There's a system of 4 masses, all connected to a cross which has a negligible mass, and which is positioned on a smooth surface. The distance of each mass from the center of the cross is L and the cross spins around its center in a constant radial velocity of ω0 rad/sec:
Now mass m4 disconnects from the cross.
What is the the radial velocity of the system after m4 disconnected, considering m1=m3 and m2=m4=M?
Conservation of momentum:
Conservation of angular momentum:
The Attempt at a Solution
I calculated using conservation of momentum that the linear velocity of the system after m4 disconnected was v2=Mω0L/(M+2m)
Now I think I should use the law of conservation of angular momentum but I'm not sure how. I think that the center of mass is L/2 to the right from the center of the cross so the distance of m1 and m3 from the center of mass is √((0.5L)2+L2). What should I do next?