Originally Posted by
AF330
Why do we say that we have changed the propeller's axe of rotation?
Because you have. This is not referenced to you in the airplane but to an outside frame of reference. Say you are in a plane going down the runway. We'll say the axis of the prop's rotation is parallel to the ground. Then pull the nose up. While to you in the airplane the prop disc is in the same place and the same angle, to someone standing on the ground it changed.
Asking why the force is applied 90 degrees off from the direction of movement is sort of like asking why gravity pulls things together.