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I was reading this textbook and in in, they stated that the earth's angular velocity was reducing due to frictional forces between the ocean water and the ocean floor and to compensate for this decrease in angular momentum, the moon is moving further away. But wouldn't these frictional forces count as internal forces, which cannot change the angular momentum? If yes, then how can earth's angular momentum reduce? I am probably missing something but I am really confused.

Qmechanic
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Siddharth Kuchimanchi
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1 Answers1

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If the moon was not present, the forces on the earth-ocean system would be internal forces. The ocean and earth would rotate together. The sloshing of the ocean would remove kinetic energy from the ocean.

The moon adds an external force. It causes tidal humps that do not rotate to stay fixed with respect to the moon (simplifying here.) From the Earth's frame, the tidal hump rotates around the earth.

This is not to say that water flows around the earth. As the hump passes over a spot, water flows from nearby regions into the hump. And then back to where it was as the hump passes.

If the earth was just ocean, internal viscous forces would remove kinetic energy from these flows. They would tend to make the ocean rotate so the humps were stationary from the ocean frame. They would slow the rotation of the ocean. The moon would exert a torque on the ocean.

To see the forces for this torque, consider that the moon creates a hump. Left to itself, the hump would rotate with the earth (and fall back to the ocean.) The moon pulls the hump so that it stays under the moon.

There is an ocean floor under the ocean. There is friction when a hump is pulled around the earth. This friction is an internal force that slows the rotation of the earth and speeds the rotation of the hump.

mmesser314
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