I'm having trouble following the physics in these, but it seems like they'd make some great problems for a more extended investigation. Check out a bike and a car, both going through a loop-the-loop where they are completely upside-down in the middle.

I wonder if I could design a calculus unit around these...

## Tuesday, September 1, 2009

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Hi Sue,

ReplyDeleteIn addition to the physics and the math of not falling off the loop, another perspective is to look at some of the curves that arise when a wheel rolls inside a circle. A point on the edge of the wheel will follow a hypocycloidal path as the wheel rolls through the loop. Coincidentally, I was just thinking about these the other day.

Yeah, I liked that post. I don't think that question is pushed by these videos as much as the first one, though.

ReplyDeletePart of the goal of this WCYDWT series is to start with images that get the kids asking the math questions.

Now if we had a video of a person inside a big tire (or something like that), rolling down a hill, we could think about where their eyes are. I know, it's not quite the problem you're proposing...

Or if you started with some video footage of a real carnival scrambler-type ride. Maybe that would get the kids wanting to explore the hypocycloids with you. Maybe talking about how to do an animation of it, and needing to know the position, would be a good start...

My precalc students and I explored some of these ideas during the spirograph activity. I've been thinking about a rollercoaster activity they could do this year as calculus students. It's tricky to program, though. I'll have to do a lot of work ahead of time so they can focus on the math behind the loop.

ReplyDeleteYeay Colleen! I will look forward to seeing that.

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