A yo-yo consists of a homogeneous slotted cylinder, radius \(R=7.0 \mathrm{~cm}\) and mass \(\mathrm{m}=100 \mathrm{~g}\). The inner slot is of negligible width, and does not significantly affect the value of the moment of inertia \(J\). In the inner slot, of radius \(r=3.0 \mathrm{~cm}\) is wrapped a string, attached at the other end to a fixed point (a hook, for example). Calculate the acceleration \(a_{c m}\) of the yo-yo when it is allowed to fall freely.