Categories
Math Physics Pre-Calculus Proofs Proving Identities Science Trigonometry

Spin One Particle Rotates Like a Vector, y-axis

InĀ 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.

Categories
Complex Numbers Math Physics Pre-Calculus Proofs Proving Identities Science Trigonometry

Spin One Particle Rotates Like a Vector, z-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.

Categories
Calculus Differential Equations Physics Science

Physics Pendulum Problem

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 T^2 = 4\pi \frac{M}{3kr^2} (L^2 + 3r^2 -3rl) .

Categories
Physics Science

A Rock on the Moon

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?