isomerization of an enol to a carbonyl compound is typically introduced during the discussion of the acid-catalyzed electrophilic addition of water to alkynes. The tautomerization of carbonyl compounds to enol…

Ion transport, involving the diffusion and migration of ions within the electrolyte, stands as a fundamental concept in electrochemistry and serves as the driving force for electrochemical reactions. Electric double layers are critical in the fields of electrochemical energy storage and chemical conversion, constituting a central focus of…

Valence shell electron pair repulsion theory (VSEPR) as explained in most textbooks predicts that substituents bonded to a central atom in AX[subscript n]E[subscript z][superscript c] species (A = main-group central atom, X = substituent, E = lone pair on central atom, c = charge) will change their X-A-X angles to bend away from the lone pairs.…

The relativistic addition of velocities is usually introduced early in the study of Einstein's special theory of relativity. The equations are simple enough, but randomly chosen velocities lead to unwieldy calculations that can dishearten the student. This paper presents tables of velocity components in two dimensions, composed of five or fewer…

The trajectory of a ball in air is affected by aerodynamic drag and lift. In general, the trajectory needs to be calculated numerically since the acceleration varies with time in both the horizontal and vertical directions. If the trajectory remains approximately parabolic, then simple analytical solutions can be found, giving useful insights into…

It is difficult for an instructor to just make up valid numbers for B[subscript x], B[subscript y], B[subscript z], E[subscript x], E[subscript y], and E[subscript z] in the creation of homework problems and test questions calculating the Poynting vector. In this paper, 25 examples are given of the electric and magnetic fields of electromagnetic…

Background/purpose. 21st-century skills are essential across all aspects of life in the modern era. Pre-service elementary school teachers must also develop computational thinking skills as part of the problem-solving process--one of the most critical 21st-century competencies. These skills are critical in science learning and serve as fundamental…

A simple experiment is described to compare the descent time between two vertically separated points when an object slides down tracks of varying shape. A surprising result is that the descent time is shortest when it follows a circular track rather than a cycloidal track. Cycloidal tracks are usually predicted to result in the shortest descent…

Electricity and magnetism are closely related phenomena with a well-known symmetry found in Maxwell equations. An essential part of any electricity and magnetism course includes the analysis of different field source distributions through Gauss's and Ampere's laws to compute and interpret different physical quantities, such as electric flux,…

Theoretical and practical foundations of basic electrochemical concepts of heterogeneous charge transfer reactions that underline electrochemical processes are presented for their detailed study by undergraduate and postgraduate students. Several simple methods for calculating key variables, such as the half-wave potential, limiting current, and…

This review describes a computational chemistry exercise aimed at enhancing the understanding of upper-division undergraduates in organic chemistry and physical chemistry regarding the structures and aromaticities of cyclobutadiene and cyclooctatetraene. This exercise exposes students to chemical problems that require computational methods as a…

Solution equilibria diagrams are excellent tools for understanding chemical speciation in multireaction chemical systems. They are usually plotted using software packages that efficiently perform advanced calculations, giving the possibility to graphically visualize thermodynamic and composition information. However, this approach frequently…

This study focuses on the experimental demonstration of the definition of kelvin using a triple point of water (TPW) cell and estimates the measurement uncertainty. The first part of this article is to construct the measurement setup and perform the measurements. The second stage is related with the calculation of uncertainty according to guides…

The fundamental mechanism of biochemistry lies on the reaction kinetics, which is determined by the reaction pathways. Interestingly, the reaction pathway is a challenging concept for undergraduate students. Experimentally, it is difficult to observe, and theoretically, it requires some degree of physics knowledge, namely statistical and quantum…