Problem 1.251

A uniform cylinder of radius $R$ and mass $M$ can rotate freely about a stationary horizontal axis $O$ (Fig. 1.59). A thin cord of length $l$ and mass $m$ is wound on the cylinder in a single layer. Find the angular acceleration of the cylinder as a function of the length $x$ of the hanging part of the cord. The wound part of the cord is supposed to have its centre of gravity on the cylinder axis.