Electrical Energy Density Derivation
In this post, we’ll do a mathy proof of the electrical energy density of an electric field. Here’s the statement: For any continuous distribution of charge where the electric field vanishes at infinity, the total electrical energy of the system is given by where is a small volume element, is […]Read More
The Wave Equation for Ideal Strings
One of the most important equations in physics is the wave equation. In this post, we will derive the wave equation for the case of a transverse wave on a string. We’ll also find this speed as a function of tension and linear density. Let’s get started. Consider an infinitesimal rope […]Read More
Energy of a Charged Sphere
In this problem, you’ll be calculating the energy of a charged sphere. This can be pretty hard if you’ve never done anything like it before. But it’s super easy once you know the trick. Give it a shot! You have a solid metal ball with a total charge and a […]Read More
Whirlpools in your Bottle
You’ve probably played around with whirlpools in your water bottle. In this problem, you’ll be analyzing an idealized form of this experiment. You have a cylinder filled with water. Put it on a spinning disc so that the cylinder is spinning around it’s primary axis at an angular speed . Gravity points downwards […]Read More
What is a 4 Vector?
Special relativity is super simple when it’s all time dilations and length contractions. But if you study relativity a little more deeply, you’ll notice a lot of talk about 4 vectors? What the heck is a 4 vector and why do you need them? A simple analogy I’m assuming you know what […]Read More
Not Your Typical Block on a Ramp
This is the shortest, most beautiful solution I’ve ever seen in a physics problem. It was found on Morin’s problem of the week site here. For more questions like these, buy his textbook Classical Mechanics on Amazon. Give it a shot. Imagine you have an infinitely long and wide plane inclined at an […]Read More
Explaining Buoyancy Once and for All
Buoyancy is everywhere in our everyday lives. Boats can sail above the water, hot air balloons rise up into the sky, and (most) humans are able to swim. In this lesson, I’ll try to explain what exactly buoyancy is, and how you can calculate it. If you’re an absolute beginner, read the first part. If you’re […]Read More
Acceleration in Special Relativity?
A lot of people think that you need to learn general relativity to deal with acceleration, but that’s not true at all! You only need general relativity when there’s gravity. To strike this point home, I’ll give you not 1, not 2, but 3 different ways to analyze accelerating objects! To understand the first solution, all you need […]Read More
The area is the same!
This is one of the coolest relativity problems I’ve ever seen. It’s taken from Problem Book in Relativity and Gravitation by Lightman, Press, Price, and Teukolsky. It’s a great compilation of problems and solutions. You should definitely check it out. Here’s the problem. Imagine you have a parallel beam of light (think of a […]Read More
How long till it crashes?
Hey guys, Check out this cool problem! Here’s the problem statement: Two point masses and are initially stationary and separated by a distance . Assume that so that the mass never moves. Under only the influence of gravity, how long does it take for the two masses to collide? This is a fantastic […]Read More