In January I wrote a piece titled “5 Physics Equations Everyone Should Know.” Lots of you weighed in with your own nominations, and there were plenty of good suggestions. So I’ve decided to do a sequel. Make that 10 equations everyone should know!
Just to be clear, this list isn’t just for scientists. You want to be a well-rounded person and understand the world, right? Robert Heinlein wrote that the great thing about humans is that they don’t do just one thing. You might be a rodeo rider by trade, but you also know about art, history, and cooking microwave popcorn. Humans are the Swiss army knives of the animal kingdom.
In the five equations below, I’m going to explain the relationships they describe—what they mean. We’re not going to grind through any derivations, so don’t worry, there’s no math required!
1. The Work-Energy Principle
Courtesy of Rhett Allen
This one is so simple, maybe it shouldn't even be an equation. But it's super powerful. The work-energy principle describes how the energy (E) of a system changes (the delta symbol Δ means “the change in”) when work (W) is done on it.
Energy is like money in that it's not real—it's just a thing that people invented to make trade easier. You might argue that a dollar is worth a certain amount in real gold, but that just kicks the problem down the road: Why is gold valuable? Because humans said so.
The same is true with energy. It's an accounting ledger, a way to keep track of interactions. Consider an example with kinetic energy. This is the energy an object has because it’s in motion, and it depends on its mass and speed. Energy is calculated in units of joules.
First you have to define the “system” you’re analyzing. Let’s say you have a system that is just a bowling ball. If you throw that ball down the lane, you’re adding energy from your body to the system. That’s the work. Check it out: The kinetic energy of the ball increases and it speeds up. When it hits the pins, it transfers kinetic energy, causing them to fly apart. Strike!