Conceptual Understanding in Introductory Physics XXV: A Free Particle?

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 […]

Conceptual Understanding in Introductory Physics XX: The Laplace-Runge-Lenz Vector

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 […]

Conceptual Understanding in Introductory Physics XII: Combining Position and Velocity

This is post is long overdue, and I’m sorry for that. Life and work got busy late in the semester. I have far many more ideas for more posts in this thread that I doubt I’ll ever be able to write them all up but I will try. In this post, I focus on an […]

Conceptual Understanding in Introductory Physics X: Resolving a Vector

For this post, I decided to ask what I think is a very simple question. It is simple at first, but it also gets to the heart of the meaning of vector quantities, at least as they are typically presented in introductory physics. It also emphasizes the fact that vector quantities have an existence all their own, […]

Conceptual Understanding in Introductory Physics IV: Can a person move at 0.99c?

I have tens of these questions ready to use here so this series will likely go on for a long time. Part of my strategy for posting each one separately is to get me into the habit of writing regular posts. While these first few are, or should be, relatively simple I promise the difficulty […]

Conceptual Understanding in Introductory Physics III: Interpreting Physical Quantities

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 […]