A weather vane initially at rest has a moment of inertia of 0.116 kg · m2 about its axis of rotation. A 75.0 g piece of clay is thrown at the vane and sticks to it at a point 15.0 cm from the axis. The initial velocity of the clay is 27.0 m/s, directed perpendicular to the vane.
Find the angular velocity of the weather vane just after it is struck.