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…

There is no shortage of great pedagogical tools available, but many require considerable investment of time and effort (and oftentimes money and equipment), which can be a significant barrier for already time-poor teachers. "Wonder Questions" is a pedagogical tool that is simple, flexible, and pedagogically powerful in three ways: (1) it…

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…

In recent years, with the more powerful functions of smartphones, the use of sensors integrated by mobile phones as an auxiliary tool for physical experiment teaching has become more popular. Combined with the related mobile phone apps, people easily can develop and expand the physical experiment contents of mechanics, optics, acoustic phenomena,…

Nearly everyone, including physics students, finds rainbows to be fascinating and much has been written about them. For example, in a 2020 paper, Kenneth Ford sets forth the basic theory of rainbows created by water droplets at the level of geometric optics and uses a graphical approach to address the question of the relative intensities of the…

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…

In this work, we study several closely related problems involving chains, conveyor belts, and rockets, which are described and solved without the application of infinitesimal calculus, or even the concept of mathematical limit. On one hand, the novelty lies not in the problems themselves, but in the method used for their solution, which brings…

So many fundamental physics problems involve rigid body rotation that mastery of the subject is essential to many science and engineering undergraduate degrees. Rigid body rotation is typically taught in introductory mechanics courses and while students are generally comfortable with the corresponding kinematic equations, torques and moments of…

The "Next Generation Science Standards" (NGSS) encourages educators to help kindergarteners formalize a big idea in physics: A push or pull can cause an object to begin moving, speed up, slow down, stop, or change the direction it is going (NGSS Lead States 2013). In this article, the authors share an exciting, classroom-tested…

The fact that a bungee jumper can reach an acceleration greater than the acceleration of gravity is, also from a physics point of view, intriguing. Taking only gravity into account, it can be explained by applying conservation of energy or by deriving carefully the equation of motion in a Newtonian approach. In this article we show how it can be…

Learning introductory quantum physics is challenging, in part due to the different paradigms in classical mechanics and quantum physics. Classical mechanics is deterministic in that the equations of motion and the initial conditions fully determine a particle's trajectory. Quantum physics is an inherently probabilistic theory in that only…

We conducted a study with introductory and upper-division physics students in a Mexican university to learn how students independently recognize the electric field's main characteristics in the electric field lines diagram and as a source or target representation in conversion processes. We used the theory of registers of semiotic representations…

Students often use incoherent strategies in their problem solving involving force and motion, as revealed, e.g. when they are asked to draw force diagrams for amusement rides involving circular motion, whether in horizontal or vertical planes. Depending on the questions asked, assignments involving circular motion can reveal different types of…

Einstein's special theory of relativity includes many non-intuitive and apparently paradoxical conclusions about space and time. One of these is time dilation, the fact that a clock moving relative to an observer runs slower than an identical clock at rest in the observer's reference frame. This is clearly exhibited in the extended mean lifetime…