Dimensional Analysis does and doesn’t have to do with actual Dimensions (the kind you think of when you’re talking Space) – and really, it sounds a lot cooler and more complicated than it really is. Still cool tho!
But first, a question for youse fools: How do physicists (and other types of mathy scientists) choose to describe the world?
Well, as far as I can tell, (as humans) we understand the world as quantities of objects with properties, and we generally talk about the relationships between objects and objects, properties and properties, objects and properties, you name it, using nothing but Natural Language. Well you can do the same thing more nicely and precisely using Mathematics.
For instance, “There were tons of spinning wheels and babies above me!” – just pick out the instances of each for yourself (don’t use highlighter on your viewport – highlight paper, not screen)
Using maths we can quantify things and define them mathematically, and talk about theirs Units, which are like the “standard amount” of whatever you’re talking about.
Remember, “units” describe “unity” (a single amount of some shit).
Now, for the actual technique. It’s a simple matter of understanding that each “quantity” is associated with a standard amount of unity, which you then multiple by a coefficient to make it possible to say “half a Newton” or “two Pascals” or something. When you perform multiplication on the “quantities” the units are also, in a sense, being multiplied too. So for example, when you divide a distance (a quantity (in SI standard, described in meters)) by a time (standardly described in seconds), you get meters per second (you may know this as Speed or perhaps as Velocity).
The technique is basically knowing this shit, and realizing that you can check your calculations by looking at whether the units themselves make sense.
So if you’re expecting Newtons (kilograms times meters per second per second) but you’re getting something weird, you’re probably off.
For a nice lil read on Dimensional Analysis, click here!