It doesn't look like the red tube is giving the rotation to the big wooden wheel. It touches it and the wooden weel suddenly starts rotating?
How is the rotation done?
Through physics and revolute joints or otherwise?
A real world object that suddenly gets a shock from a rotating object will sometimes fly, so it looks like it already works like a real world object. If you want the stick to move slowly the rotation should start slow and increase (Like it would in the real world).
How are you trying to get the stick to float? Are you trying? It takes a lot of calculation to get the right response. The water should apply an upward force depending on how much of the stick is under the surface.
Hope you can answer these questions, so maybe I can be of some assistance.