Physics: Rotational inertia. There was a quiz, then we passed around the rotational inertia sticks to feel the differences. Last, we did an activity where you tape masses to the middle and one end of a meter stick and stand them up on end with the mass at the top. The students think the one with the mass on the far end will fall faster for reasons that are completely unclear to them other than the “heavy things fall faster” preconception, which doesn’t even apply because both meter sticks+weight have the same overall mass. So, they try it out a few times, see that their initial idea is incorrect, and then we talk about moment of inertia and rotational acceleration and all that good stuff. We ended up with 20 minutes left of class, so I opened the floor up to questions, and they asked some really great ones about what if this and how about that and how does center of gravity relate and so many cool things.
The best conversation ended up being a student asking under what conditions would the one with the mass at the top fall faster, so I thought through it and said my idea was that since I is 4x as big when the mass is twice as far from the rotation, if we cut the mass by a quarter, then they should have similar I and thus should fall the same, so if we cut the mass by 5x (down to 20g), then the one with the mass at the top maybe should fall faster. So, we tried it out, and I WAS WRONG. I freaking loved it. It actually matched my idea the first trial, but we all know one trial is bad science, so we tried it a few other times, and every other time the one with the mass in the middle still reached the ground faster. My current idea is that now the weight of the meter stick is somehow affecting things, but the two meter sticks are nearly identical (and I even tried a different, even more similar meter stick just in case, but nope, same result). So, obviously, I had to do the calculations.
I assumed the meter stick had a mass of 100g and treated the masses as particles. You end up getting that my intuition was right about the one with 20g at the top having a lower I, but with the lower mass there is less torque due to gravity, so it’s angular acceleration is about 3/4 of what it is for the stick with 100g in the middle. The angular acceleration for the meter stick with 100g on the end is not quite 2/3 that of the 100g in the middle. This is the up-side of rotational motion not being my strongest area. There’s a lot of stuff I haven’t internalized yet, so there’s still a big sense of discovery and playing around to see what’s going to happen. With most of the other topics, I already “know” what the right answer is, but this is sending me into areas where I’m less confident and requiring me to really make meaning as we go.
Honors Physics: We don’t have equipment to do a good rotational motion lab, so I pulled out my trusty PhET simulations, found some attached resources that did what I wanted, and got them set up playing with bugs on turn tables.
AP Physics: The morning class got totally side-tracked, but in a super interesting way. We talked about center of mass a bit, and then moved on to rotational energy, whereupon I pulled out the rotational inertia sticks. Like you do. The students passed them around feeling the differences, and the conversation came up about which one would you rather use to hit someone. Intuition says the one with the masses out toward the ends, but you can swing the one with the masses toward the center faster, and kinetic energy is related to omega squared, so what is the physics of which one would be a more dangerous weapon? I’ve got a martial arts background and experience with a few weapons fighting forms, so I thought this was a super interesting question. We quickly ran out of time with the 40 minute class, but I think I’m going to make that the lab on Thursday for both classes. It’ll be real, actual physics, and they can argue over how they model it and the decisions that they make, and I’m really excited to see if this actually works.
The second class was super duper on board with this, too. They were a little wary of the “we get to decide how we want to model this”, because they’re used to more well-defined problems, but that’s a lot of the point. It will also help me develop more intuition surrounding rotational motion, so I am pleased as punch about the whole thing.
See what I did there?