The rotation includes the atmosphere above it (just like it includes water on its surface), and the helicopter is moved along with the atmosphere it’s hovering in. If the atmosphere were not moving along with the earth, we’d face 1,000 mph winds at the equator (and winds of hundreds of miles per hour almost everywhere else, at least everywhere where there is significant populations).
Because the helicopter isn’t high enough to be outside of the earth’s atmosphere. If it was higher, that would indeed happen.
Which is why we see video of the earth moving under the International Space Station, say. But why, if you stand on the front seat of a moving bus and jump up, you won’t land on the seat behind.
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