Exciting examples of physics principles illuminate the power and scope of our discipline. In this paper, we discuss a conservation of energy example for an introductory course. Energy conservation is applied to bird and dinosaur eggs to derive a method to predict the incubation period and the embryonic metabolism solely from the egg geometry. The…

Fermat's principle states that a light ray refracted across different media will traverse the fastest path as the physics for Snell's law. A geometric proof of Fermat's principle will be demonstrated as an intuitive approach to learn high school geometry and physical optics. It will be proved explicitly by showing that all alternative paths need…

Low cost, open-source analytical instrumentation has the potential to increase educational outcomes for students and enable large-scale citizen science projects. Many of these instruments rely on smartphones to collect the data, mainly because they can effectively leverage a dramatic price-to-performance ratio of the optical sensors. However,…

Light refracts as it travels from one medium to another. The angle of incidence "i" and the angle of refraction "r" are related by Snell's law, sin"i" ÷ sin"r"="k," where "k" is a constant. The diagram in Fig. 1 shows a geometric representation of the formula for light passing from…

Here is a way to show a sound wave travelling through air in real time. The method employs a set of low-cost microphone--LED units and demonstrates the movement of a pulse of sound as it lights up LEDs along a long (100-200 m) distance across a field. (Contains 4 figures.)

In a typical high school course, the complex physics of collisions is broken up into the dichotomy of perfectly elastic versus completely inelastic collisions. Real-life collisions, however, generally fall between these two extremes. An accurate treatment is still possible, as demonstrated in an investigation of coin collisions. Simple…

This document contains all of the Minnesota kindergarten academic standards in the content areas of Arts, English Language Arts, Mathematics, Science and Social Studies. For each content area there is a short overview followed by a coding diagram of how the standards are organized and displayed. This document is adapted from the official versions…

Both, virtual and printed 3D crystal models can help students and teachers deal with chemical education topics such as symmetry and point groups. In the present paper, two freely downloadable tools (interactive PDF files and a mobile app) are presented as examples of the application of 3D design to study point-symmetry. The use of 3D printing to…

Much of the mathematical reasoning employed in the typical introductory physics course can be traced to Pythagorean roots planted over two thousand years ago. Besides obvious examples involving the Pythagorean theorem, I draw attention to standard physics problems and derivations which often unknowingly rely upon the Pythagoreans' work on…

The logical structure of classical thermodynamics is presented in a modern, geometrical manner. The first and second law receive clear, operatively oriented statements and the Gibbs free energy extremum principle is fully discussed. Applications relevant to chemistry, such as phase transitions, dilute solutions theory and, in particular, the law…

We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…

Many illustrations and problems on the vector nature of forces have weights and forces in a vertical plane. One of the common devices for studying the vector nature of forces is a horizontal "force table," in which forces are produced by weights hanging vertically and transmitted to cords in a horizontal plane. Because some students have…

The Dirac belt trick is often employed in physics classrooms to show that a 2n rotation is not topologically equivalent to the absence of rotation whereas a 4n rotation is, mirroring a key property of quaternions and their isomorphic cousins, spinors. The belt trick can leave the student wondering if a real understanding of quaternions and spinors…

Ronald J. Gillespie, the inventor of the Valence Shell Electron Pair Repulsion (VSEPR) model, relates how his career as researcher in Christopher Ingold's laboratories started. Gillespie developed a passion for chemistry and chemical education, searching for more appropriate and interesting ways to transmit the essential knowledge and enthusiasm…

The particular problem solved in this paper is that of calculating the time required to overtake a distant object receding under cosmic expansion, and the speed at which that object is passed. This is a rarely investigated problem leading to some interesting apparent paradoxes. We employ the problem to promote a deeper understanding of the dynamic…