The explanation of wind flows around low pressure and high pressure systems is most easily achieved by considering a spinning disk rather than a spinning sphere.

The disk above is shown as spinning counterclockwise just as the Earth is when viewed from above the North Pole. The points on the disk farther from the center are moving with a greater velocity than the one closer to the center.

If a parcel which is moving with the disk moves away from the center its speed is then slower than the points on the disk at that greater distance and it lags behind. From the viewpoint of points moving with the disk the parcel appears to move toward the west. On the other hand if a parcel were to move toward the center its speed would be greater than the points there and it would move ahead. From the viewpoint of points on the disk the parcel would appear to move toward the east.

A Low Pressure System
in the Northern Hemisphere

Now consider a low pressure area on a disk as shown below.

A parcel of air at point A would move toward the center of the low pressure area. That movement would take it farther away from the center of the disk and therefore it would move to the west. A parcel of air at B would move toward the center of the low pressure area which would also take it closer to the center of the spinning disk where its speed is greater than the surrounding points. It would appear to move to the east. With A moving to the west and B moving to the east the line from A to B is rotating counterclockwise.

A High Pressure System
in the Northern Hemisphere

For a high pressure system on a spinning disk such as the one shown below

the only difference from the case of the low pressure system is that air parcels at A and B would move away from the center of high pressure. A would move to a point closer to the center of the disk where it is moving faster than the surrounding points and so appears to move east. Likewise a parcel at B would move away from the center of high pressure and also away from the center of the disk and would appear to move west. The line from A to B would be rotating clockwise.

Low Pressure and High Systems
in the Southern Hemisphere

The rotation of the Earth viewed from above the South Pole is clockwise as is the case for the spinning disk shown below.

A low pressure area would have a clockwise turning and a high pressure area a counterclockwise turning.

In summary:

• Winds Around Low pressure Systems Turn in the Direction of the Earth's Rotation
  and Winds Around High Pressure Systems Turn in the Opposite Direction of the Earth's Rotation.