I came across a question regarding linear momentum $L$ and it's conservation, however I tried and got confused. It reads: A $40kg$ girl stands on the very edge of a rotating disc of mass $50kg$ and radius $2 meters$. She then throws a rock of mass $5kg$ at a speed of $10m/s$ which causes the rock to rotate in a clockwise direction. What is the angular velocity of the disc after the rock is thrown?
My attempt was to find the angular velocity caused by the rock using $v = wr$. I am unsure of how exactly to take into consideration the inertia of the girl disc system or if this is even the right approach. Also, since the disc would be rotating in a clockwise direction after the throw, would the angular velocity be negative? Please offer assistance.