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Yes, it does, the rotation period can be calculated using 21cm radio waves and the Doppler principle.

Answer:

All galaxies rotate as do all planets around stars and just about everything else.

It is the centripetal force of rotation that prevents objects from falling together due to the attractive force of gravity.

If an isolated mass of stars or dust or gas were assembled in space and the contents had no rotational motion, the whole mass would begin to accelerate towards its own center due to gravity. So, while such clumps of matter can exist, they have all presumably condensed into planets or star or black holes.

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