Science and engineering students in the second semester of a calculus-based physics sequence typically study and measure the on-axis magnetic field for a multiple, circular turn coil. There are four benefits to this approach: 1) an analytical solution is easily obtained, 2) the coil is easily constructed using tightly wound, high-gauge wire where…

From ancient times, the different features of planets and moons have created a huge interest. Aristarchus was one of the first to study the relative relations among Earth, Moon, and Sun. This interest has remained until today, and therefore it is always relevant to make this knowledge more appealing to the younger generations. Nowadays, smartphone…

In a paper (posthumously) co-authored by Isaac Newton himself, the primacy of geometric notions in pedagogical expositions of centripetal acceleration has been clearly asserted. In the present paper we demonstrate how this pedagogical prerogative can inform the design of an experiment involving an accelerometer-equipped smartphone rotating…

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…

Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification--that physical quantities can be assigned specific numbers (with a unit). A second is to develop an intuition for…

Fractals are geometric objects used to describe irregular shapes that have a fractional dimension and commonly appear in nature. Although several proposals for the study of perfect fractals at the basic level are present in the literature, only few proposals for the study of real fractals exist, which does not seem reasonable considering the…

Gravitational lensing is an interesting phenomenon in astronomy and is most typically given rise to by galaxies. The majority of the matter in a galaxy is thought to be dark matter, and the galactic gravitational lensing effect is mainly caused by dark matter halos. In gravitational lensing-related demonstrations in physics education, the feet of…

North Korea's development of nuclear weapons and, more recently, intercontinental ballistic missiles (ICBMs) has added a grave threat to world order. The threat presented by these weapons depends critically on missile range, i.e., the ability to reach North America or Europe while carrying a nuclear warhead. Using the limited information available…

Multiple initiatives contend that all students should master computational thinking, including the "Next Generation Science Standards, the K-12 Framework for Computational Thinking," and Code.org. In turn, many physics teachers have begun to explore a variety of approaches to integrating computational modeling through programming. These…

A quick survey of physics textbooks shows that many (Knight, Young, and Serway for example) cover estimation, significant digits, precision versus accuracy, and uncertainty in the first chapter. Estimation "Fermi" questions are so useful that there has been a column dedicated to them in "TPT" (Larry Weinstein's "Fermi…

This paper describes a high school or introductory university course in scientific programming that introduces the computer revolution into the physics curriculum at the beginning. In the first one-hour lecture, Euler's method is presented and used to compute a solution to the analytically unsolvable two-body problem. In the remainder of the…

Much data, both published and anecdotal, have shown that students grasp scientific concepts more easily when they are directly involved in the learning via lab experiments or other hands-on activities. Hands-on or experiential learning also appears to aid in students' ability to retain scientific theory. One way to engage students in a first-year…

The problem of determining the angle ? at which a point mass launched from ground level with a given speed v[subscript 0] will reach a maximum distance is a standard exercise in mechanics. There are many possible ways of solving this problem, leading to the well-known answer of ? = p/4, producing a maximum range of D[subscript max] = v[superscript…

The calculation of the moment of inertia of an extended body, as presented in standard introductory-level textbooks, involves the evaluation of a definite integral--an operation often not fully mastered by beginners, let alone the conceptual difficulties it presents, even to the advanced student, in understanding and setting up the integral in the…

This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.