A Slinky is a loose helical coil spring and is a well-known educational toy. In this paper a model for a Slinky is presented. The Slinky is represented as a sequence of rigid half coils connected by torsional springs. A range of Slinky configurations in static equilibrium are calculated. Where possible the torsion spring model is compared with the…

We propose a method to measure the speed of sound in air using a motion detector. The experiment is based on the principle of a motion detector used to measure distances. This device measures the time of flight of alternating ultrasonic waves between the observer and the target. By assuming a fixed speed of sound, the time of flight can be…

In this note, the classical Doppler shift for some accelerated mechanical systems is considered under a common graphical approach. In one dimension, we study uniform accelerated motion and simple harmonic motion. In two dimensions, uniform circular motion and pendular motion are considered. In each case, an elementary treatment shows that the…

Friction is one of the most important forces studied in classical mechanics, and still is the subject of pedagogical literature. In a small series of problems stated below, we consider a particle sliding down a curve under the actions of gravity and kinetic friction. Unlike many of the referenced sources, we neglect the centripetal force arising…

There is a close connection between simple harmonic motion and uniform circular motion. This connection is widely taught and included in standard textbooks. Here, we exploit this connection to simultaneously derive two results from introductory mechanics: the period of a mass-spring system and the centripetal acceleration formula. Previously…

The trajectory of a ball in air is affected by aerodynamic drag and lift. In general, the trajectory needs to be calculated numerically since the acceleration varies with time in both the horizontal and vertical directions. If the trajectory remains approximately parabolic, then simple analytical solutions can be found, giving useful insights into…

During elementary physics courses, many examples in mechanics are studied without considering air resistance effects. We can mention, for example, projectile motion and free fall, among many others. Only brief studies of such systems in classical mechanics courses consider linear air resistance (F[subscript drag] [is proportional to] v), which is…

The present study reports an Arduino-based STEM education material that resolves the kinematics of a moving object, specifically focusing on two dimensional motion of the object. Throughout the work, a sample application that can be prepared in a classroom where students are active and including the acquisitions of Technology, Engineering, Physics…

In this article, we construct a very simple double pendulum (the concept of a pendulum should be familiar to all beginning students of classical mechanics). Since a double pendulum has two degrees of freedom, we suggest that this pendulum can be used in the classroom environment to illustrate the concept of normal modes, and we use video software…

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…

A rocket must carry the fuel it expels in order to accelerate its structure and payload. The rocket equation relates the change in speed to the fuel mass expelled. To launch a spacecraft into Earth orbit requires a multi-stage rocket, since otherwise the mass of fuel required would be prohibitive. While the details vary among historical and…

A simple experiment is described to compare the descent time between two vertically separated points when an object slides down tracks of varying shape. A surprising result is that the descent time is shortest when it follows a circular track rather than a cycloidal track. Cycloidal tracks are usually predicted to result in the shortest descent…

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…

The problem of an electrically charged pendulum above a grounded conducting surface is examined using traditional analyses, such as forces, energy, and torque. The system was numerically modelled using a finite difference method and analysed. A number of classroom activities have been suggested.

A loop-the-loop experiment usually involves a ball rolling around a vertical loop. A different version of the experiment is described where a nut was allowed to slide around a vertical loop. In both experiments there is a large decrease in kinetic energy when the ball or the nut first enters the loop.