Disk A has mass of 4 kg and a radius r = 75 mm. It is at rest when placed in contact with the belt, which moves at a constant speed v = 18 m/s. μ_k = 0.25 between the disk and the belt. If the normal reaction by the belt on the disk is equal to the weight of the disc, then the number of revolutions executed by the disk before it reach as a constant angular velocity is $\frac{27\mathrm{\beta }}{\mathrm{\pi }}$ . Find β.