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Tides cause friction in the Earth and are slowing its rotation with a rythm of 2 milliseconds per century. Due to this, and following the conservation of the angular momentum of the entire system Earth plus Moon, we have that the Moon moves away from the Earth, very slowly. I saw a calculation of this in Paul Nahin's excellent "In Praise of Simple Physics", and sure it can be found in many other places.

My question is: if we consider the isolated system of a spinning Earth + spinning Moon + rotating Moon around the Earth, which is reasonable to a high degree of approximation, the angular momentum, as it was said, is constant:

$$L_{\text{spin Earth}}+L_{\text{rot Moon}}+L_{\text{spin Moon}}=\text{constant}$$

It seems that the decrease in $L_{\text{spin Earth}}$ is totally transferred to an increase in $L_{\text{rot Moon}}$ (Nahin), nothing to $L_{\text{spin Moon}}$ (and reasoning this way you admirably reproduce the measured 2 milliseconds per century.

Why? One could say that this is what it's observed, that the Moon does not increment its speed of rotation around its axis, but then, again, why? If it's due to tidal locking, then what's the reason the Moon's spin is privileged to not receive momentum?

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    $\begingroup$ I finally deleted my answer. Forgot about it. Have a great day $\endgroup$
    – Al Brown
    Jul 30, 2021 at 14:12

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This website https://www.sciencemag.org/news/2016/12/ancient-eclipses-show-earth-s-rotation-slowing says

"The interaction between ocean tides and Earth’s continents is the biggest factor in slowing Earth down... As those landmasses get slammed by the seas, Earth loses some rotational momentum"

Since the moon doesn't have a liquid on it's surface, it's spin is not affected by a similar process - that's why angular momentum isn't transferred from a decrease in the moon's rotational momentum.

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  • $\begingroup$ Thanks, your response can be complemented with this one that I found later. Earth's bulges attract the Moon giving it a push in velocity, so moving it away: physics.stackexchange.com/questions/134625/… $\endgroup$
    – David
    Jul 29, 2021 at 22:50

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