Kinematics: The Velocity-Time Function Author’s Preface: A Collaborative Approach to Lesson Development The intention behind what I hope will be a series of articles on Kinematics (this one being the first) is to begin an open, collaborative process of lesson development on Physics Forums. In order to expedite this workflow, I am making deliberate use...

Introduction This article is written by way of a reference for my longstanding PF colleague and prolific poster of challenging Maths/geometry problems @chwala . The particular post this article will discuss is an example of one such problem which he raised on Physics Forums. https://www.physicsforums.com/threads/find-angle-adb-in-this-isoceles-triangle-given-some-extra-information.1063874/ The Problem We take the liberty of including the original...

Introduction The concept of a group is as simple as it gets: a set with a binary operation like addition and a couple of natural laws like the requirement that the order of two consecutive operations does not matter: ##(1+2)+3=1+(2+3).## That’s it. The concept of a group is so simple that I still wonder why...

The Einstein Field Equations (EFE) are ten coupled, nonlinear differential equations that describe how matter and energy determine the curvature of spacetime. First published by Albert Einstein in 1915, they form the mathematical core of general relativity, linking spacetime geometry to its energy and matter content through the equation [itex]G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}[/itex]. Key...

Introduction The figure on the right shows a “double-double” Atwood machine with three ideal pulleys and four masses.  All pulleys are released from rest simultaneously.  Which of the choices below describes the angular motion of the top pulley P after some time has elapsed and why? It rotates clockwise with increasing angular speed. It rotates...