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The Moon always shows the same face to the Earth.

This is due to the fact that the Lunar Day is exactly equal to the Lunar Year (how long it takes to orbit the Earth). It is not because the Moon doesn't rotate.

The condition where the year and day are equal is called Synchronous Rotation (Click here for movie or see Moonsync.mov on your textbook CD ROM), and in the Moon's case it has been caused by the same tidal drag that moves the Oceans and is slowing the Earth's rotation.
 

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