I have a point mass connected to a string with negligible mass. The point mass has mass $m$ and is moving at a velocity $V$. The string is of length $r$, and it is keeping the point mass tied to a center of rotation.
Suppose we were to suddenly cut the string. It is easy to see that the point mass will continue in a straight line tangential to the path at the moment it was cut at the same velocity $V$ that it originally had. And so, this implies a conservation of linear momentum.
But what about angular momentum, $I\omega=mr^2\omega$, how does it stay constant? Or does the point mass somehow lose angular momentum all together?