Tuesday's List: Fundamental Units of Physics and Derived Formulas

A few decades ago I was studying basic college physics when I tired of having to remember all of the formulas in mechanics and electricity...and decided to develop numerical strings for each type of quantity that, for me at least, were easier to retain.  Now in physics there are seven fundamental units, of which everything else can be derived (back then I only used four):

1 mass.......................kilogram (kg)  
2 length.....................meter (m)
3 electric current........ampere (A)
4 time........................second (s)    
5 thermodynamic temperature...degree Kelvin scale, or kelvin (K)
6 amount of substance...mole (mol)
7 luminous intensity.....candela (cd)

For the purposes of this article, I'll leave off the last three units, although you might find it interesting that thermodynamic temperature does not figure into the formula for energy...heat energy or otherwise.  What I did was to write out four-number strings, each number representing the exponential powers for the units or combinations thereof.  So...

mass:          1  0  0  0  kg
length:        0  1  0  0  m
current:      0  0  1  0  A
time:           0  0  0  1  s

From this we can derive more strings:

area             0  2  0  0   length-squared
volume        0  3  0  0   length-cubed
velocity       0  1  0 -1   length per time
acceleration 0  1  0 -2  length per time-squared
density         1 -3 0   0  mass per length-cubed
force            1  1  0 -2   mass multiplied by length per time-squared
energy         1  2  0 -2   mass mult. by length-squared per time-squared
power          1  2  0 -3   mass mult. by length-squared per time-cubed
pressure       1 -1 0 -2   mass per length per time-squared
charge          0  0  1  1  current mult. by time
voltage         1  2 -1 -3  mass mult. by length-squared per current per time-cubed

Each number of the string represents the exponential power of that fundamental unit within the formula...and you multiply across the string.  A unit represented by "0" simply isn't present within that formula.  I found this numerical mnemonic system, once learned, to be easier to remember...

And it's also easier to see relationships between the different formulas, for example:

We're taught that force=mass x acceleration...or:

      1   0   0   0    mass
      0   1   0  -2    acceleration
      1   1   0  -2   force     (note that when multiplying exponents you add the powers)

If you're interested, you can go through the whole physics textbook like this and the formula derivations can get to be almost a matter of second nature after a while...