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 SignThis 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 SystemsOkay 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 EnergyThis question may very well be beyond the scope of a traditional introductory calculus-based physics course, but given the recent trend in early introduction to computational physics with curricula like Matter & Interactions it may be within the scope of a reformed course. In classical physics, finding a particle’s trajectory under the influence of a […]
Read More Conceptual Understanding in Introductory Physics XIII: Differential EquationsThis 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 […]
Read More Conceptual Understanding in Introductory Physics XII: Combining Position and Velocity