Question: A diver goes off the high board, tucks into a flip. She then straightens out and enters the water vertically. What happened to her angular momentum just before entering the water?

Answer: There are no external torques acting on the diver after she leaves the board, so her angular momentum must be constant. When she straightens out, her moment of inertia is so much greater than when she was tucked that for a brief moment just before striking the water she appears to rotate no longer. However, careful attention to her motion reveals that she does not stop rotating, only that her angular velocity is very small. Her angular momentum is still the same as it was during the tuck.