The bicycle provides a context-rich problem accessible to students in a first-year physics course, encircling several core physics principles such as conservation of total energy and angular momentum, dissipative forces, and vectors. In this article, I develop a simple numerical model that can be used by any first-year physics student to…

The null result of the Michelson-Morley experiment and the constancy of the one-way speed of light in the "rest system" are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental…

A number of cars drive along a narrow road that does not allow overtaking. Each driver has a certain maximum speed at which he or she will drive if alone on the road. As a result of slower cars ahead, many cars are forced to drive at speeds lower than their maximum ones. The average velocity in the queue offers a non-trivial example of a mean…

Background: The emergence of a participatory culture, brought about mainly by the use of Web2.0 technology, is challenging us to reconsider aspects of teaching and learning. Adapting the learning-as-digital-game-building approach, this paper explores how new educational practices can help students build skills for the 21st century. Purpose: This…

In this age of the microcomputer-based lab (MBL), students are quite accustomed to looking at graphs of position, velocity, and acceleration versus time. A number of textbooks argue convincingly that the slope of the velocity graph gives the acceleration, the area under the velocity graph yields the displacement, and the area under the…

This paper presents an original undergraduate student project in theoretical mechanics: a demonstration of theory and experiment agreement inspired by a recently theoretically treated mechanical problem of coupled rolling motion of two cylinders. The problem of a mechanical system subjected to non-holonomic constraints is theoretically and…

We study the turning point problem of a spherical pendulum. The special cases of the simple pendulum and the conical pendulum are noted. For simple initial conditions the solution to this problem involves the golden ratio, also called the golden section, or the golden number. This number often appears in mathematics where you least expect it. To…

Energy is a critical concept in physics problem-solving, but is often a major source of confusion for students if the presentation is not carefully crafted by the instructor or the textbook. A common approach to problems involving deformable or rotating systems that has been discussed in the literature is to employ the work-kinetic energy theorem…

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple…

It's a situation every avid cyclist knows only too well. If you cycle up a hill and then back down with no net change in elevation, it seems as if your slower uphill speed and faster downhill speed should offset each other. But they don't. Your average speed is less than it would have been had you cycled the same distance on a level road.…

We present a study of the ascending vertical motion of a self-propelled body under a uniform gravitational field suffering the action of two different types of air friction forces: linear on the velocity, which is valid for slowly moving bodies, and quadratic on the velocity. We study the special case where the thrust force is a decreasing…

We solve for the motion of an object with initial velocity v[subscript 0] and subject only to the combined drag of forces linear and quadratic in the velocity. This problem was treated briefly by Newton, after he developed a theoretical argument for the quadratic term, which we now know is characteristic of turbulent flow. Linear drag introduces a…

This study investigated the motor strategy involved in mental rotation tasks by examining 2 types of spontaneous gestures (hand-object interaction gestures, representing the agentive hand action on an object, vs. object-movement gestures, representing the movement of an object by itself) and different types of verbal descriptions of rotation.…

We investigate the problem of the horizontal distance travelled by a mobile experiencing a quadratic drag force. We show that by introducing a normalized distance, the problem can be greatly simplified. In order to parametrize this distance, we use the Pearson VII function, and we find that the optimal launch angle as a function of the initial…

A model is presented that describes a scalar field interacting with a point particle in (1+1) dimensions. The model exhibits many of the same phenomena that appear in classical electrodynamics, such as radiation and radiation damping, yet has a much simpler mathematical structure. By studying these phenomena in a highly simplified model, the…