A space station orbits the Earth. The station is formed like a bicycle wheel with a rim and hallways connected to a central hub. The station rotates around the central hub to provide a centripetal acceleration along the outer rim to serve in place of the Earth's gravity.

Suppose the station is inhabited by 10 people of equal mass. At the moment, there are 5 people in the central hub and 5 along the outer rim. Then two people move from the rim to the hub. Immediately thereafter, four people walk at the same speed from hub to rim.

Make a graph of angular velocity of the station versus time to reflect this series of events. (10 points)