A light, unstretchable string is wound around the perimeter of a \(4.0-\mathrm{kg}\) disk that has a radius of \(0.50 \mathrm{~m}\) and is free to rotate about an axle that runs perpendicular to the disk face and through the disk center. A \(2.0-\mathrm{kg}\) block is connected to the free end of the string and allowed to slide down a ramp that makes an angle of \(\theta=37^{\circ}\) with the vertical (Figure P12.67). Calculate the magnitude of the disk's rotational acceleration. Ignore friction between block and ramp.

Data from Figure P12.67