Before students learn Kirchhoff's rules, they are typically taught how to solve "combined series-parallel" circuits. The method presented in many textbooks begins by drawing a series of simplified circuits, replacing series and/or parallel elements with their equivalent resistances, eventually reducing the circuit to a voltage source and…

The use of systems in many introductory courses is limited and often implicit. Modeling two or more objects as a system and tracking the center of mass of that system is usually not included. Thinking in terms of the center of mass facilitates problem solving while exposing the importance of using conservation laws. We present below three…

The primary objective of the activity presented here is to allow students to explore the frequency components of various simple signals, with the ultimate goal of teaching them how to remove unwanted noise from a voice signal. Analysis of the frequency components of a signal allows students to design filters that remove unwanted components of a…

Newton's second law is one of the cornerstones of the introductory physics curriculum, but it can still trouble a large number of students well after its introduction, hobbling their ability to apply the concept to problem solving and to related concepts, such as momentum, circular motion, and orbits. While there are several possibilities for…

A challenge: Can you create a stable top from a single paper clip? Several interesting solutions to this problem were provided by Takao Sakai from Japan, the requirement of each being that the center of gravity be located on the vertical y-axis at the center of the top. In the simplest configuration, we see that there exists a single angle ?…

Instructors of physics courses face the demanding challenge of creating a safe, nurturing community in their classroom while maintaining sufficient rigor. First-day activities are especially important, because they need to both motivate their students and prepare them for the course. Experienced instructors happily share their successful first-day…

Halfway through the 2015 AFC Championship game between the New England Patriots and Indianapolis Colts, game officials discovered that the Patriots were using underinflated footballs on their offensive snaps. A controversy ensued because the Patriots had actually supplied these balls to the game's referee just hours before kickoff. Athletes and…

Demonstrating probabilistic outcomes using real-time data is especially well-suited to larger lecture classes where one can generate large data sets easily. The difficulty comes in quickly collecting, analyzing, and displaying the information. With the advent of wireless polling technology (clickers), this difficulty is removed. In this paper we…

With the increased availability of modern technology and handheld probeware for classrooms, the iPad and the Video Physics application developed by Vernier are used to capture and analyze the motion of an ice hockey puck within secondary-level physics education. Students collect, analyze, and generate digital modes of representation of physics…

Problems in projectile motion are a time-honored staple of high school and even first-year university physics. They can become confusing for some students, yet boring for the stronger students. Herein we present two alternative approaches to such questions, one we call "breaking down gravity," which makes these questions easier to solve, and the…

Silently, invisibly, ceaselessly, our planet Earth is showered by radio waves from every direction and from every region of space. This radio energy originates in our solar system, throughout the Milky Way galaxy, and far beyond, out to the remotest reaches of the universe. Detecting and unraveling the origins of these invisible signals is what…

In preparing to teach the advanced physics course at my high school, I found it useful to work through the end of chapter problems in the book used by the advanced class. A problem on motion in one dimension involved a stunt woman in free fall from a tree limb onto a horse running beneath her. The problem presents a connected learning opportunity…

Project-based learning is a research-based instructional tool that has proven to be effective in all secondary curricular disciplines, particularly in the areas of science, technology, engineering, and mathematics (STEM). A project is an applied activity, often hands-on, where the students are challenged to successfully address a problem. In many…

The electrical design of the common hair dryer is based almost entirely on relatively simple principles learned in introductory physics classes. Just as biology students dissect a frog to see the principles of anatomy in action, physics students can "dissect" a hair dryer to see how principles of electricity are used in a real system. They can…

Energy concepts are fundamentally important for describing and analyzing systems ranging from subatomic particles to spiral galaxies. In general, students first encounter such concepts in introductory courses that typically focus on forms of energy, energy transfer, and conservation laws. Within these courses, conservation of mechanical energy is…