Both gears and hardcheese are spot on, you don't see space ship rotating because you, your ship, and space station are in the same moving frame of reference, rotating at the same speed; we have to consider the relative motion of objects. In fact we call the particular frame of reference you and the space station are in a rotating reference frame (picture in this link is important). The earth is a rotating reference frame and we don't feel it spinning. In fact, if you turn of rotational correction you would see the space ship spinning.
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The fact that you are in the same rotating frame of reference doesn't absolutely rule out that you might not see the effects of your rotating in real life and in the game. It’s just your so accustomed to seeing and feeling certain things on the spinning earth that you might not think about them being due space ship spinning.
Observation 1: Artificial GravityFirst, the space station's rotation is creating the artificial gravity holding your space ship down. Now, one way to explain this is to talk about how artificial gravity is the Newton’s third law force pair of your centripetal force. However, for nonscientists that explanation can be super confusing. To help explain a better way of understanding artificial gravity, I would like to share with you this video by astronauts on the international space station and this website link about the subject:
As the station rotates, a centripetal force causes the angular acceleration and rotation of both you and edge of the station. However, you still want to move in a straight line due to Newton’s first law and your linear momentum. As the website and picture above shows, it is your tendency to move in a straight line that causes you push into the outer edge of the spacecraft. In real life, it would be possible feel this pull down and the adverse effects of the g-forces from your rotation. Now besides latching the ship to the station, I am not sure how far the developers can really stimulate the inner ears feeling of gravity or the effects of g-forces. As it’s an issue in real life, I also suspect that space stations in game are intentionally big then they need to be in order to prevent and limit the side-effects of g-forces. However, seeing if g-forces and all the affects of artificial gravity have been added space stations in game is something that a pro-player could probably test. All you would have to do is turn off rotational correction and find out what happens when you abruptly make a straight landing on a ship. I am not good enough pilot to make such a landing and not blown up by ship defenses. >-<;
Observation 2: circumpolar stars and revolving objects outside the space station.Remember how I and Gears talked about how because your rotating at the same speed as space station, you cannot tell station is rotating? In other words, how you cannot tell space station motion because your relative motion is the same? We are assuming that there were no windows for you could look outside the station into space stars or see anything outside the station that might not be in the same rotational reference frame. If you were to look at the stars, perhaps the ones seen from the hatch you entered the station from, you should technically seem the slowly revolving or spinning. We call this stars that are spinning in this way Circumpolar stars. I believe actually see people look hatch before and see those stars slowly spinning though it’s at a really bad angle. The fact that there are circumpolar stars or even revolution of the stun means you are ‘seeing the ship rotate’.
Observation 3: Coriolis effect of other ships docking/taking off.
In real life, if you were in large space station like the ones from the game, the others ships landing and taking off would appear go in curved flight paths toward there docking stations. This is due to what physicists and meteorologists call the Coriolis effect, or the curved path that straight path objects seem to take because the viewer is in a rotating reference frame. The picture above shows well what the Coriolis affect is. Now, I have yet to tell if another ship actually follows the Coriolis effect because everyone I know is so bad at docking that they have to usually stop halfway and reorient themselves. In other words, I have not met someone who is good enough to dock from start to finish in a straight line. However, it should be observable.
These 3 effects are all cause by you and the station rotating, even if you cannot see the station and yourself rotating.