Why don’t we feel the motion of the rotating Earth?

There is only one reason for not feeling the motion. The planet Earth does not rotate alone, but along with it the whole atmosphere covering it moves at the same speed. Airplanes, clouds, and the flying insects like butterflies do not leave the atmosphere, and the atmosphere does not leave the planet. Under such circumstances one can never feel the planet moving. Yes, if the atmosphere was static while the Earth rotated you wouldn’t be here to read this answer!

Suppose near the equator the person is sitting on a chair. He may not be doing any movement, but as shown in the drawing planet Earth near the equator moves at the speed of 1,525 feet/second. In an hour that would be 1,660 kilometers! Where even a static object moves at such a speed, if atmosphere itself remained static, what would be the effect? A terrible windstorm would be experienced with the wind blowing at the same speed – and how that would feel, just imagine!

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