Doing a project relating calculus II and gymnastics

crazytumbler9
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Okay so our calculus professor has given us an assignment to do a project involving calculus. He found out that I was a gymnast and liked physics so he said that my project should relate calculus, physics, and gymnastics.

I'm having problems coming up with an idea in which I can actually measure what the variables I need for equations. Also it needs to be able to relate ideas from calc. II. Any ideas would be a huge help.
 
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You could explore rotational motion. Study the theory of the motion of a rigid body:

http://en.wikipedia.org/wiki/Euler's_equations_(rigid_body_dynamics )

And then generalize this to the case of a gymnast whose moment of inertia tensor will be time dependent.
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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