Quantity Dimension Formula

1. Suppose you have a bunch of measurable quantities, and you know they enter into a functional relationship. You might know, for example, that the time t that it takes a massive body to fall to the ground when dropped from rest1 is some function of • the mass m of the body, • the distance d of the fall, and • the gravitational acceleration g near the surface of the earth. That is, you might know that for some function F, t = F(m, d, g). (1) Dimensional analysis is a method for narrowing down the list of possible functions that are candidates for F. Here, in outline, is how it applies to this example. First we write down the “dimensions, ” or “dimension formula, ” of each quantity: 1In a vacuum, or ignoring drag