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bobred
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Homework Statement
A point P on a wheel of a bike radius R, P is a distance r from the axle.
The speed of the bike is v, what is the speed of the point P as a function of θ?
Homework Equations
[tex]x=R\theta - r \sin\theta[/tex]
[tex]y=R - \cos\theta[/tex]
[tex]\rho=\frac{r}{R}[/tex]
Distance traveled by the point in one revolution
[tex]D =R{\displaystyle \int_{0}}^{2\pi}\sqrt{\left(1+\rho^{2}\right)-2\rho\cos\theta}\,\textrm{d}\theta[/tex]
The Attempt at a Solution
Speed is distance per unit time, but not sure where to begin as no function contains time.
Can I make
[tex]\theta=\omega t[/tex]? If so how can I solve the integral?
James