The variation of the period of oscillation of a pendulum with the amplitude is known as "circular error" to clockmakers, and can easily be observed even without modern laboratory instruments. There have therefore been many approximate formulae for the pendulum period as a function of the amplitude, but the simple equation due to Denman,…

There is a close connection between simple harmonic motion and uniform circular motion. This connection is widely taught and included in standard textbooks. Here, we exploit this connection to simultaneously derive two results from introductory mechanics: the period of a mass-spring system and the centripetal acceleration formula. Previously…

In this study, we derived several formulas for the currents induced in a circular loop by a magnet connected to a spring-based simple harmonic oscillation system. In addition, we conducted an experiment for measuring the induced currents and compared the results with the theoretical prediction. It was confirmed that the prediction from the derived…

A video is taken of a road-sign mirage from the passenger seat in a car traveling at constant speed on a highway. The video spans the duration of seeing the mirage of the sign, viewing the vanishing of the mirage as the car approaches, and passing the road sign. The mirage angle, defined as the angle with respect to the horizontal at the moment…

Costume jewelry beads are employed to demonstrate how a beam of beads are able to transform into a simple pendulum (single bead) where the pendulum length remains constant throughout. These beads are common and inexpensive for instructors, as well as attractive and exciting for students. Beads are removed from the top, keeping the same pendulum…

In many introductory-level physics textbooks, the derivation of the formula for the speed of transverse waves in a string is either omitted altogether or presented under physically overly idealized assumptions about the shape of the considered wave pulse and the related velocity and acceleration distributions. In this paper, we derive the named…

Gravity racing can be studied using numerical solutions to the equations of motion derived from Newton's second law. This allows students to explore the physics of gravity racing and to understand how design and course selection influences vehicle speed. Using Euler's method, we have developed a spreadsheet application that can be used to predict…

Introduction: Braille readers encounter difficulties when reading mathematical expressions. In this exploratory study, we created a setting to investigate these difficulties. Method: Using a motion-capturing system, we analyzed the tactile strategies of three braille readers while they read mathematical expressions. To compare tactile with visual…

Physics and Mathematics are two deeply interlinked domains of Science. Mathematics is considered as the language in which the Physics theories are built by employing mathematical symbols and operations to make equations and representations in the world of Physics completely meaningful. In spite of being the backbone of Physics, the use of…

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures,…

In classroom science laboratories, unlike a real science laboratory, the teacher can guide students away from potential dead ends and toward data that are most likely to result in accurate conclusions. Sometimes, though, allowing students to pursue dead ends and to collect "bad" data can provide especially rich learning opportunities.…

According to the Newtonian formula for a simple pendulum, the period of a pendulum is inversely proportional to the square root of "g", the gravitational field strength. Einstein's theory of general relativity leads to the result that time slows down where gravity is intense. The two claims look contradictory and can muddle student and…

In understanding upper secondary school students' interpretations of information in symbolic representations of a distance-time-relation, little attention has been paid to the analysis of the condition of the conceptual development related to utterances. Understanding this better can help improve the teaching of attribute and information in…

Large gender gaps in performance on questions involving projectile motion have been observed at high school and university level, even amongst high-achieving students. This gap is particularly problematic because projectile motion is typically one of the first topics formally taught in physics, and this may give girls an inappropriately negative…

A simple mathematical formulation of Mach's principle is given based on a century of investigation into inertia, and used to check the results of Newton's famous bucket experiment.