Let’s take a look at how a rocket works, based on only concepts from momentum. The basic idea is that we have a system of rocket and fuel with mass $m$ and velocity $v$. If we burn fuel and eject mass, we will gain velocity. But how can we quantify this relationship? Let’s begin with the derivation of the famous Tsiolkovsky rocket equation. To begin, let’s identify the initial state of our system. At some time $t_i$, we have the momentum of our system as ...
Do we have free will? That’s a question that’s haunted many philosophers, scientists, and people contemplating their existence late at night. We might find some answers in linear regression, of all the places. Background Linear regression can be simplified to drawing a line of best fit. Given any scattered set of data points, we want to create a line that best represents the shape of the data. A simple, 2D linear regression model is given by a general form ...
The Raytheon Radarange was the first commercially available microwave. A clunky, chrome box weighing over 340 kg and costing over $5,000, the Radarange wasn’t widely adopted at the time. However, this artifact was chosen because it was a foundational step in advancing consumer food technology by changing the way Americans prepared food. The Radarange was invented as a result of melted chocolate. In a Raytheon lab, Percy Spencer realized that his candy bar melted when he placed his chocolate bar next to a magnetron. Spencer realized that the magnetron (a special type of vacuum tube) was producing electromagnetic radiation, causing his chocolate bar to melt. Fascinated by this result, Spencer then took a bag of corn kernels and placed them near his magnetron, all of which popped into fresh, hot popcorn all over his lab. Presumably after a few laughs, Spencer and Raytheon realized the true potential of the technology they had on their hands and refined it to create the Radarange, sold starting in 1947. ...
This is an advertisement for the Altair 8800 personal computer in the Popular Electronics Magazine. The Altair 8800 was the first commercially successful personal computer kit and was sold beginning in January 1975, when it was featured on the cover of the Popular Electronics magazine. This magazine had been the life and soul of the personal electronics culture in America, and being nominated to the cover marketed the Altair 8800 massively. It was sold as a DIY kit for around $400, and it was a plain metal box with switches and blinking lights. It was nowhere close to the PCs that consumers have today, but it was a massive success with the “hackers” of the 1970s. ...
From the moment we are born, there are expectations placed on us: go to school, find a job, start a family, build a life. Society gives us a blueprint on how to live a “meaningful” life. However, existentialism fundamentally rejects the premise that we have some “predetermined” purpose; instead, it suggests that it is up to an individual to find purpose in their life. Existentialists become aware of the “absurdity” of human existence: the fact that life itself lacks any inherent meaning beyond what we choose to give it. This problem, where humans seek purpose in a universe that offers none, leads to a dilemma: should we accept the illusion of meaning from society, or should we create our own? ...
We’ve seen the rise of many great empires and nations–Romans and their expansive empire, the British and their global dominance–only to see it crumble to dust. We can blame a lot of things on these collapses: new rising nations, changing technology, unexpected external factors. However, the collapse typically comes from within, as the relationship between the government and its citizens starts to crack and fail. This dramatic decay can be explained by a concept called the social contract. The social contract is one of the most important ideas in political philosophy (the study of the nature of politics, society, and the relationship between citizens and government). It states that citizens willingly consent to give up some personal freedoms to a governing authority, in exchange for the protection of their rights. To put it really simply, citizens give up some free will to gain protection from the government. The social contract was essential to the founding of the United States, but the digital age is bringing new changes to this centuries-old concept. ...
Update: This article is the reason I got a five on AP Physics C, one year later. Introduction Gauss’s Law is a law that relates the flux of the electric field on a surface to the charge enclosed within that surface. What does that even mean? In this article, I want to walk you through the basics of electromagnetism and make it seem like even you could have derived this law if you knew what Gauss knew. ...
Intro This article is going to be math heavy. Be warned. According to Google, an oscillator is a mechanical or electronic device that works on the principles of oscillation: a periodic fluctuation between two things based on changes in energy. If you take a system in equilibrium and give it a little kick, it will vibrate. We can model this with a cosine function: $$x = A \cos (\omega_0 t + \phi)$$ ...
Note to reader: if you have not read part one, do so here. So, what was wrong with Galilean relativity? It help up perfectly well, until a Scottish mathematician by the names of James Clerk Maxwell created his four namesake laws of electricity and magnetism. As a consequence of his laws, he was able to derive the speed of light in a vacuum, which was given the variable $c$. Now, according to Galilean relativity, the speed of light seen by a moving observer should be the speed of light minus the moving observer: ...
Note to reader: This is the first in a series. Relativity, we’ve heard so much about it. Created by Einstein, it’s lived in the minds of both physicists and the cultural zeitgeist. It’s the idea behind black holes, time travel, and has single-handedly spawned off so many Hollywood movies. To truly understand the beauty of special relativity, we must go back in time. Relativity is not a new concept that Einstein created; it’s been around since the time of Galileo and Newton. So what was this “original” relativity? Well, let’s understand what relativity even means. ...