Angular Collisions with Linear Motion

Problem: Two rotating doors, each 4 kg in mass and 6 m long, are fixed to the same central axis of rotation, as shown above (top view). Suppose a 4 kg bird flying with 30 m/s horizontal collides against the door and stays stuck to it, at a point 50 cm from one end. Calculate the angular speed with which the system (doors + bird) spin together.