This question came to me while I was in the pool last month. I took a basketball and I was making it spin on the surface of the water in a few different ways. When the ball rested on the surface of the water, a majority of the ball was above the surface of the water, indicating that the density of the ball is less than half of the density of water.
First I would spin the basketball so that the angular momentum vector was vertical, perpendicular to the water surface. Then I spun it so that the angular momentum vector was horizontal, parallel to the surface of the water. In each case, the spinning would slow down, although in the first case where the angular momentum vector was vertical the ball took longer to slow down.
Finally, I spun the basketball at an angle, so that the angular momentum vector was neither parallel nor perpendicular to the water surface. What I saw was consistent with what I saw earlier. The horizontal component of the angular momentum vector decayed more quickly than the vertical component, so that after maybe 10 seconds the rotation was essentially with a vertical axis.
So the question is why? Why does the horizontal component decay faster than the vertical component? I tried to think of it in terms of friction and normal forces, but there didn't seem to be a difference between the 2 cases.