It won't; a moving object has the object to continue moving. If one day the Moon mysteriously and suddenly stopped moving around Earth, it would fall upon the Earth pretty soon (in a few days), due to Earth's gravity.
In that case, the Moon would move in a straight line instead of moving around the Earth; it would quickly get away.
If the moon suddenly decided to stop pusing forward (inertia), the balance between inertia and the earths gravity would cease and the moon would come crashing into us. :)
then there would be no moon
If you were on the moon your weight would lower, as there is no gravity.
photosynthesis would stop,temperature will drop to zero,ocean surfaces would freeze,extinction human etc
You would see the moon.
you would jet a bit burnt if you where on the moon. I'll find out about the next eclipse
they would stay on the moon and they may not decay.
A full moon
The moon phases would change.
There would never be a full moon.
Earth would blow up along with the moon.