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 ...
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. ...