Tower of cylinders
Consider the infinitely tall system of identical massive cylinders and massless planks shown below. The moment of inertia of the cylinders is I = \(Mr^2\)/2. There are two cylinders at each level, and the number of levels is infinite. The cylinders do not slip with respect to the planks, but the bottom plank is free to slide on a table. If you pull on the bottom plank so that it accelerates horizontally with acceleration a, what is the horizontal acceleration of the bottom row of cylinders?