How long ago did the Moon stop rotating...

and how would life on Earth have differed before it did? Would the tides have been more, or less predictable and extreme, for instance?

That’s an interesting question. Can I throw in another since it’s related?

Is the Earth’s rotation speeding up, slowing down, or is it totally constant?

The moon didn’t stop rotating. It completes one rotation about its axis at exactly the same rate as it completes one orbit around the earth. Therefore, we always see the same side of the moon facing us. This isn’t a coincidence, it’s due to a phenomenon known as Tidal Locking, which you can read more about here: Tidal locking - Wikipedia So, it’s kind of a moot question as the tides are what caused this.

And, the Earth’s rotation is slowing down, also due to gravitational interaction with the moon. Someone more into physics can probably elucidate.

The moon never stopped rotating. If it didn’t rotate as it orbits, then it wouldn’t keep only one hemisphere facing the Earth as it does.

But the question of the Moon rotating at a faster rate - which it must have done, at one time - and how much different the tidal effects would have been, still stands as one to be answered.

The gravitational effect of a body is based on its mass and distance. How quickly that body rotates is not part of the equations.

So, there would be no effect on tides on Earth if teh Moon rotated at a faster or slower rate.

That would be the case if the moon had a uniform density and was perfectly symmetrical. If the moon’s rotation was not tidally locked, there would be minute fluctuations in its gravitational influence on the tides, no?

Okay. “No measurable effects” or “no visible effects.”

Is that nit-picayune enough?

Why must have it rotated at a faster rate at some time? Maybe it rotated more slowly and sped up as it got tidally locked.

Every other planet and their moons seem to be rotating and as far as I’m aware, none of them are speeding up - any particular reason why our moon should be different?

Teletype gave you a link. Why didn’t you bother to read i?

Yes, but the tides which caused tidal locking are tides on the Moon, not on Earth. Not water tides, of course, but “land tides”–small deformations of the solid Moon which caused friction which slowed down its rotation.

The OP seems to be asking what effect this had on tides on Earth, and as DrFidelius points out, speed of lunar rotation has no measurable effect on tides on Earth.

The moon appears to have been created shortly after the Earth was born when a mars sized object struck the Earth. The material thrown out by the impact coalesced into the moon. At that time the moon was much closer to the earth than it is now. After the Earth cooled and developed oceans the moon would have still been close enough to create Tsunami sized tidal waves on the Earth. I think Tidal forces would have also kept the Earth warmer so volcanic activity would have been higher as a result of the moon as well.

These same tidal forces have other effects on the Earth / Moon system. The Moon has slowly been causing the Earth to rotate slower and slower, while at the same time the Earth is accelerating the moon in its orbit. The added centripital acceleration causes the moon to pull away from the Earth at nearly 2 inches a year (this rate would have been much higher early in the moons life).

When the moon was first created it would not have been tidally locked with the Earth. As its rotation slowed down, it would have caused the Earths rotation to gradually speed up (or rather, not slow down as much). But since there is such a large difference between the mass of the moon and the mass of the Earth tidal effects are far larger on the moon. I think the effects of the moons rotation on the Earth would be minimal when compared to the tidal forces.

I just realized I didn’t answer all of your question - the collision that formed the moon gave the Earth a big chunk of its current spin, but that wouldn’t necessarly translate into the disk that formed after the collision. The more I think about the moon coalescing I realize it would have been very close to tidally locked with the Earth right from the start. So while it may have had some rotation early on it would have locked very quickly. I can’t find an exact number yet, but will try to find one for you. I suspect the moon would have been tidally locked well before the Earth even had oceans.

Not that I know of. However, I was challenging your statement

The fact that you don’t know of any others speeding up is not by itself a reason.

A question: Everyone always goes out of their way to point out that the moon DOES rotate, exactly once per revolution. Is it possible for a celestial body to NOT rotate at all?

I don’t imagine that there’s a way for one to form that way naturally in the early solar disk, since coalescing matter seems to pick up a spin. But could you artificially put a satellite into orbit around the earth with zero rotation? I’m having trouble picturing the physics here with the various reference frames involved. Would inertia allow it to revolve around the earth, and for that earth-satellite system to revolve around the sun, but the satellite to always be pointed to, say, the galactic northwest, without any ongoing error-correcting propulsion/etc.?

Actually, I was just going to point this out to the OP! You see, in fact, the moon has not stopped rotating!

For an artificial satellite - sure. Inertia means that it keeps its rotation rate (barring tidal forces, which are very small on a satellite, of course).
Some satellites are sun-facing, so they do only one rotation per year. I’m not aware of a sat with zero rotation indefinitely, but long-term observations on a space telescope mean that it has zero rotation for these periods.

It would take a lot of correction to maintain. It’s impossible to set it free and expect it to only orbit the larger bodies but not be tidally affected by them. The tidal pull of the larger bodies will try really hard to pull the objects into a tidal lock.

One thing nobody mentioned is the conservation of angular momentum. Since the moon and the earth were once a single rotating body, this set had an angular momentum that must be conserved.
Since the moon has slowed its rotation, conservation of momentum forced it to go farther from the planet. Since the earth is still loosing momentum due to tides, the earth-moon system must increase the distance between the bodies to keep the momentum.
If the moon had rotated more slowly at the beginning as someone has suggested, it would be approaching the earth and not receding from the planet.