A girl sits fixed on a merry-go-round of mass M = 500 kg and radius R = 2 m. The merry-go-round is initially at rest and is free to rotate without friction. The girl shoots a gun in a horizontal direction tangent to the outer edge of the merry-go-round as shown in the figure. The bullet has mass m = 0.025 kg and a speed v = 700 m/s relative to the ground. The moment of inertia of the merry-go-round is I = MR2/2.
If you ignore the mass of the girl, what is the angular velocity ? of the girl and merry-go-round after the gun has been shot?