Question

What is dimensional analysis used for?

Answer 1

Dimensional Analysis is used in engineering as a simple way to check one's work.

After someone solves a problem, especially a conversion, they need someway to check that are correct. An easy way to do that is to check the units you were given, and seen if they make sense for what you ended up with.

For example, if you have `13 color(white)(0) kg xx 15 color(white)(0) m/s^2` and you say that equals `195 N`

To check your work, let's just with the units:

`kg xx m/s^2 = N`

You want both sides of the equation to look the same. Right niw they don't but let;s break the unit Newton `(N)` into it's base parts -- `(kg xx m)/s^2`. Now let's see:

`kg xx m/s^2 = (kg xx m)/s^2`

There, now they look the same! So that is an indication that we did the math right. It doesn't guarantee we're correct, but if dimensional analysis shows we made a mistake, it gives us a chance to catch it