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**Classical Mechanics**Level 5

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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