William H. Baird

An introduction to inertial navigation

In most introductory physics courses, the first equations encountered are the kinematic equations. Though the emphasis at this level tends to be on cases of constant acceleration, many real-world examples of motion are not so simple. We describe the use of inexpensive hobbyist-grade accelerometers and spreadsheet software to explore inertial navigation via numerical integration of the measured acceleration.

Using a High-Speed Camera to Measure the Speed of Sound

The speed of sound is a physical property that can be measured easily in the lab. However, finding an inexpensive and intuitive way for students to determine this speed has been more involved. The introduction of affordable consumer-grade high-speed cameras (such as the Exilim EX-FC100) makes conceptually simple experiments feasible. Since the Exilim can capture 1000 frames a second, it provides an easy way for students to calculate the speed of sound by counting video frames from a sound-triggered event they can see. For our experiment, we popped a balloon at a measured distance from a sound-activated high-output LED while recording high-speed video for later analysis. The beauty of using this as the method for calculating the speed of sound is that the software required for frame-by-frame analysis is free and the idea itself (slow motion) is simple. This allows even middle school students to measure the speed of sound with assistance, but the ability to independently verify such a basic result is invaluable for high school or college students.

Smartphones and Time Zones

Using the Sun to tell time is an ancient idea, but we can take advantage of modern technology to bring it into the 21st century for students in astronomy, physics, or physical science classes. We have employed smartphones, Google Earth, and 3D printing to find the moment of local noon at two widely separated locations. By reviewing GPS time-stamped photos from each place, we are able to illustrate that local noon is longitude-dependent and therefore explain the need for time zones.

Gravitational potential: a thought experiment

The electrostatic potential is a key element of the second semester of introductory physics. Teaching about its gravitational analog in the first semester allows students to make more connections between the two courses. The use of a simple thought experiment with an unexpected outcome provides a method for introducing gravitational potential in a way students may remember.

Google Earth Science.

Google Earth has made a wealth of aerial imagery available online at no cost to users. We examine some of the potential uses of that data in illustrating basic physics and astronomy, such as finding the local magnetic declination, using landmarks such as the Washington Monument and Luxor Obelisk as gnomons, and showing how airport runways get their numbers. Close inspection of the images provided by Google Earth reveals that most of them are actually obtained via camera-equipped planes rather than satellites.

Low-voltage polyphasic circuits

Experimentation with polyphasic voltages is greatly simplified when microcontrollers are used to generate multiple square waves with fixed phase offsets. Each square wave is sent through a simple second-order Sallen–Key filter to produce an approximately sinusoidal voltage signal. The microcontroller allows the reproduction of split-phase and three-phase voltage relationships, mirroring those commonly distributed on the North American power grid, at safe voltage levels.

Electrical Power Quality – What’s Behind the Outlet?

Although we may consider the power outlets in our homes to be nearly ideal voltage sources, a variety of influences in and around the home can cause departures from the nominal 60 Hz, 110–120 V root-mean-square (rms) of the North American grid. Even without instrumentation, we can see that a large motor starting from rest can be sufficient to cause lights to dim momentarily (voltage sag). This dimming is due to the inrush current drawn by a stationary motor, which may be several times the current drawn at operating speed. We prepared a voltage monitoring system using a voltage divider, the construction details of which we omit in the interest of safety.

Understanding Gauss's Law Using Spreadsheets.

Some of the results from the electrostatics portion of introductory physics are particularly difficult for students to understand and/or believe. For students who have yet to take vector calculus, Gausss law is far from obvious and may seem more difficult than Coulombs. When these same students are told that the minimum potential energy for charges added to a conductor is realized when all charges are on the surface, they may have a hard time believing that the energy would not be lowered if just one of those charges were moved from the surface to the interior of a conductor. Investigating these ideas using Coulombs law and/or the formula for the potential energy of a system of discrete charges might be tempting, but as the number of charges climbs past a few the calculations become tedious. A spreadsheet enables students to perform these for a hundred or more charges and confirm the familiar results.

Advanced Imaging of Elementary Circuits

Students commonly find the second semester of introductory physics to be more challenging than the first, probably due to the mechanical intuition we acquire just by moving around. For most students, there is no similar comfort with electricity or magnetism. In an effort to combat this confusion, we decided to examine simple electric circuits with either a high-speed camera or a thermal imager in an effort to make things like current and voltage as familiar as slow motion or temperature.

The Light‐Emitting Diode as a Light Detector

Alight‐emitting diode (LED) and operational amplifier can be used as an affordable method to provide a digital output indicating detection of an intense light source such as a laser beam or high‐output LED.1 When coupled with a microcontroller, the combination can be used as a multiple photogate and timer for under