20 July 2021

Is there any need to teach dimensional analysis in AP physics? (No.)

With respect to AP Physics 1 in particular, I was asked:

Do you expect AP students to use dimensional analysis (factor-label method) when converting units?  Do they come to you with that skill?  I am considering the importance of the factor/label method to chemistry and its importance as a prerequisite skill to AP physics. 

Students pick up converting units easier using ratios.  This seems like one of those skills once they get it, it seems very useful to them later on.  I have always just assumed my physics kids could do it.  I don’t know if I am just holding onto it just because I learned it that way though.  Any thoughts?

Interesting question... I think the last statement is a wee bit on the nose.  A lot of us hold on to teaching skills and topics because of the way we ourselves learned them.  :-)  

Dimensional analysis, converting units, etc. is not useful in AP Physics 1, 2, or C.  In the very rare occasion in my class (not on the AP exam!) when I have to convert, say, from 40 mL to cubic meters, I type into google "40 mL to cubic meters".  The answer is 4 x 10^-5 cubic meters.  :-)  But, only 2 of 76 released AP Physics 1 free response questions have included even a single numerical answer.  And neither of those required anything beyond 5th grade math to acquire.  Physics 2 and Physics C have included more numerical answers, none of which require any unit conversions.

When we've introduced unfamiliar units, I deliberately use simple comparisons.  A meter per second is about 2 miles per hour, or 4 kilometers per hour.  That's easily close enough to understand whether a speed is reasonable for an airplane / automobile / runner / small slimy creature - and that's all that matters, 'cause google can do precise conversions if they're necessary.  A meter is about a yard, a kilometer is half a mile, a kilogram weighs 2 pounds.

I vehemently reject the old-school approach to physics problem solving that says "just manipulate the units until they match."  No!  Start every problem with a fundamental fact or equation.  The AP Physics exams are not going to assign problems that end in "gotcha!" because a student didn't convert centimeters to meters before plugging and chugging.  And for the frequent questions asking for derivations or justifications, the response "I got the answer because the units of momentum mean we have to have something with kg and m and s involved" simply won't fly.

Yes, in chemistry, the factor-label method is useful as students get their heads around grams, moles, and the meaning of an atomic weight.  But I let the chemistry teacher deal with that.  In physics, it is so critical to convince students that it is NOT a math course that I want to do nothing that gives the impression of a math course!  

For argument's sake, let's say I did teach dimensional analysis... I doubt that the chemistry teachers would notice any meaningful difference the following year in students' ability to execute this skill.  In the age of google, unusual unit conversion and dimensional analysis is simply not a useful skill in our students' lives -  unless they become a chemist, in which case they will figure this technique out on their own with ease.

3 comments:

  1. I hope students learn it somewhere in high school. I put dimensional analysis up there with algebra as a basic life skill -- Google or not. As an engineer, I find dimensional analysis particularly helpful when deriving formulas involving rotating objects. Say, for a spreadsheet formula or script. Google is less helpful in those situations.

    As a side note, my son will be taking AP Physics 1 this year and his school assigned summer work that included dimensional analysis, basic algebra, trig, and plotting experimental results. From a testing perspective, however, I agree that it probably won't help with the AP test.

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  2. Oy. https://jacobsphysics.blogspot.com/2009/06/in-opposition-to-summer-assignment.html

    Good luck to your son, Matt!

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  3. A fair number of parents end up hiring tutors to help their kids do their pre-AP Physics assignment. That's nice for the tutoring business. :)

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