I don't know whether this question pertains to physics. But anyways, here goes... If I were to hover 1m above the ground in a helicopter, would the ground below me change after 1 hr due to the rotation of the earth?
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You have to clearly define what you mean by hover. One definition is to exert enough downforce to keep you 1m above the ground and whatever sideways force is necessary to keep you above the same point of the ground. If that is your definition, you will stay above the same point of the ground. If you mean exerting enough downward force to counteract gravity, you will be blown by the wind in some direction. If you ignore the wind, you are correct. You will have an eastward velocity that matches the ground. The angular velocity will be reduced by the altitude. Your 1m altitude will reduce the angular velocity by $\frac 1{R_e \cos \lambda}$, where $R_e$ is the earth radius and $\lambda$ is your latitude. This will cause a tiny westward drift relative to the earth's surface. Can you calculate how much?
Ross Millikan
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It's all Greek to me, literally...The formulae etc is way above my pay grade. Only thing I understood is that the ground below would change maybe in a vacuum. – Jay Raj Feb 24 '14 at 03:12
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To calculate what happens,you need to define the forces acting. I am claiming that "hover" does not do that-there are a number of interpretations that lead to different lateral forces. Each leads to a different answer. The first two choices have no equations and seem to me accessible. If I ask a helicopter pilot to hover above a point, he will maintain the craft above that point. Any disturbance, like wind, he will do something about. That says there will be no drift. If I tell a copter to maintain altitude, it will do nothing about lateral motion. – Ross Millikan Feb 24 '14 at 03:20