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, Young, and Zemansky)
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 Additon.
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)
- Newton's laws apply to objects, not to fluids
like the atmosphere.
- According to Newton's First Law, each of the
forces acting on the air must be very weak.
- According to Newton's Second Law, there might
be lots of forces, but they must all add up to
nearly zero.
Questions or Comments
Technical: E-mail John Fulton < jdfult@nimbus.met.tamu.edu >
Scientific: E-mail Dr. John Nielsen-Gammon. < nielsen@ariel.met.tamu.edu >
Copyright © 1996-2003 Texas A&M University,
Texas A&M Atmospheric Sciences Department and
Dr. John Nielsen-Gammon.
All rights reserved.