[chris (OP)]

The Earth's moon rotates at a rate that matches its orbital period so that it always shows us the same face.

There are almost 100 moons in the Solar System. Do any others do this too, or is our moon the exception?

[evan_au]

I once saw an equation that estimated how long it would take a body to become tidally locked - it depended on the size & mass of the moon, plus the mass of the planet and its distance.
- Sort the moons by this criteria, and you see a rough cutoff age for tidal locking.
- The moons of Mars
- Many moons of Jupiter

Tidal locking also applies to planets and stars
- In our Solar system, Mercury is almost tidally locked - its "day" is comparable to its "year".
- Charon is tidally locked to Pluto, and Pluto is tidally locked to Charon.
- It is thought that many of the extrasolar planets with a very short year will be tidally locked (only there were no known extrasolar planets when I was reading this)

See: https://en.wikipedia.org/wiki/Tidal_locking#Occurrence

[Janus]

According to information I found on one site: http://nineplanets.org/data1.html ,  there are 25 moons (including our Moon) that are known to rotate with the same period as they orbit,  but there are also 32 moons for which we have no data on their rotation, so that number could also be higher.

[rmolnav]

I once saw an equation that estimated how long it would take a body to become tidally locked - it depended on the size & mass of the moon, plus the mass of the planet and its distance.

That equation considers basic factors, but should include some other important factors such as initial moon´s angular momentum, and its composition, especially:
- Solid material: its elasticity.
- Liquid    "       : its viscosity.
Also, but less important, besides planet´s mass, other features count. Though they could be difficult to include in an equation ...

[Janus]

I once saw an equation that estimated how long it would take a body to become tidally locked - it depended on the size & mass of the moon, plus the mass of the planet and its distance.

That equation considers basic factors, but should include some other important factors such as initial moon´s angular momentum, and its composition, especially:
- Solid material: its elasticity.
- Liquid    "       : its viscosity.
Also, but less important, besides planet´s mass, other features count. Though they could be difficult to include in an equation ...

The full equation is here:
https://en.wikipedia.org/wiki/Tidal_locking

It takes the initial rotation rate, plus the dissipation function and Love number for the satellite into account.   The last two, as point out in the article, are not well known for any bodies other than the Moon, but can be roughly estimated.

[rmolnav]

The full equation is here:
https://en.wikipedia.org/wiki/Tidal_locking
It takes the initial rotation rate, plus the dissipation function and Love number for the satellite into account

Thank you. That´s much more reasonable ...
Those factors count, because the locking is originated by continuously changing deformations (due to the spinning), caused by internal stresses generated by an imbalance between centripetal and centrifugal forces across the satellite. The energy is dissipated as friction heat, that varies with material properties such as elasticity, viscosity, etc.

[Petrochemicals]

How very interesting

[rmolnav]

How very interesting

Thank you.
Recently, after a comment of somebody else, I sent what follows to another thread (about the equivalence principle !), but, as you can see, it is about something much more connected to this thread question. I was planning to put it here too, but had not found the moment ... "Perfect" moment now ! (slightly edited, as afterwards I found a detail that I thought should be better explained):
"... But let us consider our moon, in earth´s gravitational field.
It´s somehow in free falling, because only gravity there affects its movement. But due to its initial speed, it´s rotating around earth (more precisely, around earth/moon barycenter). And it´s tide locked to earth, with two opposite bulges as our planet (but, being all its surface solid, relatively much smaller), one of them towards us.
At last phase of that locking, with very low angular spinning (in excess of current one) speed, tidal friction was tending to null.
Why did it stop in its current position? My "educated" (?) guess was (long ago) that as it is anisotropic, in its current position density distribution must be such that some mass concentration happens at farther and nearer parts, corresponding to parts were centrifugal and centripetal forces are bigger, respectively.
It probably even passed a little bit that position, and lowered a little back its speed afterwards, with a kind of "oscillating" spin "stopping" at current angular speed (2π radians every 28/29 days)
That was my guess, and later I learnt some facts that seem to agree with it. But I´ll leave it there.
If moon had been fully isotropic, most probably we´d now be seeing a different "semi-moon" ..."
I add now that, due to other relatively small changes in total gravity there, Moon is not 100% exactly showing us same half side: it continues to oscillate, though very little ... And not only in East-West direction: its axis of rotation oscillates too ...