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."