Applet shows a rod rotating about a fixed vertical axis on a smooth horizontal table. The position of the axis is shown by a black dot. The center of mass (shown in blue color) of the rod is in circular motion. After some specified rotation the support yields and the rod then begins to rotate about an axis through its center of mass with the center of mass translating at the velocity it had at the moment the support yielded.
The angular momentum about the position of the support before and after the support yields are equal.