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Where this gets complex is that it's not a normal bicycle wheel. It is a normal wheel with weights on the spokes connected to the hub by springs. So as the wheel increases it's angular velocity, the weights move outward, changing the overall moment of inertia for the wheel.

I'm going to assume that the weights are a second rim with fixed mass, but variable radius, and both 'rims' are thin shells (so I= mr^2). I'm also just (for now) looking at a torque being applied to the 'real' rim and not considering the inertia or accelerations on the whole wheel as if it were rolling down a hill.

Any thoughts on how best to approach this? This is what I have so far:

[tex]\dot{\omega}[/tex] = f(T,I)

[tex]\dot{T}[/tex] = f([tex]\dot{F}[/tex],r1)

[tex]\dot{I}[/tex] = f(m2,[tex]\dot{r}2[/tex])

[tex]\dot{r}2[/tex] = f(m2,[tex]\omega[/tex],k)

[tex]\dot{F}[/tex] = f(t)

thoughts? and easier way to approach it?