TL;DR If you want a quick way to gauge whether or not students understand the concept of potential energy, you can ask them to explain the origin of The World’s Most Annoying Negative Sign. It is merely a consequence of the very definition of potential energy, which is almost never explained coherently. In all of […]Read More The World’s Most Annoying Negative Sign
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 […]Read More Conceptual Understanding in Introductory Physics XXV: A Free Particle?
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 […]Read More Conceptual Understanding in Introductory Physics XXII: Energy in Multiparticle Systems
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 […]Read More Conceptual Understanding in Introductory Physics XXI: Deriving Expressions for Kinetic Energy
This post is inspired by the October 2015 AstroNotes in The Physics Teacher. I have sometimes introduced vectors into my introductory astronomy course and students were able to do most of the things described below. We never discussed angular momentum or the Laplace-Runge-Lenz vector, but the other quantities were familiar. I was not permitted in […]Read More Conceptual Understanding in Introductory Physics XX: The Laplace-Runge-Lenz Vector
With little advanced notice, I was assigned a section of conceptual physics to teach this semester (because second semester astronomy was cancelled due to low enrollment and replaced with a section of conceptual physics with the same low enrollment..go figure). After teaching Matter & Interactions for over a decade and after much enlightenment I have […]Read More Introducing Noether’s Theorem in Conceptual Physics
This question is straight to the point. It emphasizes terminology and associated conceptual understanding. Without using equations or numerical examples, describe the connections and differences among the following quantities or concepts: electric potential energy, electric potential, change in electric potential energy, change in electric potential, potential difference, and electromotive force. Electromotive force and potential difference […]Read More Conceptual Understanding in Introductory Physics XVII: Potential Confusion
This series continues with a question which, I hope, causes readers and students to reflect on something that is frequently omitted from traditional introductory physics courses. I contend that words are all we have to convey conceptual understanding in physics or any other topic. Yet, in science courses, and especially in physics courses, we tend […]Read More Conceptual Understanding in Introductory Physics III: Interpreting Physical Quantities