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…

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.

In high school, and also in introductory physics courses in higher levels of schooling, the law of universal gravitation of planets is introduced by postulating Johannes Kepler's three laws, and later Isaac Newton's law of the inverse of the square of the distance to the Sun. The justification of the laws is only achieved in advanced courses in…

Experimental results are presented concerning the motion of a ball that bounces up an incline a few times then bounces back down again. The number of bounces up the incline is typically small since the speed of the ball in a direction parallel to the incline decreases rapidly, not only during each bounce but also while the ball is in the air. The…

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 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.

On 24 June 1994 at Fairchild Air Force Base, during practice for an air show, a low-flying B-52H aircraft banked its wings vertically and crashed. Emphasizing the activity of modeling drag and gravity, these notes examine the possibility of recovery with several models. First, with algebra, historical data lead to a model where in a free fall near…

A rocket in free space accelerates from rest by continuously expelling fuel; as its speed increases, its mass decreases. At what speed (and remaining mass) does the rocket carry maximum momentum? Maximum kinetic energy? The answers provide insights into the dynamics of variable-mass systems, and have applications to planetary defense that are…

Smartphones and their internal sensors offer new options for an experimental access to teach physics at secondary schools and universities. Especially in the field of mechanics, a number of smartphone-based experiments are known illustrating, e.g., linear and pendulum motions as well as rotational motions using the internal MEMS accelerometer and…

This paper has a pedagogical aim. Indeed, by using the relativistic velocity-addition and Einstein's equivalence principle (EEP), we want to analyse in a simple way the physics of time on a rotating non-inertial frame. We use a didactic approach considering four friends. The first is in the laboratory, the second at rest on the disk at radius r,…

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…

If an empty coffee cup is spun on a horizontal surface about a vertical axis in an anti-clockwise direction, then the whole cup rotates slowly backwards, in a clockwise direction, about a vertical axis located outside the cup. Clues to this curious behaviour are presented by comparing it with other spinning objects.

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…

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…