Epic Rotational Derby

This year in my AP Physics C class I did a Rotational Derby Lab, students have no prior knowledge of rotational inertia formulas and observe races between different objects. The original lab I saw required materials I did not have. I asked some other teachers that do it and got a list together of things I had access to. I ended up with enough of some for eight lab groups and some odds and ends to be shared among them.

All lab groups: cardboard toilet paper roll, PVC pipe, wood dowel of similar radius and lengths; 0.5 kg brass cylindrical mass, hollow plastic ball, ping pong ball, golf ball.

Shared among groups: wood dowels cut the same length and of the same radius as the brass mass, empty oatmeal container, empty paint can, wooden sphere, "sloshy" cans of broth and "nonsloshy" cans of chili.

Students were confused at first at the sheer amount of materials so I made a list on the board for them of everything and added "hollow" or "solid" after each.

"Do we have to write down hollow or solid?" they would ask. I told them they might want to make note of it. Those that didn't ended up adding it later when they realized that information helped them to see patterns in which object "won" the race.

Students were to race two objects at a time down a stack of two whiteboards, releasing them at the same time using a meter stick. Often their predictions were wrong, they usually conducted repeat trials to be sure of their results. There were lots of side experiments going on, racing objects against each other I had not required. (Part of my ulterior motive for having so many objects available to them.)

Their exclamations of frustration or elation would have confused anyone walking by:
"What is with this sloshy can? It always wins!"
"No!!! Tube you were supposed to beat the ping pong ball!"
"Wait .... why the heck did the golfball win?"
"Why did they tie!?"
"No no no do it again, you started the oatmeal before the chili."

I was laughing all day and it was great to see them conducting their own experiments to try and figure out why one won out over another. One student vehemently insists it was voodoo magic.

In one class two groups merged to try and release more materials at once:

Which of course lead to what I wanted to test as well: All the things. At once.

So I grabbed a wooden box I had in the prep room that was wide enough and we set about it. Two students released them all but we found using  two different meter sticks made the release different for the two sides. We used an equivalently long piece of PVC and got the following results:

I took a still from the front video and we ranked the objects as best we could. A grid on this surface could help make it definitive.

1.“Sloshy” can of broth

2.Wood smiley face

3.Golf ball

4.0.5 kg brass cylinder

5.Wood dowels (2)

6.Yellow and red/blue ball

7. Ping pong ball

8. “non sloshy” can of chili

9. Empty paint can

10. PVC Pipe

11. Oatmeal container

12. Cardboard tube

Students had recorded the mass and radius of each object the day they completed the lab. The next day, after learning rotational inertia formulas, they were able to calculated an inertia value for each object. We did not take the different amounts of friction on each object into account but they saw the general trend that the objects with equations that would have higher inertia values if they had the same mass and radius into account were last to the race. The solid objects beat the hollow ones every time; solid objects were #2-5 and hollow cylinders were #9-12. Sloshy vs nonsloshy is a bit more complicated and students don't calculate a rotational inertia value for them. After some information on rotational kinetic energy they realize that the higher rotational inertia an object has, the more energy is going into its rotation and less is going into its translation therefore it will "lose" the race. Applying this idea to the sloshy can students realized that the sloshy contents aren't rotating (much) and therefore that was a lot of mass that was just translating down the ramp. The nonsloshy can however, has a lot of mass to rotate in that can and acts more like a solid cylinder with a lot of rotational energy and less translational kinetic energy than the sloshy can.

The kids really enjoyed the lab and while it was not as accurate as it could be it really helped them to understand what affected an object's rotational inertia and  I think set us up really well for rolling next week. Almost the entire lab fits into three oatmeal containers for storage as well.