The "Next Generation Science Standards" (NGSS) challenges science teachers to think beyond specific content standards when considering how to design and implement curriculum. This lesson, "Windmills by Design," is an insightful lesson in how science teachers can create and implement a cross-cutting lesson to teach the concepts…

As we typically teach in an introductory mechanics course, choosing a "good" coordinate frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely powerful problem-solving tool. While the former idea is typically discussed in the context of…

The teaching of the principle of conservation of linear momentum is considered (ages 15 + ). From the principle, the momenta of two masses in an isolated system are considered. Sketch graphs of the momenta make Newton's laws appear obvious. Examples using different collision conditions are considered. Conservation of momentum is considered…

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…

The traditional introductory-level meterstick-balancing lab assumes that students already know what torque is and that they readily identify it as a physical quantity of interest. We propose a modified version of this activity in which students qualitatively and quantitatively measure the amount of force required to keep the meterstick level. The…

The effects of self-assembly on the hydrolysis kinetics of surfactants that contain ester bonds are discussed. A number of examples on how reaction rates and apparent reaction orders can be modulated by changes in the conditions, including an instance of apparent zero-order kinetics, are presented. Furthermore, it is shown that the examples on…

In this paper, we examine a first-year torque and angular acceleration problem to address a possible use of the forelimbs of "Tyrannosaurus rex." A 1/40th-scale model (see Fig. 1) is brought to the classroom to introduce the students to the quandary: given that the forelimbs of "T. rex" were too short to reach its mouth, what…

The familiar system involving a uniform ladder sliding against a vertical wall and a horizontal floor is considered again. The floor is taken to be smooth and the wall to be possibly rough--a situation where no matter how large the static friction coefficient between the ladder and the wall, the ladder cannot lean at rest and must slide down.…

Most introductory physics courses include a chapter on "RC" circuits in which the differential equations for the charging and discharging of a capacitor are derived. A number of papers in this journal describe lab experiments dealing with the measurement of different parameters in such "RC" circuits. In this contribution, we…

Measurements are presented on the rise of a spinning egg. It was found that the spin, the angular momentum and the kinetic energy all decrease as the egg rises, unlike the case of a ballerina who can increase her spin and kinetic energy by reducing her moment of inertia. The observed effects can be explained, in part, in terms of rolling friction…

In a typical high school course, the complex physics of collisions is broken up into the dichotomy of perfectly elastic versus completely inelastic collisions. Real-life collisions, however, generally fall between these two extremes. An accurate treatment is still possible, as demonstrated in an investigation of coin collisions. Simple…

In nonrelativistic quantum mechanics, the total (i.e. orbital plus spin) angular momentum of a charged particle with spin that moves in a Coulomb plus spin-orbit-coupling potential is conserved. In a classical nonrelativistic treatment of this problem, in which the Lagrange equations determine the orbital motion and the Thomas equation yields the…

On Aug. 13, 2011, at 8:45 p.m. country music fans were eagerly awaiting the band Sugarland to make its entry onto the main stage at the Indiana State Fairgrounds. Also competing for the fans' attention was an approaching storm. Sugarland never made their entrance. At 8:49 p.m. the stage rigging was hit by 59 mile/h (94 km/h) winds causing it to…

Understanding energy usage is crucial to understanding modern civilization, as well as many of the challenges it faces. Energy-related issues also offer real-world examples of important physical concepts, and as such have been the focus of several articles in "The Physics Teacher" in the past few decades (e.g., Refs. 1-5, noted further below).…

An equation of state of a system is a relationship that connects the thermodynamic variables of the system such as pressure and temperature. Such equations are well known for classical gases but less so for quantum systems. In this paper we develop a van der Waals equation of state for a dilute boson gas that may be used to explain the occurrence…