Matter & Interactions I, Week 1

This is the first post of a series of sixteen in which I will attempt to describe the weekly goings on in my introductory calculus-based physics course. You probably already know that I use Matter & Interactions for this course, and I have since 1999. In fact, I was the first instructor in North Carolina […]

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Learning Critical Thinking Through Astronomy, Week 1

This is the first post of a series of sixteen in which I will attempt to describe the weekly goings on in my introductory astronomy course. As many of you already know, I don’t use a traditional textbook and, instead, use my own activities based on the critical thinking model of Richard Paul and Linda […]

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Conceptual Understanding in Introductory Physics XXV

This question emphasizes geometry and should be done without use of a coordinate system. It should also be done using only symbolic manipulation of vectors. Here it is. Consider a particle moving with a constant, non-relativistic velocity. Starting with a general expression for kinetic energy in terms of either velocity or momentum, prove that the […]

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Help Me! Question About Tensors and Projections

I need some help. I am working hard to find ways to bring more geometry into introductory calculus-based physics (and conceptual physics as well). By geometry, I mean specifically the geometry associated with vectors and tensors, and the information encoded therein. Yes, I said tensors. I have been heavily influenced by these notes by Kip […]

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Did Feynman Invent Feynman Notation?

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 […]

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HELP! A Stubborn Vector Identity to Understand

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 […]

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Conceptual Understanding in Introductory Physics XXIV

This question was inspired by chapters 13, 14, and 15 of Matter & Interactions and would, I think, make a good final exam question even in courses where M&I isn’t used. The story line in those chapters makes a wonderful progression through different charge distributions and their fields and interactions with other similar charge distributions. […]

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Conceptual Understanding in Introductory Physics XXIII

This question came to me while I was planning for this semester’s introductory calculus-based e&m course (using Matter & Interactions of course). My overall desire and plan is to move away from the traditional number crunching type of problems, where all students really do is manipulate coordinate components of vectors or perhaps vector magnitudes, all […]

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Conceptual Understanding in Introductory Physics XXII

This question was prompted by the treatment of energy concepts in traditional introductory textbooks. Most such treatments tend to share an error in reasoning when it comes to applying energy principles to systems consisting of more than one particle. I may need to come back and edit the question so that it more accurately articulates […]

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Conceptual Understanding in Introductory Physics XXI

Okay this may not be the most interesting thing to think about, but it’s a question I’ve been asked on several occasions. For that reason alone, I started thinking about it. I also think it’s another situation where coordinate-free vector manipulation can simplify otherwise messy questions and problems. So, here’s the question. Give three different […]

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