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Is it possible for the earth to change speeds while spinning on its axis?

Yes, actually the earth does very gradually change quite a few of its orbital and rotational parameters - because of various conservation laws of physics, however, it cannot do this all on its own - it needs help. The help it gets is from the moon and from the other planets, and also from tidal interactions with the sun. The earth has long been exchanging angular momentum with the moon - you might be interested in looking up articles on the moon-earth relationship - the length of the day on earth used to be much shorter and the moon much closer (I think that is right anyway).

Arthur Smith

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