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Since the Earth is rotating it should have acceleration (in the sense that there is change in direction of velocity). So if we throw a ball upwards won't this acceleration affect its trajectory in some way? (If yes is it due to the smaller size of the ball and length of its path, compared to that of the Earth, we are not feeling it?)

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There are several effects. The most obvious one is that, on the equator, your ball will experience about 0.2% less downwards acceleration than at a pole (because of the centrifugal pseudoforce). There are less obvious pseudoforces, too, the Coriolis forces. When you throw the ball straight up at the equator, it will seem to lag behind the earth's rotation: For every meter it goes up, if it wasn't for air friction, it will seemingly speed up in a westerly direction by 0.0003 km/hour (or about 1.5 times the speed of sound, the surface rotation speed of the equator, for every earth radius the ball goes up). At other lattitudes, there is even a seemingly horizontally rotating component. All of these effects are hard to see unless you look at large scale low-friction phenomena (weather systems, ocean currents).

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  • $\begingroup$ Thanks @pyramids. Sorry that I cannot up vote the answer due to insufficient reputation. Can you kindly explain your answer? I didn't understand the part concerning "centrifugal force". Also please tell me about the calculation of 0.0003 Km/hr. $\endgroup$ Apr 6 '15 at 17:49
  • $\begingroup$ Imagine you're a kid being spun around by an adult holding your hands and spinning so fast you fly off the ground. The force that seems to push you outwards, reuiring a great pulling force via your hands, is a pseudoforce called the centrifugal force. If you do move away from the center of rotation, you will keep your speed---which is slower than a radial beam would spin at that distance. For the earth, it is slower by $\Delta v = (\Delta R / R) * \omega$ where $R$ is earth's radius (about 6000 km), $\Delta R$ your change in height (1m) and $\omega=$ 40000km/24hour, so 0.0003 km/hour. $\endgroup$
    – pyramids
    Apr 8 '15 at 9:03

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