Would it be possible for something to cause the Moon to start rotating at a different rate, breaking its tidal lock with Earth, without ripping it apart?
If so, would the Moon's tidal lock eventually stabilize?
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Yes, theoretically it is possible to impact the Moon with enough moment and low enough energy to have it change its rotation periode, which actually is the same as its orbital periode (this is the tidal lock). Best candidate will be a high-mass, low-speed asteriod impacting almost tangentially and on the rotation plane.
Is this really possible? I would bet that it will never happen.
Supossing that it happens, will Moon get tidal locked again? Yes. As long as there are water on Earth suffering tides from Moon, these same water will attract one side of the Moon differentially from the other, so Moon will get locked again with the same face towards us.