Sir Isaac Newton, the father of mechanics, is one of the most important scientists who ever lived, changing the standards by which scientists think. His genius in mathematics and mechanics is exemplified by his creation of calculus to explain observations of the world around him. In addition, his laws of motion opened the door to progressive new thinking, enlightening the minds of thousands to the nature of things. His laws of motion make up the foundation for which dynamic meteorology exists.

It is important to note here the definitions of velocity and acceleration. A quantity which has magnitude is called a scalar. If a quantity has magnitude and a sense of direction, it is called a vector, represented graphically by an arrow.

- Speed is a scalar because it indicates "how fast" something is travelling. Its unit of measurement is the change in position (or distance)/the change in time, e.g. m/s.

- Velocity is the vector representation of the scalar speed, therefore it must be given direction, e.g. eastward at 10 m/s.

- Acceleration is the vector representation of the change in velocity/ change in time, e.g. m/s². Because acceleration is a change in velocity, an object may be accelerating even if its speed is not changing if its direction is.

IMPORTANT FORCES IN THE ATMOSPHERE

Perhaps the most readily known force in the atmosphere is gravity, and yet surprisingly, very little is known about this omnipresent force. It was Newton who first tried to understand this force, even if an apple did not fall on his head.

Gravity is a force that exists in every object that has mass. However, it only becomes significant in objects whose mass is very great such as celetial objects, i.e., planets stars and moons. Gravity is therefore dependent upon the object's mass.

The strength of the gravitational force is also dependent upon the distance between two objects. Since gravity is an attractive force, the greater distance between two objects, the smaller the force. Gravity is then formulated as follows:

g = G*m1*m2/r²

where r is the separation between two objects of mass m1 and m2 and G is the universal gravitational constant.

Because a force gives way to an acceleration, we will often give gravity an acceleration value of 9.8 m/s² (10 m/s² for simplicity). This is found by using the earth's mass and disregarding an object's mass. Notice that the earth is so much more massive than any object on the earth, we will assume that the object in question will accelerate toward the earth at 10 m/s². Notice the falling object's mass is not taken for consideration. As Galileo proved, two falling objects will fall at the same rate. However, the force of the object hitting your head is not independent of mass, since F = ma, where a is actually g.

Centrifugal force is another force that one may be familiar with because of the great appeal of amusement parks. Centrifugal force actually does not exist but because as an object changes direction it experiences an inertial change, that inertial resistance is termed centrifugal force. Actually the change is brought about by a physical force (a twisting track or a string attached to a rock. It is this force that causes a centripetal acceleration (toward the center).

Centripetal acceleration is defined as:

ac = v²/r

where v is the velocity and r is the radius of curvature.

Therefore, the faster an object travels or the tighter the turn, the stronger the "centrifugal" force.

In WWI, the Germans developed a cannon which could fire at Paris, but even taking into account winds and air resistance, the cannons consistently shot to the north of the fabled city.

Railroad tracks that allow travel in only one direction tend to wear out on the right side.

These two events illustrate a very real result of a force that does not really exist! This force is called the coriolis force. The coriolis force results from objects moving on a rotating sphere. The force is called apparent because when viewed from outer space, objects on the earth travel in a straight line. But when in the earth's frame of reference, moving objects will deflect to the right in the Northern Hemisphere and to the left in the Southern.

The coriolis force is defined mathematically as:

CF =

where k=1.46*10-4, and _ is the latitude. Basically, this formula states that the faster an object moves and the closer to the poles it is, the stronger the coriolis force.

Before we continue with the rest of the atmosphere's forces, let us first compare two examples of the relative strengths of the centrifugal and coriolis forces.

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- For a tornado, let us assume v = 50m/s and r = 200m.

If _ = 40°, sin_ = .643.

ac = v²/r therefore, ac = 50²/200 = 12.5 m/s²

CF = therefore, CF = 1.46*10-4*.643*50 = .005 m/s²

We can compare answers and say that compared to the centrifugal force, the coriolis force is insignificant.

- For a low pressure system, let us assume v = 10m/s, r = 500km which is 500,000m and _ = 40°.

ac = v²/r therefore, ac = 10²/500,000 = .0002 m/s²

CF = therefore, CF = 1.46*10-4*.643*10 = .001 m/s²

We can compare force and say that the coriolis force is five times greater than the centrifugal force. This is too small a difference to ignore.

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Friction simply stated is a force that acts to slow an object. Friction is important when air is moving near the earth's surface but not as important higher in the atmosphere. More will be stated later as we talk about combining these forces.

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