What happens when you toss a ball in the air (assume an open top car) and _then_ the car drives off? The ball does not come along for the ride.
Similarly, if you toss it up in the air while driving and then brake, the ball will not brake with you.
The same happens if the ball is in the air a tiny bit in a closed roof car, the effect is just less pronounced because you can’t throw it as high.
Whether the car brakes, or turns to the side, in either case it’s just a change in the car’s movement vector. Either the direction or magnitude (or both) change.
The air from the vent is a different temp than all the other air. It is like a gaseous from of that ball we just studied. It won’t keep its shape but it will not blindly follow the car while it (the AC air) is up in the air.
So really, the AC air in a turning car behaves just like (our first example) that ball you threw up in the air and then have the car start driving. Just like the ball, the AC air has no physical reason to keep itself aligned to the car’s changing situation, because it is not connected to the car right now.
_Alternate option I considered: why does the drink in your glass slosh around when you walk and turn around?_
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