This has already been answered several ways, but I will try one more.
The aircraft's inertia is proportional to its weight, which equals Lift in steady flight.
It has various kinds of speed stability designed in, and the restoring forces are significant fractions of the Lift force.
This means the restoring forces are significant fractions of its weight, and and so the correcting accelerations are significant fractions of "g" (9.81 m/s/s or about 20 kts/sec).
Imagine a trimmed aircraft with centred controls flying in zero wind.
Now imagine a 10 kt wind starts to blow from the left.
Because of dihedral, you should soon get something like a 1/4 of the Lift force accelerating the aircraft to the right.
That's a 1/4 of the weight. Which will accelerate the aircraft at 1/4 G, which is about 5 kts/sec acceleration.
So 2 seconds after the wind started to blow, the sideways airspeed has gone.
Inertia (or Momentum if you prefer) is relevant for a couple of seconds after the wind changes, but not at all after that.
The bottom line is: aircraft are designed not to fly sideways.
Now imagine a 10 kt wind starts to blow from straight ahead.
Precisely because the aircraft has inertia, it will not instantly change ground speed, but it will instantly gain airspeed.
If the aircraft is travelling at 90 kts, the Lift will increase by about 25% (airspeed squared counts) and gravity will slow it as it climbs.
After a few seconds the airspeed and Lift have returned to normal again, but the groundspeed has changed.
The bottom line is: aircraft wing Lift depends on airspeed, not groundspeed.
I have not worked the numbers in detail, because I am trying to get a point across, not write a book.
Over a one hour flight, there may be a few seconds of transient adjustment to changing wind conditions, and the detailed aircraft behaviour over those few seconds will depend on the aircraft's inertia.
Those few seconds are of no significance.
The aircraft flies in the air, and the air moves over the ground. End of!
Last edited by 24Carrot; 9th Dec 2012 at 14:45.