Q:

Is it possible to have a non tidally locked moon?

Fo my question, I'd like the moon to orbit around a saturn-like planet without rings.
This moon would be located at a million kilometers away the host planet.
the moon's size would be about 12 000 kilometers wide.
The moon would also be habitable and shelter a wide biodiversity and a stable climate.
Knowing that it wouldn't be tidally locked, it would have a 24 hour day and would take a few months to orbit around it's planet. How could it be able to do so? I hope you can answer me with a lot of details and thank you.

A:

Yes. Tidal locking is the end of a process (of tidal acceleration) that might take millions of years. A moon (or any other body orbiting a larger body) will avoid tidal locking…

the more massive it is,
the faster it rotates around its axis to begin with, and
the farther it orbits from the larger body to begin with.

Tides diminish in strength at rate proportional to the cube of the distance between the bodies, so the "distance" component of the equation is by far the most important.
If the moon was captured recently (in geological terms) it will take some time to become tidally locked. It will take a lot longer if it was captured in a faraway orbit. And even longer if, when captured, it was spinning rapidly. Note, however, that as tidal acceleration begins to act, the slowing down of the moon's spin will induce friction. Expect to have a geologically active moon, churned by the planetary tides.
For reference, an Earth-sized moon orbiting a Saturn-sized planet at one million km would take only about 12 days to complete an orbit. For a smaller gas giant (with the mass of Neptune), you could have an Earth analogue in orbit 2 million km away with a period of 76 days. Just play around with the numbers in the equations (WolframAlpha is your friend!).

