# Where do you like to go? Up or Down

Take a solid cylinder of radius $$R$$, roll it with angular velocity $$\omega_{0}$$ and carefully keep it on an inclined plane having inclination $$\theta$$, and coefficient of kinetic friction $$\mu_{k}$$, such that $$\mu_{k} > \tan \theta$$. Find the maximum velocity of the cylinder (in $$\text{cm/s}$$) before it comes to an instantaneous stop.

Details and assumptions:

$$\omega_{0} = 3 \text{ rad s}^{-1} , R = 18 \text{ cm}, \mu_{k} = \frac{1}{3}, \tan \theta = \frac{1}{4}$$.

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