Conceptual Understanding in Introductory Physics XXXVI: Geometry and Work

This question is particularly revealing in that it assesses whether or not students understand the coordinate-free nature of work as a dot product. Be prepared to hear such nonsense locutions as “negative force” or “negative displacement” but don’t be shocked when you hear them. I think it’s a product of the relatively poor treatment vectors […]

Conceptual Understanding in Introductory Physics XXXV: Free-body Diagrams

Free-body diagrams are ubiquitous in introductory physics courses. They should be straightforward, but I’ve noticed that student frequently struggle with them at first because they want to include velocity or momentum in addition to forces. For this question, choose an arbitrary (the more arbitrary, the better) physical situation. It could be something from your or […]

Conceptual Understanding in Introductory Physics XXXIV: Parallel and Perpendicular Components of Force

Draw an arrow representing an arbitrary force vector and another arrow representing an arbitrary momentum arrow. Label both arrows. Ask the student to perform the following task: Decompose the force vector into a component parallel to the momentum vector and a component perpendicular to the force vector. Tell whether or not the given force will […]

Conceptual Understanding in Introductory Physics XXXIII: Drawing Systems

The instructor draw a random diagram showing an arbitrary number of interacting (e.g. gravitationally) entities (e.g. stars, asteroids, etc.) represented as numbered dots. The student is asked to perform the following tasks: Draw a system boundary such that the system experiences a net external force. Name each entity that contributes to this net external force. […]

Conceptual Understanding in Introductory Physics XXXII: Practice With Simple Vector Comptuation

This question is a numerical version of the previous question. For a given arbitrary vector quantity , calculate the following quantities. Use a different vector quantity for each student, and have them do the calculations in a programming language in real time (like GlowScript) to demonstrate coding proficiency. Additionally, these calculations can be done very […]

Conceptual Understanding in Introductory Physics XXXI: Practice With Vector Notation

This is the first in a series of sample questions I’ve used in oral interviews.

Oral Interviews as Assessment

TL;DR I have begun using oral interviews as a replacement for traditional written tests and quizzes. There are many advantages for faculty and students, including elimination of paperwork, better chances for understanding students’ state of comprehension, a more relaxed environment, and no possibility for gaming for points. The ongoing pandemic has amplified many questions I […]

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 […]

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 […]