We started balancing objects on metersticks on Friday. We graphed the relationship they found, and since most groups change the mass and then measured the distance the mass had to be placed at, we had a lot of graphs that looked like this:
Most of the boards had good equations, but had a hard time figuring out the units for the constant of proportionality. I picked a group that had gotten what we all agreed should be the constant of proportionality. I asked this group for the mass of their fixed mass and its distance from the pivot point. They had a 50 gram mass that was placed 45 centimeters from the pivot point, which is what I wrote out below their equations.
At this point in this class, there was a loud communal groan. "Why do you keep doing this to us, Mr. Lerner?" one student asked.
"I didn't do this; the physical world did."
It does seem like the mass times the distance equals the mass times the distance. But is it really mass? Couldn't it be force?
We got out the force meters, keeping our fixed masses at the same position. (Next year, I'm going to use spring scales.) Everyone just pushed down on one side of the meterstick until I came around and asked what they could do on the other side of the meterstick.
We realized that clockwise and counterclockwise seem to be the way to talk about these influences, not left or right or up or down. These clockwise and counterclockwise influences need to balance to keep an object in rotational equilibrium, just like forces must balance to keep an object in translational equilibrium.
We ended the period working on a few questions, one which seemed really easy and two which seemed really hard. Let's whiteboard those tomorrow.