AP® Physics: Solving the Same Problem Again and Again!

In AP® Physics, we are deep into rotation now (see earlier post about rotation skills).  We have investigated RMM.1 (uniform circular motion), RMM.2 (rotational inertia), RMM.3 (rotational motion and second law with torque), and RMM.4 (conservation of energy with rotation).  At this point, we have enough rotational skills under our belts that we have options when approaching a problem.  The same problem can now be solved different ways!  As a teacher, I LOVE options.  The students are slightly less thrilled than I.  Options can cause stress.  What if they pick the "wrong" method?

This year I have been striving to emphasize how cool it can be to solve the same problem different ways.  Not only do the students become more comfortable applying different skills, but they also start to see which strategy is more efficient depending on the given and sought information.

One problem that has been awesome for this practice is the following:

A hollow, spherical shell with mass, M, rolls without slipping down a slope (θ).  Find the acceleration, the friction force, and the minimum coefficient of friction needed to prevent slipping.

This is a very typical and, in a lot of ways, simple problem.  Nothing fancy.  Normally, I wouldn't have the students do this problem before we had discussed torque.  However, I decided to deviate from the norm and see how they would approach it using energy, kinematics, and translational second law.  Whiteboarding took much longer without the more direct torque approach (about 40 min), but my determined physicists did it!  And their smiles of accomplishment were wonderful to see.  In case you are interested (of course you are! who am I kidding!?), I wrote up a nice solution below for the coefficient of friction portion.
solving rolling without slipping physics problem without torque
For those of you who look at this with confusion, the important message is that the black, green and pink sections show how many different skills the students needed to pull from to put this together.  Then, a week later we learned torque.  It took them 10 minutes to do the problem!  They were pretty impressed with themselves!  Notice, all of this work (below) is in black as all of this was done with essentially one type of tool.
Solving rolling without slipping down a ramp with torque

What I am going to do now?  

I want to embrace this practice of re-solving more actively and consciously.  I absolutely do this throughout the year, but I'm planning on reworking my unit packets to more deliberately incorporate this scaffolded solving experience.  I have done this a little bit in my forces packet (second unit of the year).  I can share those details in a future post!  In addition, with the help of the modeling instruction resources, I already have a lot of this in place (along with many modifications to make it more my style) for physics (regular level).  The dream would be to do this across all units for all problems in AP®!  Every summer, I make solid strides in this direction (updating, rewriting, and resolving my packets), and I am excited to tackle this further this June!


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