|MadSci Network: Astronomy|
First, it is important to emphasize that this is purely a hypothetical exercise. In order to stop the Earth from rotating, a force would need to be applied to the Earth. The only natural force I can imagine capable of doing this would be a massive impact. Such an impact would make the one that wiped out the dinosaurs look puny. Nonetheless, let's consider hypotheticals.
As the answer you've cited states, even if the Earth stopped rotating (magically), the atmosphere would keep moving. Over some time it would slow down because of friction between the land and air. However, initially it would be moving at speeds of several hundred kilometers per hour.
The friction between the moving air and the still land would cause the air to become extremely turbulent. The region of turbulent air would increase its height. (Formally, this region of turbulent air is known as a boundary layer because it is a boundary between the still land and the relatively calm, but moving air.) The speed at which the region of turbulent air increases its height is roughly comparable to the speed of the air or several hundred kilometers per hour. Thus, within 10 min., and probably somewhat quicker, the region of turbulent air would expand to encompass our (ill-fated) passengers and their plane.
As anybody who has ever ridden on a plane knows, when a plane encounters turbulence, the ride can get extremely bumpy. Turbulent air essentially lifts and drops the plane.
As our hypothetical region of turbulent air engulfs the plane, initially the plane might be simply moved up and down. This is because turbulent air is initially most "turbulent" on large length scales, say, hundreds of meters to kilometers in size. These length scales are larger than a typical plane, so the plane will simply rise or fall (like being in an updraft or downdraft) in response to these large flows of air. However, the speed at which the air is moving might be 100 km/hr. The plane will be moved up or down a considerable distance quite rapidly, and the occupants will almost certainly feel considerable "g" forces. It would probably make flying through a thunderstorm (usually a fairly bumpy experience because of the updrafts and downdrafts inside thunderclouds) feel fairly smooth.
Unfortunately, the turbulent air also becomes "turbulent" on smaller length scales, like the size of the plane. Thus, the occupants will soon experience, for instance, the nose of the plane being pushed up while the tail is pushed down. I will not speculate on whether the forces involved will be enough to break the plane apart, but I think that might be likely.
Thus, at best I think the occupants of the plane might escape with some serious injuries; at worst, they might find their plane breaking up around them (assuming they were still conscious).
I think the major danger to birds would be initially that they would be hit by flying debris. A secondary concern of theirs would be that they would be caught in a turbulent flow of air and either swept up so high that they don't have enough oxygen to retain consciousness or slammed into the ground.
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