Pictured above is a biker (traveling in a curve) whose center of mass has two forces acting on it. These two forces - a horizontal centrifugal force F(centripetal)* and a vertical gravitational force mg - yield a resultant force which pulls the biker's center of mass diagonally towards the ground.
Here is my question: why does the biker [who I've pictured as a black stripe] stay in place if (and only if) he positions himself according to the resultant force as shown in the image?
My instructor told me that the biker would begin to tilt left or right for any other configuration, and that kind of makes intuitive sense, but I'd rather not base my knowledge on iffy intuition alone.
*I have mistakenly named the centrifugal force as centripetal in the image
EDIT: Could it be that the position of the biker as shown in the image is the only one in which a "conversion" from tilting to the left to tilting to the right occurs (so that the system is balanced, in a sense)?