Patrick Teaches Physics

When we start learning physics in school, I think we're usually told to convert all quantities into SI base units (metres, kilograms and so forth).  This isn't bad advice as it can certainly prevent some problems.  But it's not always optimal.  And at some point, when we delve more deeply into a particular branch of physics, we will need to become comfortable with somewhat "niche" units. A simple example of sticking to non-base units is the measurement of density.  Suppose I am given a small cuboid of some material and asked to measure its density.  I get a ruler and measure its dimensions: 3.5 cm x 2.2 cm x 4.7 cm I put the sample on an electric balance and find its mass to be 120 g These units -- centimetres and grams -- are what my tools use.  If I convert into metres and kilograms, here's what my calculation looks like: If instead I'm a bit more sophisticated, I can stay in my original units: The second method is more efficient: there's simply less...

There is probably no habit that a physics student can learn that has a higher return on investment than including units in calculations.  To see what I mean, consider this routine momentum calculation: Can't remember the units for momentum?  Don't have to, they're already there on the page!  This is particularly useful if you are not using base SI units: you don't get confused or forget which units you're using along the way. Better than that, this method gives us a powerful way to check our own calculations.  In the next example, I calculate the time required for an object to fall a distance: What!?  Metres per second isn't a unit of time!  I've made a silly mistake re-arranging the equation; the kind of mistake it's easy for a student to make, and even pros do occasionally.  But pros tend to catch such mistakes because they have kept track of the units.  That means we can fix it: The unit being right gives us some confidence the number is right....