I have a helicopter flying, but it is at rest in relation to the Earth, i.e., it's just hovering. That means the aerodynamical force equals minus the weight, so the forces cancel out, and the helicopter doesn't fall. But now, since the weight was cancelled, I can't say there's a centripetal force acting on the chopper and instead of rotating with the Earth, it should go off on a tangent. But that doesn't happen in reality. I wonder what's wrong with the reasoning.