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I see a lot of questions regarding situations what would happen if the world would stop spinning. This got me to wondering how much energy it would actually take to stop the world from spinning.

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The rotational kinetic energy of a (uniform) solid sphere rotating about an axis passing through the center of mass is given by $\frac{1}{2}I\omega^{2}$, where $I=\frac{2}{5}MR^{2}$. So $K=\frac{1}{5}MR^{2}\omega^{2}$. Using $M=6\times10^{24}\,\mbox{kg}$, $R=6400\,\mbox{km}$, and $\omega=\frac{2\pi}{T}$, with $T=24\,\mbox{hrs}$, we get $$K\approx2.6\times10^{29}\,\mbox{J}.$$

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    $\begingroup$ The earth being more dense in the middle, it would be a bit less than that. It could be calculated by layers as well, but that would take longer. jersey.uoregon.edu/~mstrick/AskGeoMan/geoQuerry57.html To put 2.6 x 10 29th Joules in perspective, it takes the sun about 11 minutes and 20 seconds to produce that much energy. It's a lot of momentum. $\endgroup$ – userLTK Mar 10 '15 at 22:50

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