How does dimensional analysis work?
Dimensional analysis is simply a way of testing whether the base units of a given equation work out. It operates on a simple principle: the units you have on one side of an equation must match those that you have on the other.
It's analogous to baking a cake. Your cake can only have what ingredients you put in to it.
Consider the following equation:
Force in base units is
Mass is just
So now let's evaluate this by plugging in these units into the equation:
This equation works, therefore it can be classified as dimensionally correct.
Let's look at another equation:
Now let's just plug everything in:
Notice that I have not included the
Now we simplify:
Since this equation does not work out, this equation is not dimensionally correct.
Hope that helped :)