Posts

Absolute Velocity1 Knowing one’s speed is important in daily life. A 60 km/hr car is much more dangerous than a stationary one. However, the physically important source of danger here is the difference in speed. A 60 km/hr car is 60 km/hr faster than you, so any collision (resulting in a large and dangerous acceleration) would feel not so great. If we moved parallel to the car at the same speed, we would find that we could treat it just as a stationary car....

Hello Brachistochrone The brachistochrone is the curve that minimizes the time it takes for a frictionless object to slide along to reach from the top to the bottom across some horizontal span, where the object starts at rest. For this article, I want to introduce the brachistochrone1 from the aforementioned definition. The solution to the brachistochrone problem has been well covered and then some, so for the curious I have included articles for one to learn more!...

Visualizing Roots After watching a 2loop video, I decided to write some Julia code to visualize this my self. Here is the Pluto notebook. With that code I made this pretty visualization. This is actually made with Makie’s datashader method where 20th roots where solved for all combinations of coefficients of $1$ or $-1$. The fullsize image can be generated with the Pluto code.

Falling Under Air Drag A classic physics problem is to compute the time $t$ it takes for a particle to fall from a height $h$, under the influence of gravity and air resistance. This problem can, perhaps surprisingly, be solved analytically with only a handful of steps. Let’s assume a particle dropped from rest (initial velocity zero), subject to gravity $g$ and a drag force proportional to $v |v|$. That is, the force can be written as...

War on Julia Playing real war is no fun the card game called War is1. It takes a while to play though so I thought how long would it at take on average. To do this I programmed war on Julia. Here is the julia notebook code/html view. On avrage it takes about $134$ turns but half the games take less than $100$ turns. Half can go one for a long time....

Going around the circle n times So I was thinking about going around the circle some integer number of times 1 or by some rational fraction of the circle. If you go around the circle $n$ times, where $n$ is an integer, you end up where you started 2. If you go a rational fraction of the circle, you do not end up back at the start after one move. To keep the math straightforward, let’s say we move by a rational number, $\rho \equiv a/b \in \mathbb{Q}$, where $a, b \in \mathbb{Z}$, and we move around the circle $\rho\pi$ radians....

Here is just a quick joke post. Please don’t cancel me! If a 1-body problem is trivial, the 2-body problem is solvable, and the 3-body problem is impossible, why is the 0-body problem sad? Because it has no body!

The Infinite Resistor Grid Nerd Snipe I have to admit it. I got nerd sniped. Really, this blog post is about finding the equivalent resistance in question and more! To be transparent, after a good long think and retries I got the answer, so I will try to document/recollect that journey here. First, let’s set up the problem. The Problem Set Up We are given an infinite grid of resistors, each with a resistance of $R$....

Perusing Reddit I found someone asking about a hanging chain. The post in question has a semi-quality video of someone whirling a chain from one end in a circle. The rest of the freely swinging chain forms a particular shape as it rotates around some center axis. In short, this happens because of the centrifugal force from the rotation axis against the binding force of the chain links. I want to take some time to really understand this with physics, of course....

5 Centimeters per Second …they say it’s five centimeters per second. The speed of a falling cherry petal. Five centimeters per second. According to the hit 2007 animated short film, 5 Centimeters per Second 1, this is the speed at which cherry petals fall. Of course, I’m skeptical, and as a physicist I want to model the heck out of this. So, in this article I would like to propose a model for a thin, circular flower petal to be the spherical cow of flower petals....