A solid cylinder of radius \(R\) is set into rotation about its axis with angular speed \(\omega_{o}\) then lowered with its lateral surface onto a horizontal plane and released. If the coefficient of friction is \(\mu\), find after how much time (in seconds) will the cylinder start pure rolling.

If the time is given by \(t = \dfrac{ R \omega_{o}}{n \mu g}\), find \(n\).

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