Physics

Last time we derived the following Lagragian \begin{equation} L = \sum_{i}^{N}\left( \frac 12 m_i \dot x_i^2 - m_i x_i \right) +F x_1 -\sum_{i=2}^{N}\frac{q}{\gamma - 1} \frac{1}{(x_{i+1} - x_i - \ell_{i})^{ \gamma - 1 }} \end{equation} Where all the the parameters and variables are unitless. Let’s a deeper look at this Lagragian. One thing that stands out is the form of the air compression energy. It only depends on the difference of position variables of the form $x_{i} - x_{i-1}$....

I think it is interesting to sometimes tackle toy examples. For a recent project on a gig economy site, I was presented with a particular physical system which had some nice properties. So here I would like to share with everyone. The system is quite simple, it’s just a vertical cylinder of alternating plugs of water and of air. In the figure above we have a four water plugs as shown as a cross section of a tube....

The amount of apples can be represented by a number $1,2,3\ldots$. The length and time can also be represented by decimal/real numbers $1.3, \pi, 3,\ldots$. The phase of an electric circuit can be represented by complex numbers! In this sense, physics is useful by abstracting away our world into the world of math. Beyond numbers, another mathematical object is used to represent things like velocity and position. This is the humble vector, an object with both magnitude and direction....

Unit Conversions 1 meter = 100 millimeters = 3.281 feet = 39.37 inches. This is an example of unit conversion. Sometimes, unit conversion is used to convert quantities from an unfamiliar unit to a familiar one. Currently, 1 US Dollar is equivalent to 151 Japanese Yen1 2. At times, the change of unit is for clarity, to express quantities of large or small amounts into comprehensible numbers. For instance, instead of several thousand steps, I find the unit of several miles3 more graspable....

I was watching a YouTube video 1. The video was about the speed of light in a medium, and I thought it would be interesting to do some relaxing programming with Julia. Specifically, I would like to simulate some light propagating through media with varying dielectric properties. This post will follow these steps: Derive the equations from Maxwell’s equations in a dielectric. Simulate the wave equations. Explore! From Maxwell’s Equations Here are Maxwell’s equations as known in a dielectric in general3....

Enlightenment Two videos came out (Veritasium, Dialect) about measuring the one-way speed of light. Both are the usual fare for science videos, though Dialect is on the spicy side. For a bit of primer, the one-way speed of light is the distance traveled per time taken between two points. The two-way speed of light is the round trip distance traveled per time taken between two points. The aforementioned videos claim we cannot actually measure the one-way speed of light....

Shoots (Snakes) and Ladders Shoots and ladders is the classic game for kids 1. The rules are simple. Each player starts with their pieces starting at the start of the board. For each player’s turn, they role a six diced dice where the rolled number is the number of spaces to move forward. To win, you must be the first player to reach the end of the board. For simplicity, we will consider reaching the end as rolling enough to move past the last position....

The Universal Number (As of current knowledge) every possibly measurable quantity can be represented with $10^{134}$ bytes (or bits). Why? First, I would like to make some assumptions! Let’s same you make a measurement to distinguish the physical states of the world. For example, a potato could of many lengths! We use rulers to distinguish which universe1 we are in such that the potato is so long. Effectively, the smallest length increment is the Planck length....