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Coriolis Effect causes strong winds in the upper atmosphere, and it's purely due to differences in the linear velocity of Earth's rotation across latitudes.

Now the Earth is spinning with the energy it received while it was born from the sun 4.5 billion years ago. There has been no more energy gain in terms of rotation, right?

Now, if, theoretically, we placed flying windmills to harvest the strong winds caused by Coriolis Effect, the energy has to come from somewhere, right? And that has got to be from the earth's inertia.

So would this stunt slow down the Earth over time?

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    $\begingroup$ The Coriolis effect can not remove total angular momentum from the planet's rotation, so no, it will not slow down. All the energy harvested would come from solar radiation that drives atmospheric circulation. $\endgroup$
    – CuriousOne
    Jul 25, 2016 at 1:43
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    $\begingroup$ Does the Coriolis Effect cause the wind, or merely deflect a high-to-low-pressure flow into a circular path? $\endgroup$
    – DJohnM
    Jul 25, 2016 at 6:00
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    $\begingroup$ First of all, the Coriolis force does not cause wind. Wind is the result of pressure differences that are in turn caused by temperature differences. Earth's rotation will finally come to an end (as did the Moon's) due to friction by the liquids on and within the planet. $\endgroup$
    – Aziraphale
    Jul 25, 2016 at 13:49

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The Earth+windmill system has conserved angular momentum. When the windmill starts spinning the angular momentum of Earth must change in response. However this change is marginal. Furthermore the windmill system will stop spinning when the wind dies down and this will restore the original angular momentum of Earth (when I say Earth I mean everything inside of Earth's atmosphere except for the windmill).

It is important to not confuse angular momentum and energy. In contrast to angular momentum, the energy taken out of wind by the windmill is not given back when the windmill stops spinning. The source of this energy is solar.

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Coriolis force on a moving object originates when you look at its motion from a non-inertial reference frame. Earth is a non-inertial reference frame, but that fact alone is not sufficient to cause Coriolis force on air. Air must also be set into radial motion by some agency, that agency being our Sun, as pointed out by @James Rowland and @CuriousOne.

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