Answer: All objects attached to the world take the same amount of time to complete one revolution. Objects near the center have less distance to travel, and therefore need less speed to complete the trip.
This can be proven with a simple experiment. Have one person run around the perimeter of the room. Have a second person stand in the middle and face the other person while he completes one lap. Both people made one rotation, but they expended very different amounts of energy doing it.