- #1

QuantumDuality

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## Homework Statement

A disc of radius R rolls without slipping along the parabola y= ax

^{2}. Obtain the constrain equation

## Homework Equations

Because there's no slipping, then:

##R d \theta = ds (1)##

Where ##\theta ## is the angle between the line from the center of the disc to a fixed point and the line from the center of the disc to the contract point with the parabola

Also:

##ds = \sqrt{(dx)^2 + (dy)^2} = \sqrt{1 + 4a^2 x^2} dx (2)##

## The Attempt at a Solution

So I just have to equate (1) and (2) to get the constraint equation?, Because I have seen a generalization of the constraint equation for an arbitrary curve that use

##ds = R(d\theta + d\phi) ##

Where ##\theta## is an angle between a radius to a fixed point and the radius parallel to the y axis, while ##\phi## is an angle between the radius parallel to the y-axis and the radius to the contact point

Here's the generalization:

https://campus.mst.edu/physics/courses/409/Problem-Solutions/HW#4/HW4_prob3_ hoop on curve.pdf