For those of you who know how to solve absolute value inequalities, here is how they also mean something like “numbers between 8 and 14.”
Category: Math
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 $latex T^2 = 4\pi \frac{M}{3kr^2} (L^2 + 3r^2 -3rl) &s=3$.
A moderately difficult trig identity: prove $latex \frac{ \frac{1}{tan(x)}+cot(x) }{ \frac{1}{tan(x)}+tan(x) }= \frac{2}{sec^2(x)} &s=3$ using u-substitution.
This video walks through doing $latex \int \frac{x^3}{1+x^4}\,dx&s=3$ using u-substitution.
Prove 2 lines parallel using CPCTC
Geometry proofs don’t have to be nightmares. You can create your chain of logic just right if you start at the END. I’ll show you what I mean…
Once you’ve established that curl F = 0, you know that F is the gradient of some potential ⱷ. You can use the Fundamental Theorem to evaluate ∫F.dr — if only you could find the potential function. In this video I go over a straighforward method of finding the potential function using partial integration. (Note: the sound quality gets wonky near the end but you can still hear what I’m explaining perfectly well. Apologies and I’ll figure out eventually why that happens.)
A step-by-step example of how to find the area of a polygon
Finding the area of a polygon seems impossible given just the side length or just the length of a radius or apothegm. But here’s how to do it, step by step.