Today in non-major, algebra-based physics we went over the fairly classic problem of determining which will win a race down a hill, a sliding block or a hoop, cylinder, or solid sphere? I like working through this problem because it’s a great way to show students the value of not plugging in numbers too early, but rather let the equations play out so that you whittle the problem down into what really affects the difference in answers between all the options. It’s also a nice example of thinking about a distribution of initial energy; in this case, the object will go slower when some of its potential energy gets converted into rotational kinetic energy. The object that has the least amount of energy going into rotation (or none, in the case of the sliding block) will have the most available to go into its translational kinetic energy. And that will be determined by the objects’ moments of inertia.
Everything was proceeding like it has in years past when I’ve taught this section, but then a question came up: should we account for friction? One student in particular noted that he thought that there had to be friction present in the rolling objects’ case, even if you said the sliding part was frictionless. And for the conservation of energy equation to play out, you really did need to include it.
I’ve got some ideas, but I want to ask you all – what do you think? Part of me feels that this is connected to an oddity I see in a lot of my non-majors, in that they are always wanting to think about friction, air resistance, etc. (Compare that to my physics majors, who in today’s Matlab class were very pleased to not account for air resistance in a model we coded for hitting a baseball a certain distance.) I’ve been thinking a lot about why my non-major students are so attached to the ideas of friction and drag. In class we talk a lot about setting up models, adding in additional factors as we get more and more specific with the model. But this year’s class especially isn’t happy with the discussion. They ask, “if we live in a world with friction, why would we even bother to ignore it?” I was talking with a colleague in the health sciences, and he said that the students (many of them the same ones I have in my class) ask essentially the same thing for some models he talks about. So at the very least, their questions like this aren’t limited to physics.
But to get back to the original question, do we need to include rolling friction in the analysis of which rotating object will go down the ramp the fastest?
*”hup” is how my college physics professor pronounced “hoop” when we covered this. He said, memorably, “what is that, a hup?” and I almost always dissolve into giggles thinking about it even now. I guess you had to be there.
[Image Creative Commons licensed / Flickr user phonogalerie.com]