Despite the worsening classroom culture, there are still good things going on. Here are some student ideas to make sense of why pendulum depends on length but not amplitude:
When you raise the amplitude, you increase the distance back and forth, but you also increase the potential energy, which as the pendulum bob falls, increases the kinetic energy, which increases the speed the bob has. With an increase in distance but also speed, it’s plausible they could take the same time.
When you increase the length, you have put the mass farther away, which we’ve seen makes things harder to turn (Note: we had played around with lead bricks near the center of rotation vs. the edge of rotation). Therefore, with more of the mass farther out from the rotation, the slower it will turn around the pivot point, making the time increase to get around and back again.
When you increase the length (and keep amplitude fixed), you change the total distance the ball swings back and forth, but you don’t change the speed it has, because it still falls through same change in height. [Note: We had to check and verify that this seemed plausible–that the change in heigh is same. We were using the Phet Simulation, shined onto the whiteboard, so we could easily mark and see that this was the case… ] With more distance, but same speed, it must take
less more time.
What I liked about these ideas was that they involved reaching back to concepts we had learned early. They were bringing up both results from observation we’ve seen before (the lead bricks), and ideas about energy.
It’s all too common for students to see physics as sets of unrelated ideas. We learned about energy, then we learned about moment of inertia, and now we are learning about pendulums. Here, in this moment at least, we were seeing energy, moments of inertia, and pendulum as inter-related, and seeing energy and moment of inertia ideas as tools for making sense of the pendulum phenomena.