A disk of radius R rolls without slipping inside the parabola y=a*x^2. Find the equation of constraint. Express the condition that allows the disk to roll so that it contacts the parabola at one and only one point, independent of position.(adsbygoogle = window.adsbygoogle || []).push({});

I know the equation of constraint:

On the disk, s=R*theta.

So ds=R*dtheta

But ds is also equal to square root of (dx^2 +dy^2)

Pulling out a dx, ds=sqrt(1+(dy/dx)^2)

I know dy/dx=2ax

So sqrt(1+4a^2x^2)dx=Rdtheta

Actually, I'm not sure what to do with this. Integrate? It gets kind of messy, and I don't think I'm doing it correctly. But once I get the simplified equation of constraint, I set this equal to the function y=a*x^2?

I think I have to use Euler's equation in here somehow...but I don't see how it's relevant.

Thanks to any help!

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# Homework Help: Equation of Constraint

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