# Rolling coin

A U.S quarter is rolling on the floor without slipping in such a way that it describes a circular path of radius $$R=4~\mbox{cm}$$. The plane of the coin is tilted at an angle of $$\theta=45^{\circ}$$ with respect to the horizontal plane (see the figure below). Find the coin's period $$T$$ in seconds, that is, the time it takes for the coin to go around the circle of radius $$R$$. The radius of a U.S quarter is $$r=1.2 ~\mbox{cm}$$.

Details and assumptions

Assume $$g=9.8~\mbox{m/s}^{2}$$.

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