The cross diagram is a way to illustrate and plan the solutions for all kinds of constant-acceleration kinematics problems--including projectile motion, multistage, and multiple-object problems. The cross diagram arranges the kinematic variables in a logical way, making the kinematic relationships between them easy to identify. Combined with a…

Lissajous figures are parametric equations that deconstruct into equations of simple harmonic motion. They were a source of inspiration by artists and mathematicians alike, well before the digital age, due to their esthetic forms and simple equations that could be easily deconstructed. Here for the first time in literature, we present Lissajous…

An experiment is described where a pendulum bob was allowed to roll back and forth across an inclined plane. The period of oscillation is larger than that for oscillation in a vertical plane, in part because the effective value of "g" is reduced on an inclined plane. The experiment highlights the differences between all three common…

It is well known that Newton's work on mechanics depended in a crucial way on the previous observations of Galileo. The key insight of Galileo was that one can analyze the motion of bodies using experiments and mathematical equations. One experimental observation that roughly emerges from this work in modern terms is that two objects of different…

Bridges are a popular topic in this journal, because they are a very visual display of static and dynamic physical principles. In this paper, we provide an intuitive derivation of the equations associated with suspension bridge cables and load-bearing arches, which is of pedagogical interest in illustrating the consequences of Newton's laws for…

The cases of constant and quadratic damping of free oscillations are missing from standard textbooks, even at college and university level. The case most examined is that of linear damping, the reason being that the student can work out a closed form which describes all stages of motion. The case of constant damping is straightforward to be…

In the context of quantum mechanics, students are often asked to use delta functions to solve problems. Here, we investigate three typical problem-solving processes using delta functions: a delta function potential well problem, a position space delta function problem, and a momentum space delta function problem. We studied students'solutions in…

A rocket in free space accelerates from rest by continuously expelling fuel; as its speed increases, its mass decreases. At what speed (and remaining mass) does the rocket carry maximum momentum? Maximum kinetic energy? The answers provide insights into the dynamics of variable-mass systems, and have applications to planetary defense that are…

One of the easily accessible results in elementary fluid mechanics is the so-called Torricelli's theorem (or law), which states that the velocity U[subscript th] of the fluid exiting from an orifice at depth "h" from the free surface of a container filled with fluid, is the same as the velocity of a free-falling body from rest over a…

The static equilibrium properties of a spool, resting on an incline and subject to the tension exerted by a string wrapped around the core cylinder, are studied by means of Newtonian mechanics. The overall behaviour of this system is imagined to be similar to that of a doggie kept on a leash. Starting from the well-known mechanical properties of…

In an attempt to address the need for an alternative presentation of the quantum mechanical position and momentum spaces, we provide a presentation that is more constructive and less calculative than those found in literature. Our approach is based on a simple, intuitively understood relation that expresses the physical equivalence of the quantum…

Newton's cradle is often discussed in science classrooms as a clear example of the laws of conservation of momentum and energy although it has been shown that this use is somewhat misleading. Approaches to understanding the behaviour of this apparatus are often over-simplified and deficient or over-complex and with little impact among teachers. In…

A significant approach that should be followed by physics teachers at the secondary education level in order to enhance students' understanding is to highlight the generality of the mathematical procedures that describe different physical phenomena. In this paper, the common procedure that is used to calculate the duration of various physical…

Problems involving rotating systems analysed from an inertial frame, without invoking fictitious forces, is something that freshman students find difficult to understand in an introductory mechanics course. In this article we try to see what could be the factors that lead to this difficulty and propose a set of arguments that could be used to…

Use of three-force member concept for rigid bodies whenever possible, to circumvent the more taxing use of equilibrium equations has been long-established. However, most students fail to reap its benefits due to a number of reasons, including the fact that its importance is hardly emphasized to them; skills and details needed for the concept are…