The Milky Way Galaxy has rotating spiral arms of which are Solar System is part. We are hardly stationary while the rest of the matter in the Galaxy spins about its center. Our entire Galaxy is rotating while at the same time zooming to the nearest Cosmic Bar for a Drink before heading off into oblivion. Here is an excellent web page
The Milky Way
The universe is in state of expansion or inflation, thus our Galaxy, along with all matter, is on some trajectory away from a hypothesized Big Bang Center.
I think.
-Zeno