Vector Formalism in Introductory Physics II: Six Coordinate-Free Derivations of the BAC-CAB Identity

TL;DR: The BAC-CAB vector identity is probably the most important vector identity, and has potentially important applications in introductory physics. I present six coordinate-free derivations of this identity. By “coordinate-free” I mean a derivation that doesn’t rely on any particular coordinate system, and one that relies on the inherent geometric relationships among the vectors involved. […]

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Vector Formalism in Introductory Physics I: Taking the Magnitude of Both Sides

TL;DR: I don’t like the way vectors are presented in calculus-based and algebra-based introductory physics. I think a more formal approach is warranted. This post addresses the problem of taking the magnitude of both sides of simple vector equations. If you want the details, read on. This is the first post in a new series […]

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Matter & Interactions II, Week 11

More with circuits, and this time capacitors, and the brilliantly simple description M&I provides for their behavior. In chapter 19, we see that traditional textbooks have misled students in a very serious way regarding the behavior of capacitors. Those “other” textbooks neglect fringe fields. Ultimately, and unfortunately, this means that capacitors should not work at […]

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Matter & Interactions II, Week 10

Chpater 18. Circuits. You don’t need resistance. You don’t need Ohm’s law. All you need is the fact that charged particles respond to electric fields created by other charged particles. It’s just that simple. When I took my first electromagnetism course, I felt stupid becuase I never could just look at a circuit and tell […]

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Angular Quantities II

In this post, I will address the first question on the list in the previous post. What exactly does it mean for something to be a vector? In almost every introductory physics course, vectors are introduced as “quantities having magnitude and direction” and are eventually equated to graphical arrows. A vector is neither of these, […]

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Angular Quantities I

This is the first in a series of posts in which I want to share some hopefully interesting things about mathematical descriptions of rotational motion. This series was inspired by a talk given at the 2015 winter AAPT meeting in San Diego. The author claimed to have found a way to represent angular displacement as […]

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