I have 2 objects which are intially connected together, $O_1$ and $O_2$. When they are connected together, they have a rotation rate about their center of mass of $w_1$. $O_2$ is cleanly released from the connected system, and $O_1$ is now rotating at a rate of $w_2$.
Given that any mass properties of the system can be measured, and that the mass of $O_2$ is known, how can one find the mass of $O_1$, given that this is the one property of the system which cannot be directly measured? Also, what will happen to $O_2$ after release?
One can assume that there is absolutely no friction/resistance.