Problem 1.255

A spool with a thread wound on it is placed on an inclined smooth plane set at an angle \(\alpha=30^{\circ}\) to the horizontal. The free end of the thread is attached to the wall as shown in Fig. 1.61. The mass of the spool is \(m=200 \mathrm{~g}\), its moment of inertia relative to its own. axis \(I=0.45 \mathrm{~g} \cdot \mathrm{m}^{2},\) the radius of the wound thread layer \(r=3.0 \mathrm{~cm}\) Find the acceleration of the spool axis.