Okay. Take four cases, case A is air moving into a weather system from the north, case B is air moving in from the south, case C is air moving out to the north, and case D is air moving out to the south. This is all for the northern hemiplane; it would be the reverse in the south.
Case A
There is a slight gravitational tug to the west that increases as the air moves south into the weather system. Because of this increasing pull, it moves westward, contributing counterclockwise angular momentum to the system.
Case B
Air in equilibrium with a strong gravitational tug to the west begins moving north, and as the gravitational pull weakens it moves to the east, contributing counterclockwise angular momentum to the system.
Case C
Air begins moving to the north, where the westward gravitation is weaker. Therefore, it begins moving to the east and contributes clockwise angular momentum to the system.
Case D
As the air moves south, the gravitational tug to the west increases, and it moves west, contributing clockwise angular momentum to the system.