The earth's rotation rate is slowing down because of friction against the tidal bulges caused by the gravitation of the moon (major factor) and the sun (lesser factor). The earth's rotational energy is dissipated as heat, but where is the angular momentum going, and what physical mechanism brings that momentum there?
Every action has an opposite and equal reaction. If the tidal forces work against the earth's angular momentum, then the earth's angular momentum works against the source of the tidal forces. Specifically, the rotation of the earth exerts a force on the 'bulges' described by the problem. The movement of these bulges caused by the earth's rotation translates to a gravitational force being exerted right back against the moon and the sun. It's easy to forget that gravity works both ways, especially when its effects are only obvious in one direction. Still, the earth does its best to move the sun and the moon to match its own rotation, and angular momentum is conserved.
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