# The cylinder rolls

A spinning cylinder with angular velocity $$\omega_{o}$$ of Mass $$M$$ and radius $$R$$ is lowered on a rough fixed wedge of angle $$30^{o}$$ with the horizontal and coefficient of friction $$\mu=\frac{1}{\sqrt{3}}$$. The cylinder is released at a height of $$3R$$ from horizontal. Find the total time taken by the cylinder to reach the bottom of the incline in $$seconds$$

Take $$R=3.6~m$$, $$g=10~m/s^{2}$$ and $$\omega_{o}=17~rad/s$$

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