# Cylinders don't jump and slip!

**Classical Mechanics**Level 5

Find the **maximum** value of the velocity \({v}_{o}\) which still permits the cylinder to roll onto the inclined plane section without a jump.

If it's maximum value can be expressed as

\[{v}_{o_\text{max}} = \sqrt {\cfrac {gR}{a} (b\sin \theta - c)}\text{,} \]

then find the value of \(a+b+c\).

**Details and Assumptions**

\(\bullet \) There is sufficient friction on the entire surface (with coefficient of friction \(\mu\)).

\(\bullet \) Here \(a, b, c\) are positive integers such that \(\text{gcd}(a, b, c)=1\).

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