# Rolling Down Rolling Down Rolling Down

A Spinning cylinder of mass $$m=5 \text{kg}$$ and radius $$R$$, is lowered with the angular velocity $$\omega_0$$ in the clockwise direction on a rough inclined plane of angle $$30^{ \circ }$$ with the horizontal and coefficient of Friction $$\mu$$.

The cylinder is released at a height of $$3R$$ from the Horizontal.

Evaluate the total time taken by the cylinder to reach the bottom of the incline (to 3 decimal places).

Details and Assumptions:

$$g = 10 \text{m}/{s}^{2}$$ , $$\mu = \dfrac{1}{\sqrt{3}}$$ , $$R = 5 \text{m}$$ , $$\omega_0 = 2 \text{rad}/s$$

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