Too often, students in introductory courses are left with the impression that Einstein's special theory of relativity comes into play only when the relative speed of two objects is an appreciable fraction of the speed of light ("c"). In fact, relativistic length contraction, along with Coulomb's law, accounts quantitatively for the force on a…

Teachers have been building mystery circuits or so-called "black box circuits" to use as a demonstration with their students for years. This paper presents an easy way to make simple mystery circuits using inexpensive light fixtures (see Fig. 1) available at almost any home improvement store. In a black box circuit, only the lightbulbs are visible…

The following idealized problem is intended to illustrate some basic thermodynamic concepts involved in kinetic friction. A block of mass m is sliding on top of a frictional, flat-topped table of mass M. The table is magnetically levitated, so that it can move without thermal contact and friction across a horizontal floor. The table is initially…

The pages of "The Physics Teacher" have featured several clever designs for homemade diffraction gratings using a variety of materials--cloth, lithographic film, wire, compact discs, parts of aerosol spray cans, and pseudoliquids and pseudosolids. A different and inexpensive method I use to make low-resolution diffraction gratings takes advantage…

Ordinarily, opening a door by pulling on the knob or handle causes a net torque on the door, and hence an angular acceleration, about a "vertical" axis. However, it may be that the top or bottom of the door sticks to the door frame; this horizontal force perpendicular to the plane of the door causes a torque on the door about a "horizontal" axis.…

In electric or mixed electric-mechanic systems, the distinction between potential and kinetic energy is not as clear as in purely mechanical systems. A solution for the motion of an inductively loaded rail generator is presented. In this case, the magnetic field energy (1/2)Li[superscript 2] can be written "formally" in terms of a potential…

The appendix on the centres of gravity that appears at the end of Galileo's book, "Two New Sciences", is analysed. It is shown that the method used by Galileo in this work has an interesting reasoning and also shows preliminary ideas about scaling and advances some ideas about series convergence. In addition, we note that the geometrical language…

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…

This paper presents an experimental technique to observe the vibration tracks of string standing waves. From the vibration tracks, we can analyse the vibration directions of harmonic waves. For the harmonic wave vibrations of strings, when the driving frequency f[subscript s] = Nf[subscript n] (N = 1, 2, 3, 4,...), both resonance and non-resonance…

The design of the FMEL, a floor-mirrored Einstein-Langevin "light clock", is introduced. The clock provides a physically intuitive manner to calculate and visualize the time dilation effects for a spatially extended set of observers (an accelerated "frame") undergoing unidirectional acceleration or observers on a rotating cylinder of constant…

We develop a two-dimensional flight simulator for lightweight (less than 10 g) indoor planes. The simulator consists of four coupled time differential equations describing the plane CG, plane pitch and motor. The equations are integrated numerically with appropriate parameters and initial conditions for two planes: (1) Science Olympiad and (2)…

When Alice went "Through the Looking Glass", she found herself in a situation where she had to run as fast as she could in order to stay still. In accordance with the dictum that truth is stranger than fiction, we will see that it is possible to find a situation in special relativity where running towards one's target is actually…

The problem of motorbike feathering has been analysed by writing the angular momentum theorem for non-inertial reference systems. The acceleration, for which the ideal line joining the median points of the axles of the two wheels makes an angle [theta] with the horizontal, has been calculated neglecting air friction and considering that the…

The motion of a ball rolling without slipping on the lateral section inside a fixed vertical cylinder is analysed in the Earth referential frame which is assumed to be Galilean. Equations of motion are rapidly obtained and the golf ball paradox is understood: these equations describe a motion consisting of a vertical harmonic oscillation related…

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…