A small gun is attached to a vertical disk mass M=2.0kg and of radius R=2.0m (see the figure below), which is free to rotate about its center. The gun is placed at a distance R/2 from the disk's center. The disk is initially at rest. The gun then fires a bullet horizontally to the left at speed v=500m/s. The mass of the bullet is m=20g, and the mass of the gun mg=500g. The moment of inertia of the disk about its center of mass is MR2/2. [Consider the gun as a particle located at R/2 from the center of the disk] (a) Calculate the angular velocity of the disk after the bullet is fired (ignore friction). (b) If it takes 1.0ms for the bullet to be fired from the gun, calculate the torque on the applied to the disk to accelerate it