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…

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…

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.

Presented here is an adaptation of George Gamow's derivation of the centripetal acceleration formula as it applies to Earth's orbiting Moon. The derivation appears in Gamows short but engaging book "Gravity", first published in 1962, and is essentially a distillation of Newton's work. While "TPT" contributors have offered several insightful…

The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most familiar tools of special relativity, in arguments presented at three differing levels: (1) utterly elementary,…

Fleming's right-hand rule and the right-flat-hand rule are generally applied for determining the direction of flow of induced emf/current in straight conductors. The right-hand-fingers rule is applied for coils only. The right-hand-thumb rule can be applied for either straight conductors or coils. Different rules have to be applied for different…

This paper was first motivated by the following question: "A pair of twins, R and S, each gives the "same" hard push on a block. R's block is on a rougher floor than S's. Who does more work?" It is shown that S will do more work on his block if there is no constraint on the distance over which the force is applied. On the other hand, if the…

An analytic approximation of the solution to the differential equation describing the oscillations of a simple pendulum at large angles and with initial velocity is discussed. In the derivation, a sinusoidal approximation has been applied, and an analytic formula for the large-angle period of the simple pendulum is obtained, which also includes…

Making connections is one of the most important foundations involved in learning mathematics. Two projects are presented in this article: one involving Newton's Second Law of Motion and the other involving the determination of star numbers, a type of figurate number. The two invoke seemingly different modalities for students at different levels of…

The Lorentz velocity addition formula for one-dimensional motion presents a number of problems for beginning students of special relativity. In this paper we suggest a simple rewrite of the formula that is easier for students to memorize and manipulate, and furthermore is more intuitive in understanding the correction necessary when adding…

Based on relativistic velocity addition and the conservation of momentum and energy, I present simple derivations of the expressions for the relativistic momentum and kinetic energy of a particle, and for the formula E = mc[superscript 2]. (Contains 5 footnotes and 2 figures.)

The topic of coupled oscillations is rich in physical content which is both interesting and complex. The study of the time evolution of coupled oscillator systems involves a mathematical formalization beyond the level of the upper secondary school student's competence. Here, we present an original approach, suitable even for secondary students, to…

Faraday's and Furry's formulae for the electromagnetic momentum of static charge distributions combined with steady electric current distributions are generalized in order to obtain full agreement with Poynting's formula in the case where all fields are of class C[superscript 1], i.e., continuous and continuously differentiable, and the…

Explores the basic physical laws of the juggling activity. Derives some equations involving height, angle, time, and distance for common juggling objects. Describes the relationships among height, length, mass, number of clubs, number of spins, angular velocity, time, and angle in club juggling. (YP)