Checkboard,
You are correct. That is what I intended to imply by stating "in the real world it is a bit more complicated".
This can be illustrated if we consider an aircraft in level flight. If we put in a sudden elevetor up motion the downforce on the tailplane will increase. This will do two things:
Firstly the total down force on the aircarft will be greater than the total up forces, so the aircraft will accelerate downwards. This will cause all points on the aircarft to move downwards.
Secondly the aircraft will rotate tail down. If it rotates about its C of G all points ahead of the C of G will go up and all points aft of it wil go down. But the C of G is itself going done together with the rest of the aircarft. The point about which the only motion is rotation, will be that point, somewhere ahead of the C of G, where the upward motion due to rotation exactly balances the downard motion of the whole aircraft. So in this case the aircraft will actually rotate about a point slightly ahead of the C of G.
But the additional tailplane down force will be very small compared to the mass of the aircarft, so the downard motion will be very small. The tailplane is a long way aft of the C of G, so the rotation will be comparatively large. So the real centre of rotation will still be very close to the C of G.
The JAR answer, in common with that in most text books considers only the rotation and ignores the vertical motion.
Crab@,
You also are correct. This in turn means that if an aircraft rotated about its AC it would be neutrally stable. Rotating about the AC would not generate any change in moments, so there would be no tendency for the aircraft to correct itself after disturbances. It would simply sit at whatever attitude we (or chance) put it.