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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