The various aspects of projectile motion have been analyzed many times in this journal. As a sample, over the years, authors have investigated particular details of the path of a projectile and different situations for launching projectiles. Others have written about a nifty way to determine the maximum height of a projectile, finding the range of…

Modern MEMs gyros/accelerometers allow the angular velocity of pendula to be precisely measured and the angular acceleration to be calculated. For a compound pendulum, "I"[subscript p][umlaut over theta]=-"mga" sin[theta]Ip[umlaut over theta]=-mgasin[theta], where "a" is the distance of the center of mass from the…

We describe a simple, intuitively appealing interpretation of the observed ellipsoidal shape of the rotating Earth: it is that surface everywhere perpendicular to the net force upon it.

A new system for tracking a metal ball rolling on the slope of the touch panel of a tablet computer was developed. The widespread introduction of tablets in educational environments allows the use of a convenient dynamic measurement in schools.

Acceleration of moving objects is usually measured by photoelectric gates. In this paper, a method of acceleration measurement is proposed by pasting white card stock and black tape on a pulley and then using an Arduino to time the motion. This method only needs one photoelectric sensor to measure the acceleration. In contrast, using photoelectric…

Inspired by a commercially produced scattering experiment that was popular beginning in the 1960s, we have developed a Nerf-projectile-based educational activity to demonstrate the basics of particle scattering experiments.

How many vertical jumps does it take to jump off of a rotating merry-go-round (MGR)? The answer is hidden in the expression: "r[subscript n]" = "r[subscript 0]" (1 + ["beta superscript 2") ["superscript n/2"]. When you make a vertical jump on a train moving on a straight line at constant speed (inertial…

Aristotle's wheel paradox is a fascinating example of a classical puzzle that can pique a student's interest. The existing explanations in the literature are limited to discussions of the wheel trajectory; in this paper, we study the paradox from the viewpoint of motion decomposition, an approach we consider more intuitive. The motion of the point…

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…

The center of mass (CM) is an abstract quantity but essential as a reference point used to understand the position and movement of an object or a system of objects. Many researchers have used video recordings to analyze and understand the movement of objects in a system. In a system with colliding objects, the motion can be obtained precisely from…

The use of toys as teaching aids in physics classrooms has a rich history, and the role of play in science education is a well-established line of research. Much of what has been written on the topic has included discussions of specific toys and the implications of using those toys to teach physics. One of the toys from my childhood that seems to…

The relativistic addition of velocities is usually introduced early in the study of Einstein's special theory of relativity. The equations are simple enough, but randomly chosen velocities lead to unwieldy calculations that can dishearten the student. This paper presents tables of velocity components in two dimensions, composed of five or fewer…

The dynamics of yo-yo motion are considered in this article. Many textbooks have examined the "rolling" motion of a yo-yo as it moves vertically up or down. However, in the vicinity of the lowest point, a jerk in the string occurs as the center of mass transitions from a linear motion to a pure rotational motion (with respect to the end…

The variation of the period of oscillation of a pendulum with the amplitude is known as "circular error" to clockmakers, and can easily be observed even without modern laboratory instruments. There have therefore been many approximate formulae for the pendulum period as a function of the amplitude, but the simple equation due to Denman,…

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…