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How did moment of inertia affect the length of the day? Please try to explain briefly.

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    $\begingroup$ This sounds like a homework question. $\endgroup$ – zeta-band Apr 1 '19 at 18:08
  • $\begingroup$ You mean the moment of inertia of our planet right? $\endgroup$ – AoZora Apr 1 '19 at 18:11
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If you are talking about the moment of inertia of the earth, then the answer is that increasing the moment of inertia $I$ of a planet makes its days last longer.

The reason is that the angular momentum can be written as: $$L=\omega I$$ where $\omega=2\pi/T$ , $\quad T\;$ being the duration of a day. For a spinning planet, the angular momentum related to the rotation of the planet around its axis is nearly conserved, since the external forces applied to the planet are reasonably weak (Sun, Jupiter and the Moon gravitational attraction in our case).

So if $L$ is nearly conserved then an increase in the moment of inertia causes a decrease in the angular velocity $\omega$ and therefore an increase in the duration of the day $T$.

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  • $\begingroup$ And watch a ballerina - when they extend their arms out they slow down - they're increasing their moment of inertia. When they put their arms above their head they speed up - they're decreasing their moment of inertia. $\endgroup$ – Cinaed Simson Apr 1 '19 at 20:17

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