Conceptual Understanding in Introductory Physics XXX: Two Expressions for the Cross Product

I just realized this is the thirtieth post in this series! I don’t know if anyone has found this series helpful, but I think these questions collectively might make a pool of original exam questions. That’s mainly how I see them anyway. This post is almost a word for word duplicate of the last post […]

Conceptual Understanding in Introductory Physics XXIX: Two Expressions for the Dot Product

Students sometimes see vector dot products in their calculus classes before they see them in their physics classes. Dot products are often presented with two seemingly unrelated definitions, one of which is geometric and coordinate free and the other is in terms of components in a particular basis. Yet, the two give exactly the same […]

Conceptual Understanding in Introductory Physics XXVIII: Div, Grad, and Curl

You may not agree that the topic(s) of this question belong in an introductory calculus-based physics course, but I’m going to pretend they do for the duration of this post. Gradient, divergence, and curl are broached in Matter & Interactions within the context of electromagnetic fields. Actually, gradient appears in the mechanics portion of the […]

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, […]

Conceptual Understanding in Introductory Physics XXVI: System Schemas

This question might serve as a final exam for an introductory physics course. It could serve that purpose for my own courses, but it may not be appropriate for your courses so don’t worry if that’s the case. If you do not include system schemas in your course then this question won’t make any sense […]

Learning Critical Thinking Through Astronomy, Week 5

I originally had one set of plans for this week but as sometimes happens, those plans changed radically. Instead of starting in on the next series of activities, we spent some time doing some formative assessment (and I’m really beginning to hate the word “assessment” because of the current political climate in which it’s (mis)used […]

Matter & Interactions I, Week 5

This week, we transitioned to chapter 1 of the Matter & Interactions textbook (fourth edition). I have WebAssign problem sets for each chapter available for formative assessment and practice while working their way through the reading. I encouraged them to use the book the way it was intended to be used, specifically by stopping and […]

Matter & Interactions I, Week 4

This week we formally wrapped our coverage (I hate that word) of special relativity. My goal never has been for students to do complicated numerical problems. Instead, I wanted them to understand the foundations of special relativity with an emphasis on the invariance of light’s speed, the loss of absolute simultaneity, and loss of absolute […]

Matter & Interactions I, Week 3

This week, we encountered what, in my opinion, is the most fundamental aspect of special relativity: the loss of absolute simultaneity. The Michelson-Morley experiment established that light’s speed must be invariant. An immediate consequence of this is that two events that are simultaneous in one inertial frame cannot be simultaneous in any other frame. Last […]

Learning Critical Thinking Through Astronomy, Week 3

This week, we dived into Activity0102, which introduces two huge concepts. The first is that there are different types of knowledge and therefore also different types of questions. Students are presented with a group of questions, let’s call them Group 1 Questions, and are asked to decide what they have in common. I’ve used this […]