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It's not some force keeping them the same, it's no force changes the speed of the moon. From my limited understanding the moon was created when a smaller planet crashed into the earth:
They both got the same momentum, therefor they started rotating at the same speed, once per day.
There is nothing out there which would be able to change the speed of the rotation of the moon. There is also nothing which would change the speed of the rotation of the earth. Therefor they keep spinning at the same speed.
The moon rotates about once every 28ish days, the same as it's orbit. That's what being tidally locked means.
Other people have explained it, and the same thing happens with other moons in the solar system, including some orbiting gas giants where your explanation couldn't have worked.
The Earth's gravitational field elongates the moon slightly, and an elongated satellite tends more to stabilize its rotation with the longer diameter fixed to point at the center of its orbit.