Answer
2 revolutions.
Work Step by Step
To find the distance traveled by the center of the coin, use the formula for the circumference $$C=2\pi r$$ Substituting the known fact that $R=2r$ (twice the radius of a quarter) yields a circumference of $C=4\pi r$. Displacement and angular displacement are related using the equation $$s=r\theta$$ Solving for $\theta$ yields $$\theta=\frac{s}{r}$$ Substituting known values of $s=4\pi r$ and $r=r$ (the radius of the $coin$) yields $$\theta=\frac{4\pi r}{r}=4\pi rad.$$ Converting these radians to revolutions yields $$4\pi rad. \times \frac{1 rev}{2\pi rev.}=2 revolutions$$
