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Earth is an oblate spheroid spinning about the axis with largest moment of inertial. The effect shown in the video does not happen in such a case. It's called the intermediate axis theorem because it happens only when an object is rotated through an axis that has neither the largest nor the smallest moment of inertia, but one that's in the middle.

And the answer to your question lies here. https://www.youtube.com/watch?v=E31FHHH9is4

The Earth isn't round.

I said it was an oblate spheroid. I never said it was round.