Vertical jump height is a widely used variable in sport science and physical education. This narrative review summarizes various numerical methods used to calculate vertical jump height. In force plate technology, the jump height is most commonly calculated using the flight time (FT) or the takeoff velocity (TOV), which provide only the distance…

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 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 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…

Even though many physics teachers take their students on a calculation adventure through circular motion and Newton's universal law of gravity to determine Earth's velocity, most of us leave it at that. We present the final result and say, "Look, Earth is moving around the Sun at about 107,000 km/hr (66,000 mph), yet we can't feel the motion…

We report an educational tool for the upper level undergraduate quantum chemistry or quantum physics course that uses a symbolic approach via the PySyComp Python library. The tool covers both time-independent and time-dependent quantum chemistry, with the latter rarely considered in the foundations course due to topic complexity. We use quantized…

One of the easily accessible results in elementary fluid mechanics is the so-called Torricelli's theorem (or law), which states that the velocity U[subscript th] of the fluid exiting from an orifice at depth "h" from the free surface of a container filled with fluid, is the same as the velocity of a free-falling body from rest over a…

In this article, we demonstrate the use of a simple pendulum to explore the concepts of kinematics and dynamics. A simple homemade pendulum and a phone-based accelerometer are used to determine, at various points in time, the acceleration of a moving train. The dynamical and kinematics data from the homemade pendulum and the accelerator can then…

One of the main topics of elementary physics is the idea that every material is composed of "little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one other." These particles could be atoms or molecules. Atoms are the smallest part into…

As a boy I spent many hours skipping stones across the surface of the water on the shore of Lake Michigan. The challenge was to get as many skips or as much distance as possible. Zero skips was a bust. One or two skips was disappointing, three or four skips was mediocre, and six or more skips was exhilarating. The angle of the stone with respect…

Males (n = 29) and females (n = 34) performed vertical jumps. Jump height was estimated from force platform data using five numerical methods and compared using intraclass correlation ([rho]), and linear and rank regression standard error of estimate ("SEE"). Take-off velocity plus center of mass height at take-off and mechanical work…

In general, undergraduate experimental physics laboratories do not usually have experiments designed to address rolling friction and to measure the value of the rolling friction coefficient. This work explores an experiment, which has the potential to arouse students' curiosity about rolling friction by addressing a counterintuitive aspect of the…

An important step in learning to use math in science is learning to see symbolic equations not just as calculational tools, but as ways of expressing fundamental relationships among physical quantities, of coding conceptual information, and of organizing physics knowledge structures. In this paper, I propose "anchor equations" as a…

A fairly recent paper resolves a large discrepancy in the internal energy utilized to fire a cannon as calculated by two inertial observers. Earth and its small reaction velocity must be considered in the system so that the change in kinetic energy is calculated correctly. This paper uses a car in a similar scenario, but considers the work done by…

There are five unique points in a star/planet system where a satellite can be placed whose orbital period is equal to that of the planet. Simple methods for calculating the positions of these points, or at least justifying their existence, are developed.