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.