If you’re studying General Relativity or Tensor Calculus you’ve slammed into the Riemann tensor and its flurry-of-gammas-and-indices definition. But at its heart, the Riemann is just saying “move a vector around a tiny parallelogram first one way and then the other. Get a different result one way? Then the space is curved.” This video matches up the symbols and indices to that basic definition. I always remember something better when it makes sense. This video should help you remember the Riemann’s definition too.
Category: Science
In The Feynman Lectures on Physics, Volume 3 Chapter 5, Feynman poses a challenge to the reader: show that a particular combination of plus, minus and zero states of a spin one particle transforms under a rotation just like a vector does. In this previous video I reviewed the details of proving it for rotations around the z-axis. Here I go over the more complicated proof for rotations around the y-axis.
In The Feynman Lectures on Physics, Volume 3 Chapter 5, Feynman poses a challenge to the reader: show that a particular combination of plus, minus and zero states of a spin one particle transforms under a rotation just like a vector does. Here I go over how to work that problem using only what was covered in the book up to that point.
Getting the Period of a Spring-Operated Physical Pendulum
A juicy physics problem that requires delving into the differential equation for pendulum motion. A rod of mass M on a pivot a distance r from the end is driven by a spring of constant k pulling the end back and forth to make an (admittedly stupid) physical pendulum. We have to show that its period T is given by 
A Flying Rock on the Moon — a Kinematics Problem
A nice tough physics kinematics problem: how high will a flying rock on the moon rise if all you know is how long it took to pass a viewport?
This video walks you through the multifarious steps and guides you past all the gotchas in solving an equilibrium problem. I’ll assume you know what equilibrium problems *are* and just need some practice *doing* them.