Crisis Is the Best Motivation
I was stumped. Absolutely stumped. I’m teaching rotation for the first time and had just finished blazing through rotational kinematics. I wasn’t thinking more than a day or two ahead (still am… thankfully, spring break is next week). So Friday happened, and I had no idea where to go next.
Sunday evening rolled around, and still nothing. I was at the “google iterations of different phrases” stage of desperation. And at some point in my google hole, I was looking at a cook-book lab for torque. And then… huzzah! An idea.
— Trevor Register (@TRegPhysics) March 23, 2015
I wasn’t sure at the time if it was going to work, but I didn’t have anything else to work with…
It’s All About the Ratios
Students quickly notice that ratio nature of this lab. I stressed in the beginning to pick 2-3 combinations of masses that were even multiples of one another: “Picking a few data points where the ratio of masses is easy to see will help you see the pattern. Then, apply that pattern to your data points that aren’t even multiples to see if it still holds up.”
I wasn’t sure about giving them that tip when I did, but I knew that we didn’t have 2-3 days to spend on this. As it turns out, it was the right thing to do. Sure, it takes a little bit of the discovery away, but not in a way that lessens the benefit of an activity that essentially has them inventing torque.
Once most groups had noticed the pattern, I asked each group to write an equation for the pattern they’d discovered that included the force of both hanging masses and the distance of each from the center. Each group was instructed to include that on their results. All of the groups came up with a ratio equation, which later I asked them to “get all the R’s on one side and all the L’s on the other.”
Comments on Torque
At this point, everyone’s back in their desks ready to take notes. I introduce the concept of torque and talk for a few minutes about it being an analogue to force for rotational dynamics. I also include some snippets from the rant below.
What fascinates me about this lab is that it allows students to go through an incredibly authentic scientific experience because they essentially invent the torque quantity. This activity answers the question Why is torque = force*distance, which is something that I never understood. Because of this whole ratios thing! Nature has decided that if the force*distance on one side of a reference point is the same as the force*distance on the other side of that point, then the object’s angular velocity doesn’t change. The “invented quantity” aspect of this activity lays the entire foundation for rotational dynamics as everything else depends on knowing what a “torque” is.
All in all, this lab is simple and straightforward. No tricks, twists, or surprises. And I’m sure it’s not a new or unique approach in the grand ‘ol world of physics education, though it’s very new to me. But I think that’s a big part of why I like it. If you’ve got suggestions on how to improve it, I’d love to hear ’em!