Do comets spin? Why do satellites/space station not spin? Do comets spin? Why don't satellites or space-station spin? If spin is fundamental thing, then it should be found in all (moving) objects.
 A: By way of analogy, does your car spin? Your car might well go into a spin if you try to turn while driving over a patch of black ice, but that isn't a desirable outcome. Humans have developed lots of schemes to avoid undesired rotation.
This is particularly so with satellites. You will find lots and lots of articles about controlling the attitude and rotation of a satellite if you go to scholar.google.com and search for "spacecraft attitude control".
The space station is rotating, at one revolution per orbit. This rotation is by design and is carefully controlled. All satellites have a very carefully designed and controlled orientation and rotation. They would be non-functional if they didn't.
A: Yes comets spin. Satellites do too - typically they are set to spin in such a way as to point to earth at all times - which means they spin once per orbital revolution. Often small adjustments are made with the use of reaction wheels - move the wheel one way and the satellite turns the opposite way. 
There is no reason why any object should have to have any specific angular momentum - but we know that within a closed system the angular momentum won't change.
A: The international space station does spin, with period of 1 earth orbit. This keeps the stations nator axis orientated equally through out an orbit relative to the surface of earth.
A: Like several others have said here, you seem to be conflating the spin in quantum mechanics to the spin of macroscopic bodies in classical mechanics, which doesn’t make much sense because quantum mechanical spin and the rotation of macroscopic bodies aren’t related in that way. Spin in quantum mechanics is an intrinsic angular momentum that particles have, while the “spin” you’re thinking of in macroscopic bodies isn’t the same. Not every macroscopic body necessarily has to rotate, while
particles have an intrinsic spin associated with them. 
At least that’s what i’ve heard anyway. 
