I'm sorry, I just can't resist sticking my oar in here....
Overpitched, here's another thought experiment for you... imagine you're flying in calm air (ie no wind), circling round and round at constant IAS, bank, etc etc. On the ground below you, as far as the eye can see in all directions, is the world's biggest conveyor belt, which is currently switched off. An observer is standing on the conveyor belt directly underneath the centre of your circles.
Now, what happens if, just as you're turning through North, we turn on the conveyor belt and it starts moving North at, say 25kt? The ground observer and everything else you can see now appears to be moving North, or (more likely) you will believe yourself to be drifting South. Don't touch the controls! Would you expect to feel anything unusual through the seat of your pants, or see anything unusual on the instruments, as you continue circling?
I hope you'll say "no". Now, why not?
cbl.