TL;DR: Vector dot products are not like products of real numbers, for which there is an inverse operation to “undo” multiplication. I don’t think we should introduce dot products as a form of “multiplication” in introductory physics courses because it may reinforce the urge to “divide by a vector.” A better approach may be to […]Read More Vector Formalism in Introductory Physics III: Unwrapping Dot Products Geometrically
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. […]Read More Vector Formalism in Introductory Physics II: Six Coordinate-Free Derivations of the BAC-CAB Identity
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 […]Read More Vector Formalism in Introductory Physics I: Taking the Magnitude of Both Sides
I’m writing this a whole week late due, in part, to having been away at an AAPT meeting and having to plan and execute a large regional meeting of amateur astronomers. This week was all about the concept of electric potential and how it relates to electric field. I love telling students that this topic […]Read More Matter & Interactions II, Week 6
As usual, I’m posting this the Monday after the week named in the title. This week was all about chapter 6: energy and the energy principle. This is where Matter & Interactions really shines among introductory textbooks. I remember as a student being so confused by sign conventions that I honestly never knew when to […]Read More Matter & Interactions I, Week 13
In section section 27-3 of The Feynman Lectures on Physics, Feynman describes a notation for manipulating vector expressions in a way that endows nabla with the property of following a rule similar to the product rule with which our introductory calculus students are familiar. It allows a vector expression with more than one variable to be […]Read More Did Feynman Invent Feynman Notation?
Over the past three years or so, I have been researching the history and implementation of Gibbsian vector analysis with the intent of finding ways to incorporate it more thoroughly and more meaningfully into introductory calculus-based physics (possibly algebra/trig-based physics too). Understanding the usual list of vector identities has been part of this research. One […]Read More HELP! A Stubborn Vector Identity to Understand