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# Ferrel'slaw

Ferrel's law, named after American meteorologist W. Ferrel (18171891), is the rule that air or water moving horizontally in the Northern Hemisphere is deflected or pushed to the right of its line of motion while air or water moving horizontally in the Southern Hemisphere is deflected to the left of its line of motion. Ferrel's law, which predicts the directions of the large-scale circulations of the earth's atmosphere and oceans , is a restatement in global terms of the action of the Coriolis force.

The Coriolis force is a consequence of the conservation of angular momentum and arises as follows. Consider a spinning disk with an ant perched on its outer edge. The ant's angular momentum (P ) is given by its mass (m ) times the square of its distance from the center of the disk (r 2) times the radial velocity of the disk (ω, how fast it is turning): P = mr 2ω. If the ant crawls along a straight radial line toward the center of the disk, its radial velocity ωthe number of turns around the axis it makes per secondremains constant. Its mass m also remains constant. However, its distance from the center r decreases. By the above formula, therefore, its angular momentum P also decreases. Yet a force is required to change the angular momentum of an object. Therefore, as it walks straight toward the center of the disk the ant must experience a force (a sideways push on its feet) that decelerates its rate of spin. From the perspective of the ant, the result is straight-line relative to the disk, and this sideways push seems required to balance a force tending to accelerate the ant sideways in the direction of the disk's rotation . This apparent force, which only seems to act while the ant is in motion toward or away from the disk's axis of rotation (i.e., is changing its angular momentum), is termed the Coriolis force. If the surface of the disk is too slippery to enable the moving ant to completely resist this apparent force, the ant will be deflected by it, relative to the disk's surface, in the direction of the disk's spin: that is, it will retain some or all of its original angular momentum by rotating more rapidly as it nears the disk's axis of rotation, just as a spinning ice skater's limbs rotate more rapidly as she or he retracts them toward her or his axis of rotation.

An ant trying to crawl axisward on a slippery disk is like a body of the air trying to drift northward or southward on the spinning (rotating) earth. Because Earth rotates eastward, air moving toward the axis of rotation (i.e., toward either the North or South Pole) tends to preserve its angular momentum by accelerating eastward; that is, it experiences an eastward Coriolis force that deflects it in the direction described by Ferrel's law. Eastward acceleration of a north-moving object in the Northern Hemisphere is to the right, as viewed along the object's line of motion; of a south-moving object in the Southern Hemisphere, to the left. Movements away from the axis of rotation are deflected westward in both hemispheresagain, to the right of the line of motion in the north, to the left in the south. The result is that high pressure systems, as seen from space tend to spin clockwise in the Northern Hemisphere and counterclockwise in the Southern Hemisphere. Low pressure systems spin in the respective reverse direction.

Ferrel's law applies equally to air and ocean movements, so the oceans circulate in the same sense as the air in both hemispheres. However, though it is often said to do so, Ferrel's law does not govern the direction of whirlpool spin in draining sinks and toilets. The Coriolis force is too weak to determine the behavior of fluids in such small basins.