Facile Physics

The Beauty of Unit Analysis

Tags: physics intro units

Every introductory science student hates units. I know that I hated it. After all, you spend an hour calculating the speed of a raft in a river after a bird lands on it, only to have your teacher dock you a point for writing “10” as opposed to “10 m/s”. It feels like tedious nitpicking and a cheap way to maintain a curve in the class.

This is unfortunate, because unit analysis is quite possibly the most power tool that you can learn in science. It’s so powerful that you’re about to answer a bunch of impossible trivia questions, despite the fact that I haven’t even taught you anything yet.

1. How far is it from Parshall, North Dakota to LaGrange, GA?
   1. 1400 miles
   2. 1400 pounds
   3. $1400
   4. 1400 years
2. How much does an average aardvark weigh?
   1. 160 pages
   2. 160 miles per hour
   3. 160°F
   4. 160 pounds
3. What is the warmest temperature every recorded in Athens, Illinois?
   1. 37 acres
   2. 87 watts
   3. 107°F
   4. 47 gallons
4. For how long did Pharaoh Ramses the VI rule Egypt?
   1. 6000 miles
   2. 3000 days
   3. 9000 ounces
   4. 2000 horse power

The answers are at the end of the post, but you don’t really need to look at them. You already know that you got the answers right.

There’s no way that the warmest day in Athens, Illinois was 47 gallons, because what does that even mean? You’ve probably never even heard of the town, but only one of those answers could even possibly be right. After all, you’ve never turned into the news to hear the local meteorologist say that today’s high will be 37 acres.

However, you’ve probably encountered someone giving a temperature in Fahrenheit at some point. That has to be the right answer, simply because you know that the others MUST be wrong. That’s how unit analysis let you answer four quiz questions that would have made Ken Jennings punch Alex Trebek in the face.

Still, this probably doesn’t seem like a big deal. After all, how often does someone try to tell you that they’re thirty feet old? Well, it turns out that it happens quite a lot.

Just this last week, I had a computer program try to tell me that the distance between the fibers in the sample I was looking at were 200 per nanometer apart. Now, even if you’re unfamiliar with the nanometer, you’ve probably encountered someone measuring how big something is in meters or kilometers.

Have you ever encounter someone measuring how big something is in “per meters” or “per kilometers”? No, you haven’t, because it’s stupid. So, the moment that I saw that the answer was in “per meters”, I knew that the answer was wrong. You now also know that it’s wrong. You don’t know anything about the fibers in my sample or even what my sample was, but you know that the fibers are not 200 per nanometer apart. You just out-smarted the computer because you knew unit analysis and it didn’t. Congratulations!

There’s far more to unit analysis than this. Entire laws of nature can be derived simply by jamming together the units until they fit. While I’m going to save that for a later post, I hope that you understand that there’s more to units than science teachers punishing their students.

For the record, the answers were b,d,c,b