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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