a) Force F is applied to the rim of a uniform disk (M = 6.77 kg, R = 0.658 m). The disk is mounted on a fixed frictionless axis through its center, and the force is applied at an angle β = 26.7o to the radius. The disk starts at rest, and reaches frequency f = 30.2 revolutions per second after rotating through an angle θ = 561 radians. Find: – F, the magnitude of the force. N – L, the magnitude of the final angular momentum of the disk. kg.m2/s b) A group of N = 625 astronauts, with average mass m = 86.2 kg, work on a space station. The station is in the form of an approximately solid disk (M = 46700 kg, R = 673 m). (You may treat the people as point particles.) Suppose the space station spins at fo = 6.61 revolutions per minute when all the astronauts are in their quarters on the very edge of the space station. Find ffinal, the frequency of revolution if the entire population moves into an auditorium in the very center of the space station. Assume there are no external torques on the disk. revolutions/minute