Newton's Second Law can be stated simply as:

" Force equals mass times acceleration "

and more completely as

" The rate of change of the velocity of a particle, or its acceleration, is equal to the resultant of all external forces exerted on the particle divided by the mass of the particle, and is in the same direction as the resultant force. "

(Sears, F. W., H. D. Young, and M. W. Zemansky, 1979: University Physics 5th ed., Addison-Wesley Publishing Company, 404 pp.)

We need to apply these textbook definitions to the atmosphere, but since air is a continuous fluid, there is no particular "particle" we can use. Instead, we will again take an air parcel, consisting of an arbitrary volume of air, and state Newton's Second Law in such a way that the exact size of the air parcel doesn't matter.

We start with:

Force = Mass * Acceleration

Now consider these forces acting on a given volume of air:

Force per unit volume = Mass per unit volume * Acceleration

Density is defined as the amount of mass per unit volume, so we can restate the second law as:

Force per unit volume = Density * Acceleration

Finally, it is customary to bring the density term to the other side of the equation:

Force per unit volume ÷ Density = Acceleration

What if there's more than one force? Just add all the forces up:

(Force 1 per unit volume ÷ density) + (force 2 per unit volume ÷ density) .... (Force N per unit volume ÷ density) = Acceleration

or in graphical form:

Which states that the sum of the forces per unit mass equals the acceleration.

For an optional review of adding vectors, you can go to a high-school-level lesson on Vector Addition.

Acceleration in the atmosphere

In the atmosphere, for the most part, the acceleration of air parcels is fairly small. In fact, under many circumstances, the acceleration of the air is so small that it can be neglected (which means, it is roughly zero). Air moving in a particular direction at a particular speed tends to continue moving at that direction and speed, at least for a while. What does that mean in terms of Newton's laws?

(choose one answer to continue; only one answer is correct)

1. Newton's laws apply to objects, not to fluids like the atmosphere.
2. According to Newton's First Law, each of the forces acting on the air must be very weak.
3. According to Newton's Second Law, there might be lots of forces, but they must all add up to nearly zero.

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