Another way to look at it...

Due to its rotation, the earth's surface (and the air surrounding it) are moving eastward at 1000 mph or so.If you take into account the speed of the earth in its orbit around the sun, the atmosphere is moving at many thousands of miles per hour... Do you notice a difference in how a plane flies going east or going west on a calm day? (I'm talking about a model aircraft flying within a few hundred feet of the ground here... let's not get into upper atmosphere phenomena here...)