An alternative method for obtaining analytical solutions of the time-independent Schrödinger equation (TISE) is developed and applied to 1-dimensional model quantum systems of interest in atomic and molecular physics. The method is based on proposing a wave function that is a product of two functions, one of them an integrating factor. The…

In this article, we will present the HEC BB bag, a simple but elegant model originally invented to help students imagine how air molecules move around in vacuum. The HEC BB bag is made by packing 20 to 30 BBs in a resealable plastic bag of several tens of square centimeters (see Fig. 1). When inflated fully via a straw, the volume of the bag is…

In physics education, the topic of electromagnetic induction is an important but also challenging topic for many students. The early introduction of formulae, e.g., Faraday's law of induction, seems to hinder rather than to foster the understanding of the topic's underlying principles. In this paper, we present the basic idea for a teaching…

A classical mechanical structure with an internal degree of freedom is shown to reflect off a potential well. Such behavior is impossible for point-like or rigid classical particles. This numerical study provides insight for students studying internal energy and degrees of freedom.

If a ball rolls in a circular path on a horizontal surface at constant speed then its horizontal rotation axis changes direction with time. A simple experiment is presented showing that the torque applied to the ball is equal to the rate of change of its angular momentum, even though the magnitudes of its angular velocity and angular momentum…

Science and engineering practices (SEPs) and crosscutting concepts (CCs) constitute a significant part of "A Framework for K-12 Science Education" (NRC 2012). As teachers, the role of the authors is to highlight the pivotal role that both scientific knowledge and the practices used to generate knowledge play in learning. This article…

We will present a problem-solving method for the dynamics of a projectile that has two perpendicular acceleration vectors through rotation of the axes. This methodology of reparameterizing the two-dimensional system simplifies the speed optimization calculus.

Science does not belong to just one civilization, one culture, one country, or one gender; it belongs to all who want to unfold the mysteries of nature. Most scientists agree that science currently is, and indeed always has been, international and multicultural in character. Our teaching at all levels should reflect this multiculturalism as part…

Research-based assessments (RBAs) measure how well a course achieves discipline-specific outcomes. Educators can use outcomes from RBAs to guide instructional choices and to request resources to implement and sustain instructional transformations. One challenge for using RBAs, however, is a lack of comparative data, particularly given the skew in…

Measurements and calculations are presented showing how the trajectory of an object sliding across an inclined plane varies with the launch and incline angles. The trajectory depends on the magnitude and direction of the sliding friction force. The experiment is easy to set up, can be analysed using a video camera, and would be suitable for a…

Calculations are presented showing that the usual 'faster than g' demonstration has a surprising property. That is, a rod hinged at its bottom end rotates at an exponentially increasing rate until it falls with maximum vertical acceleration, unlike an object that falls freely by gravity alone. If the rod is hinged at its top end and released from…

The purpose of this publication is to present a novel approach to the demonstration of the Dzhanibekov effect. The main idea of our version is to use a lightweight spinning top of a spherical external form but distinct principal moments of inertia floating in the upward flow of air. As a result, the Dzhanibekov effect can be easily demonstrated…

Physics teachers are sometimes asked to teach an astronomy course for non-majors. One can't make that class dance and sing without the starry night, but on a brightly lit campus viewing deep sky objects may seem impossible. Hence instructors often opt for planetarium shows. However: 1) Planetariums aren't the real thing. 2) People living in large…

The subject of mathematics is important for many other subjects, including physics. The questions we ask in physics often need a mathematical translation to be graphically interpreted and transformed. Students learn physics when interacting with physical questions; questions from physics also give insights and discoveries in mathematical problems.…

In traditional introductory physics courses, concepts of distance, displacement, speed, velocity, scalars, and vectors are generally taught near the beginning of the course. However, students often contend with preexisting notions, such as the idea that speed and velocity are synonyms, which present some of the first conceptual hurdles that they…