This study investigated evidence of how students' mental models of fundamental kinematic relations evolved (i.e., developed cognitively over time) as observed during an introductory course in calculus-based classical mechanics. The core of the curriculum is based on a claim known as Galileo's principle of relativity. The course material comprised…

The law of conservation of momentum is a fundamental law of nature. It states that the momentum of an isolated system is conserved. In high school or introductory-level physics courses, for simplicity, teachers and textbooks always use collisions in one dimension as the examples to introduce the concept of conservation of momentum. To solve simple…

An important step in learning to use math in science is learning to see symbolic equations not just as calculational tools, but as ways of expressing fundamental relationships among physical quantities, of coding conceptual information, and of organizing physics knowledge structures. In this paper, I propose "anchor equations" as a…

The 1969 version of "The Italian Job" is used as context for teaching turning forces and introducing or enhancing the understanding of equilibrium and Newton's Third Law of Motion. A Harrington Legionnaire coach is used as the getaway vehicle for a gold heist and the film ends on a genuine cliffhanger, with the rear half of the coach…

Describing the motion in a vertical roller coaster loop requires a good understanding of Newton's laws, vectors and energy transformation. This paper describes how first-year students try to make sense of force and acceleration in this example of non-uniform circular motion, which was part of a written exam. In addition to an analysis of the exam…

The aim of this paper is to propose a method for solving head-on elastic collisions, without algebraic complications, to emphasize the use of the fundamental conservations laws. Head-on elastic collisions are treated in many physics textbooks as examples of conservation of momentum and kinetic energy.

The Bernoulli's principle states that the quantity p+ pgz + pv[superscript 2]/2 must be conserved in a streamtube if some conditions are matched, namely: steady and irrotational flow of an inviscid and incompressible fluid. In most physics textbooks this result is demonstrated invoking the energy conservation of a fluid material volume at two…

An astronomy "experiment" composed of three parts is described in the article. Being given necessary data a simple model of inner planets of the solar system is made in the first part with planets' circular orbits using appropriate scale. In the second part revolution of the figurines used as model representations of the planets along…

Instead of solving ordinary differential equations (ODEs), the damped simple harmonic motion (SHM) is surveyed qualitatively from basic mechanics and quantitatively by the instrumentality of a graph of velocity against displacement. In this way, the condition b ? [square root]4mk for the occurrence of the non-oscillating critical damping and…

By describing the motion of a charged particle in the well-known nonuniform field of a current-carrying long straight wire, a variety of teaching/learning opportunities are described: 1) Brief review of a standard problem; 2) Vector analysis; 3) Dimensionless variables; 4) Coupled differential equations; 5) Numerical solutions.

Consider a skier who goes down a takeoff ramp, attains a speed "V", and jumps, attempting to land as far as possible down the hill below (Fig. 1). At the moment of takeoff the angle between the skier's velocity and the horizontal is [alpha]. What is the optimal angle [alpha] that makes the jump the longest possible for the fixed magnitude of the…

This paper is essentially about the general form of Newton's second law for variable mass problems. We develop a model for describing the motion of the one-dimensional oscillator with a variable mass within the framework of classroom physics. We present a simple numerical procedure for the solution of the equation of motion of the system to…

The technique of bump drafting, also known as two-car drafting in motorsports, is analysed in the framework of Newtonian mechanics and simple aerodynamic drag forces. As an apparent unnatural effect that often pleases the enthusiasts of car racing, bump drafting provides a unique pedagogical opportunity for students to gain insights into the…

The following kinematics problem was given to several students as a project in conjunction with a first-semester calculus-based physics course. The students were asked to keep a journal of all their work and were encouraged to keep even their scrap paper. The goal of the project was to expose the students to the process of doing theoretical…

Newton's second law is one of the cornerstones of the introductory physics curriculum, but it can still trouble a large number of students well after its introduction, hobbling their ability to apply the concept to problem solving and to related concepts, such as momentum, circular motion, and orbits. While there are several possibilities for…