# Rolling Cylinders

A uniform cylinder of mass $$\SI[per-mode=symbol]{2}{\kilo\gram}$$ and radius $$\SI[per-mode=symbol]{0.5}{\meter}$$ rests on a plank of mass $$\SI[per-mode=symbol]{12}{\kilo\gram}$$. A force of $$\SI[per-mode=symbol]{12}{\newton}$$ is applied to the plank.

There is no friction between the ground and the plank, and the cylinder rolls without slipping on the plank.

If the acceleration of the plank in $$\text{m/s}^2$$ can be represented as $$\frac ab,$$ where $$a$$ and $$b$$ are coprime positive integers, what is the sum $$a + b?$$

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