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29 June 2017

Making appropriate simplifying assumptions is a physics skill that we all must teach.

The comment section of my post about the 2017 AP Physics 1 exam is full of interesting discussions about the recent test.  One of the reasons I write this blog is to provide a venue for intelligent, professional teachers to share ideas and find advice.  I appreciate the good-faith questions, the reasoned comments.  I don't read posts in other venues about recent AP tests because they are too often full of us-vs.-them bile, full of ignorant complaints about the exam that really boil down to "I and my students were unprepared for this exam, and now I'm angry about my own failure."  Those who post to this blog display far more class than that, and I appreciate it.

The purpose of this post is to respond to and rebut some of the comments about the 2017 exam.  I'm going to say some of the posters are wrong; or at least that they hold some incorrect basic assumptions about AP physics.  I want to be clear -- I have total respect for those who have posted.  I mean no criticism of their motives.  It is entirely appropriate to discuss, or even criticize, AP exam questions.  The College Board does not and should not demand Trump-style loyalty; as much as I support those who create the AP Physics 1 exam, I will not fall into the role of Fox News.

Nevertheless, I see a continual theme in these comments, and in questions from teachers at my summer institutes, that betrays a fundamental misunderstanding about teaching first-year physics.

It is our job to teach students to make appropriate simplifying assumptions about physics problems.

A lot of discussion back in May concerned problem 4 on the 2017 exam.  A light disk collides with a heavy, pivoted rod.  The question asked, essentially, where should the disk hit the rod in order to induce the largest angular speed in the rod - close to the pivot, or far away from the pivot?  The straightforward solution required referencing either torque or angular momentum.  The best answer explains that the angular momentum of the disk mvr is larger when r, the distance from the pivot, is larger, giving the disk more angular momentum to transfer to the rod.

But wait, some folks said.  The problem never said the rod was uniform.  What is the rod weren't uniform?

As far as I can see, the answer still stands.  No matter the shape of the rod, the disk still transfers its angular momentum to the rod, and thus farther from the pivot means more angular momentum transferred.

Commenters made several arguments.  Let's start with:  (1) If we look at some possible mass distributions for the rod and disk using computer simulations, it's possible in some cases to get bigger speeds closer to the pivot.

I don't see it myself, but I'm not ruling out the possibility.  I know the problem stated that the rod was much more massive than the disk; I strongly suspect that the only way to get bigger speeds closer to the pivot is to make the disk itself big.  That said, I could easily be wrong here.

The big, friendly point, though, is that it doesn't matter.

The first step in solving any physics problem, at any level, is to make appropriate simplifying assumptions.  For example, when we calculate the normal force on me when I stand still, we ignore the buoyant force of the air on me, we ignore the force of Jupiter on me.  We just say the normal force in this case equals my weight.  It's not useful physics to say, "Well, what about the case when the wind is blowing 50 mph and your right foot has trouble staying planted?  And that buoyant force can in fact be calculated, it's nonzero.  Oh, and the force of Jupiter exists, it's just very small compared to your weight."

These statements are entirely correct... and they're entirely irrelevant to the problem as stated in an AP Physics 1 class.  We always make the simplifying assumptions that allow us to solve the problem.  THEN, if it turns out that our solution doesn't match a measurement, we can consider if other issues must be taken into account.  This is not just an introductory physics thing - this is how I was taught to do research.  Solve the basic problem first, then add complexity.

Once you have to concoct far-out situations to perhaps find a situation that could cause an argument, that argument is about semantics, not physics.  If you sound like a lawyer, you're wrong.

(2) But what if a student was confused, and dealt with a non-uniform rod?

Firstly and most importantly, no one did.  At all.  I was table leader for this problem.  I asked everyone I knew to watch for anyone who treated the rod as non-uniform, or for any student who indicated that she might be confused by the lack of specificity.  Not one of the 170,000 students that we looked at was, in fact, confused by the uniformity or non-uniformity of the rod.  Not one.  

I didn't ask development committee members, but I suspect they didn't consider the structure of the rod, either.  Set up the experiment in your classroom - who's going to use a non-uniform rod?  And if they do, either (a) the problem still works the same way, or (b) you have a problem way, way beyond the scope of AP physics 1.  

It is our job as physics teachers NOT to lawyer up in response to a question that might, maybe, in a professional physicist's mind have a deeper layer.  Rather, it is our job to show our students how even seemingly complex problems can have simple solutions which can be verified by experiment.  It's our job to teach students to answer the simple question rather than become paralyzed by the complex details.  We must show how "eh, the population of the US is something like 300 million people" rather than "we cannot make any statement about the US population because someone is born every 7 seconds, rendering any estimate immediately obselete.  

Excessive precision and detail is not to be lauded.  Excessive precision and detail is the enemy of understanding in introductory physics. 

1 comment:

  1. My initial thought seeing the disk hit the rod was that the problem was going to ask about the "sweet spot" on a bat, which involves a different imperfection: that the rod isn't perfectly rigid. But since the sweet spot would still be closer to the far end of the rod than toward the center, it wouldn't change the answer at all (as far as I can see). It might however lead to some interesting data sets and class discussion if a class's lab method of testing this is to launch some clay at a baseball bat.