Concept Modeling · In My Class Today · Teaching Methods

Pass Along – Modeling Waves

The pass along activity is one I developed shortly after attending a Kelly OShea workshop. I wanted to combine modeling with the strengths of white board speed dating and board walks. At the time I didn’t have the large whiteboards and for this particular activity I decided a piece of paper would work best.

Students have already done a reading on waves ahead of time (hopefully).

Part I: I ask students to draw in a pictorial representation of what a longitudinal and a transverse wave might look like.

This is inevitably the most common drawing. Students obviously did the reading, but struggle with a pictorial representation

Students are then told to pass along their paper. I predetermine groups randomly for this activity. Three is best, but if I don’t have a factor of 3 then I put the stragglers into groups of 4. It looks like this:

Student 1 -> Student 2 -> Student 3 -> Student 1

Part II: After students have passed along, they are required to look at the work done by their peer and explain, in words, why that person drew what they drew. Much like speed dating, this requires each of the students to get in the minds of their peers, but without the opportunity for their peers to explain.


Students then pass along again.

The third person takes a look at the previous two answers and then has to think of a way to model each wave type with their bodies.

After the three pass alongs, students get into groups, at this point each paper has been touched by the same persons. They discuss their answers and then they have to get up in front of the class and model with their bodies each wave type.


The physical modeling is great in that the kids are up and moving, but it also provides an opportunity to have a discussion about the model. 7th hour we had a discussion about whether or not doing the worm accurately models a wave (nope, the particle is moving across the room). Similarly, I had a few groups move their whole line down the room which brought up the discussion point about what a wave transfers and doesn’t transfer.

Afterwards, we will go out as a whole class and model transverse and longitudinal waves using an 8-step count.

A unique representation of a longitudinal wave I hadn’t seen before
Concept Modeling · Teaching Methods

Slicing a Cylinder for Moment of Inertia Integration

Guys….we’re in the throws of rotation. And at least one of my poor students has calculus immediately preceding AP Physics C. I feel so bad for her. The day we started she had made up a calc quiz, came to day 1 of rotational inertia, then went to calculus. Oh did I feel her pain.

Arguably the most difficult part of deriving rotational inertia is the visualization of how to go about the integration. I mean, let’s be honest, once we find how to express dm the integration is always an easy one.

Part of the problem is getting students to understand what it means to say things like dm, dV, dA, etc. They understand the definition linguistically, but it’s really hard to think of it practically. Tell them that dr^2 is zero and their minds are blown and bothered.

Day 1 of cylinders did not go well. Arguably, in part, because we were short on time. But also because the what why how was overwhelming.

I remembered a demo someone had shown where they 3D printed their objects to roll down the incline. They had actually made nesting cylinders, which then served as a great way to discuss integration.

I’m trying to think of a way to visualize each of the d-steps of the cylinder integration for my students with materials I have on hand. As I’m digging through the closet I notice the slinky coil. It’s nearly perfect!!!

Ideally, I wish I had one with nice thick coils so we could take about the cylinder with R1 and R2, but this will suffice for the most challenging part.

So imagine you have a cylinder of length L, and inner radius R1 and outer radius R2 and would like to determine the moment of inertia about its center…

IMG-2037 (1)

First, as always let’s define rho, but we have to find dm in terms of r. So how do we do that?

Well, let’s take some horizontal slices, where each slice is dm… now we can see that dm = rho*dV…but wait… what is dV?

Well, if we make those slices infinitely small…is there really a volume left?


Ah! so dV is really dA, and we are looking at it across the length of the slinky, so dm = dA*L!

Conveniently, I know that A=pi*r^2, so dA = 2*pi*r dr

And the rest is substitution!