Grace decides she's going to play a dart game at the county fair. The dart board is a rotating circular structure with balloons attached at different places with different point values. When the board is spinning it has an angular velocity of 6 radians per second. She fires six darts popping three balloons near the center of the board increasing the board's moment of inertia from 1.5 kg m^2 to 2.3 kg m^2. What is the dart board's angular velocity after Grace throws the darts? Neglect any external torque from the darts