The uneven heating the earth's surface leads to movements of air. How the heat energy is converted to kinetic energy is the topic of this section.
The first law of motion we will consider is
1. Newton's first law (law of inertia). It states that for a body to change its state of motion, it must be acted upon by an unbalanced force.
2. Newton's second law. It states that the force required to accelerate a body of mass is given by:
F=ma
a=the acceleration (rate of change of velocity).
There are two types of forces 1) those that exist regardless of the sate of motion of the air
examples: Gravitation Attraction and Pressure
and
2) those that arise only after there is motion.
examples: Friction and the Coriolis Force
Gravitational Force is defined as:
Fg=Mg
where Fg = gravitation force
M= mass of the air
g = gravitational acceleration (9.8m/s2)
This is the downward force applied to an air mass that accounts for the change in pressure from the ground surface up through the atmosphere.
Remember Forces tend to be balanced by opposing forces
Pressure Gradient Force.
This force acts in the opposite direction and balances the gravitational force. It is defined as
The magnitude of the pressure gradient force is a function of both the pressure difference between two locations and the distance between them. It must also account for the difference in air density. We can write the relationship as follows:
where:
It is this force that causes winds to blow. The force moves air from regions of high pressure to regions of low pressure
The larger the pressure gradient the greater is the force applied to the air. Therefore, the greater the force, the greater is the speed of the wind. Note that the closer the contours are to one another the steeper is the pressure gradient.
Ultimately, the source of the differences in pressure between two locations is a function of differential heating of the Earth's surface.
The units used are in millibars which are equivalent to 100 pascals. You can say that 10 millibars equals 1000pascals or 1000 kg/m*s2
What would be the pressure gradient force in the atmosphere above two locations separated by 550kilometers where point A had a pressure of 550millibars and point B (elevation is 5kilometers) had a pressure 540millibars? The density of air at 5kilometers is 0.75kg/m3
We must convert to similar units. First convert the difference in millibars to kg/m*s2.
550-540=10millibars or, 1000kg/m*s2
density is 0.75kg/m3
So, the Force equals 
Coriolis Force "Merry-GO-Round Force"
Fc=2Vwsin (ø)
At the Northern Pole the apparent rotation is to the left
At the Southern Pole the apparent rotation is to the right.
This is an Apparent Force as observed on the Earth. The deflection observed by an observer on the Earth is related to the latitude, greatest at the poles and zero at the equator.
V=velocity (wind speed),
w= the angular velocity or the rate of the Earth's rotation
sin(theta is the latitudinal)
Coriolis Force is not a "real" force. It is really the effect of the Earth's rotation on a moving body.
1) The Coriolis Force always deflects winds at right angles to the direction of the airflow in the Northern Hemisphere.
2) The Coriolis Force affects only wind direction, not wind speed
3) The Coriolis Force is affected by wind speed/ the greater the wind speed--the greater the deflection (see equation above).
4) is strongest near the poles, becoming weaker toward the equator and is nonexistent at the equator
In the upper atmosphere (above 1km) where frictional forces are small all of the forces tend to balance. This is referred to as Geostrophic Equilibrium and can be written:
where 
=pressure gradient perpendicular to the flow
Where the the pressure gradient force is balanced by the Coriolis Force the winds flow along parallel to the isobars. These are called Geostrophic Winds. The steeper the pressure gradient, the stronger the winds.
Curved Paths
Gradient Winds are winds that followed the curved paths of highs and lows.
Centripetal Acceleration
Particles tend to move in a straight line unless acted upon by a force. Therefore, particles following a curved path are acted upon by a centripetal force toward the inside of the curvature.
