Category: Physics Club
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How Differential Equations Describe the Physics World – Why Carrying Pole Has to Be Floppy Before It Helps You
Ask anyone who grew up carrying things in the Chinese countryside and you will get the same sentence, delivered with total confidence and zero elaboration: a bamboo carrying pole is easier on you than a rigid one. 省力, in the one word they always use — not “more comfortable”, n …
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Bertrand’s Theorem: Only Two Forces in the Universe Let Orbits Close
Two posts ago I argued that the exponent 2 in $1/r^2$ is doing far more work than it looks like it’s doing — it hides the dimensionality of space, and it’s the whole reason a spherical shell is hollow. Last post I turned the crank on the differential equation and got a conic sec …
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How Differential Equations Describe the Physics World – Why Planetary Orbits are Ellipses
In a previous article I talked about how to use only one simple spring force to set up a differential equation and solve it to give the dynamics of SHM, which is a typical projection of uniform circular motion. Forces that follow the Hook’s Law seem to be very special in real world. T …
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Playing Pool with Pi – Part 3 – What Happens to the π When the Blocks Aren’t Perfectly Bouncy?
Last time I wrote about the block collision puzzle: heavy block, light block, wall, no friction, perfectly elastic collisions, and the number of clacks turns out to be the digits of π. Perfectly elastic. That assumption did a lot of work. Real collisions lose energy. Steel on steel gives yo …
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The Privilege of the Inverse Square: Two Proofs of the Shell Theorem
In the last post I borrowed a point from Feynman: the mathematical form of a law carries far more physics than the sentence it seems to be saying. This post is a worked example. Nominally we are proving the shell theorem. What we are really after is a more pointed question — why is gravity …
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The Unreasonable Effectiveness of Mathematics in the Natural Sciences — Lecture share
Today when reading useless articles on 知乎, I found a pretty interesting problem discussing the inherent relationship between physics and mathematics. It really echoes my thoughts recently. Personally, I realized this magical connection when I started to learn physics&n …
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Playing Pool with Pi – Part 2 – Two Blocks, One Wall, and a Very Silly Way to Compute π
I want to tell you about the strangest place I have ever seen π show up. Here’s the setup. You have a frictionless floor. There’s a wall on the left. Next to the wall sits a small block of mass $m$, just sitting there. Coming in from the right is a big block of mass $M$, sliding …
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Wanting a Mechanism Is Wanting a Story
On Feynman’s second lecture in “The Character of Physical Law” Popular physics books rarely fail by being too hard. They fail by being too easy. You understand every sentence and none of the whole. Finish a book about gravity and what you’re holding is a row of indep …
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Playing Pool with Pi — Part 1 — Why can Simple Harmonic Motion be Described by Circular Motion
Introduction Recently, when we studied oscillation or SHM —- fundamentals of waves and periodic motions —- Birdy(鸟哥) asked me a question that “seemed” to be so obvious: why the equation of oscillations are derived from the circular motion? Here are some explanation …