This is the title of section 1.4 in Phil Nelson's book, Biological Physics.

I really like the way he uses subsection titles which convey useful information. Here are some:

1.4.1 Most physical quantities carry dimensions

1.4.2 Dimensional analysis can help you catch errors and recall definitions

1.4.3 Dimensional analysis can also help you formulate hypotheses

I think something that we just have to keep "hammering" students on is keeping track of units at each step of a calculation and canceling them out.

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I agree in principal, but the way it is done now (or at least, when I went through) does not emphasise why keeping track of dimensions is useful. It wasn't until I started tutoring first years that I 'discovered' how useful it can be.

ReplyDeleteIn my intro courses, I give the example of forgetting to copy down the square when calculating kinetic energy, say with m = 5.0 kg and v = 2 m/s:

ReplyDeleteK = 1/2 m v^2

= 1/2 * (5.0) * (2)

= 5.0

If the mistaken student had kept track of his units in the second line, he'd have seen that his answer came out to kg*m/s, not kg*m^2/s^2 = Joules. (Granted, most of them still don't listen.)

I do find it difficult, however, to require students to keep track of units when it comes to E&M, since the units are less "physically intuitive."