## 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 …

## Time Steps and Binary Representation in Computer Simulations

TL;DR Using a time step whose decimal representation isn’t exactly representable in binary may lead to confusion over how much total time has elapsed in a computer simulation. It may be worth discussing in class, or worthy of an investigative or inquiry activity. Sometimes, a problem comes up repeatedly over the years and every time …

## So you want to be a GlowScript developer? Here’s how!

TL;DR Developing for GlowScript requires setting up a rather extensive, but straightforwardly installed, development environment. Actual coding is done in JavaScript.  GlowScript is an online programming environment inteneded to be used to teach computation in introductory physics, although it has other applications and purposes. Although GlowScript users write code in Python (Specifically VPython, which is …

## A Response to Physics Today’s Article on the Benefits of a Master’s Degree in Physics

I have submitted the following comments to Physics Today in response to Toni Feder’s article “A physics master’s degree opens doors to myriad careers” published in the April 2019 issue, pp. 22-25. I must add two cautions to Toni Feder’s piece on the benefits of a physics master’s degree. After I completed my MS in …

## Vector Formalism in Introductory Physics VI: A Unified Solution for Simple Dot Product and Cross Product Equations

TL;DR: Simple vector dot products and cross products may be “undone” using formal methods consistent with Gibbsian vector algebra. Writing the cross product and dot product of an unknown vector relative to a given vector in a canonical form allows a well known vector identity to be used to isolate the unknown vector. Special cases …

## Vector Formalism in Introductory Physics V: Two Equations, One Solution

TL;DR: Solving seemingly trivial dot product and cross product equations leads to an astonishing result, namely that they have the same solution, which can be derived both geometrically and algebraically. Establishing this common solution is an important step in motivating formal Gibbsian vector algebra. In the previous two posts, I demonstrated that the simple dot …

## Almanacs in Astronomy Classes

In memory of my maternal grandmother Dorothy Marie Blalock Clark (1912-1997) TL;DR: Ubiquitous farmers’ almanacs are an inexpensive printed source of accurate astronomical information despite being mostly advertising vehicles. This information can be used in the classroom to generate questions and learning about not only astronomy, but also history, mathematics, and computation.  Thanks to my …

## Two Different Obsevers, Same Class

I’m going to present two observers’ accounts of a classroom observation that took place on April 24, 2018 beginning at 9:30 am. The class was an introductory astronomy class with eight students on the roster, five of which stopped attending without withdrawing (faculty are now forbidden “by law” from withdrawing students) and three of which …

## Vector Formalism in Introductory Physics IV: Unwrapping Cross Products Geometrically

TL;DR: Vector cross 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 cross 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 …

## Proving the Absence of Length Contraction Perpendicular to Velocity

When teaching conceptual physics, students almost always ask why length contraction only occurs parallel to velocity and not perpendicular to it. That’s a meaty conceptual question and one that always leaves me looking for a convincing, non mathematical explanation. Earlier this semester, I finally found what I think is the best one I’ve ever heard …

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