We wrap a light non$-$stretching cable around a solid cylinder with a mass of $60$ kg and a radius of $2$ m$.$ The cylinder rotates with negligible friction about a stationary horizontal axis. We tie the free end of the cable to a block of mass $10$ kg and release the block from rest at a distance of $2$ m above the floor. As the block falls, the cable unwinds without stretching or slipping. Find the speed of the falling block and the angular speed of the cylinder as the block strikes the floor.