I’m teaching an intro course to incoming mechanical engineering students wherein I survey *all* of Mech Eng. This year, I’m concluding each lecture with “Things I Wish I Knew as an Undergrad.” Today’s lecture: Units. What I wish I knew: Units are your friend! A thread follows...

Professors don’t just deduct points for not showing units as a way of lowering the average on the exam. Rather, carrying units on all calculations is the best way to check your work as you go. In requiring you to show units, your professor is trying to *improve* your grade.

Units are a type of checksum: All terms that are added or subtracted or terms on either side of the = sign *must* have the same units. Verifying unit consistency is the most reliable way to verify a calculation. If the units are correct, the answer is almost certainly correct.

Examining units can also provide deep insight into a problem. Groupings of parameters that have no dimension (i.e., units cancel out) are convenient not just because they have the same value regardless of the system of units you use, but in addition:

Dimensionless groupings that don’t depend on unit system invariably have great physical significance. By examining the dimensions of the parameters alone, G.I. Taylor in 1940s was able to solve the dynamics of blast waves, including—famously—the blast from the first atomic bomb.

Finally, even in coding, carry units in your computations. Debugging is easier when the numerical outputs can be checked against your physical intuition of the magnitude of the answer. This point may be contentious for modelers, but I’ll leave the last word with Oran & Boris: