http://www.Media4MathPlus.com In this issue of Math in the News we examine the Polar Vortex. We examine the physics of the cyclonic winds that make up the Polar Vortex and under what conditions the current expansion of Arctic weather affects a large part of the United States.

1. Examining the Polar Vortex
Math in the News
Issue 88

2. Polar Vortex
The bitterly cold winter of 2014 that has
affected much of the U.S. is due in part to the
Polar Vortex. To learn more about this weather
phenomenon, click on the video.
http://youtu.be/ACHxHQOme90

3. Polar Vortex
A Polar Vortex is a swirling mass of wind that
circulates around the polar regions of the
Earth. To better understand the forces at work
in this swirling mass, let’s look at a simpler
example of circular motion.

4. Polar Vortex
Imagine a ball of mass
m circling around a
center point. The
radius of the circle is r
and the speed of the
ball is v. Its centripetal
force, which keeps the
ball going in a circular
motion, is shown in
this equation.

5. Polar Vortex
Let’s rewrite the
equation to isolate the
speed of the swirling
air mass. The result is
a radical function. It
tells us that the speed
of a Polar Vortex
is, among other
things, a function of its
mass.
m•v
F=
r
¯
v=
2
F •r
m

6. Polar Vortex
The mass of the swirling winds is not an isolated
object, as in the ball rotating around a center
point. But the column of air does have mass.

7. Polar Vortex
The mass is based on the air density. The product
of air density and the volume of air results in the
mass of the Polar Vortex.
Mass = Density • Volume
m = r •V

8. Polar Vortex
When the air density
increases, so does the
mass of the column of
air. Going back to our
velocity equation, you
can see that the graph
of the velocity-versusmass equation results
in a decreasing
velocity for an
increasing mass.
m = r •V

9. Polar Vortex
The result of a highpressure system is
that the speed of the
Polar Vortex
decreases. There is
less force containing
the Polar Vortex.

10. Polar Vortex
With a decreased force
containing the
Vortex, there is a
greater likelihood of
the polar winds
seeping out beyond
the Arctic. And this is
what has happened.

11. Polar Vortex
In fact, because the air pressure isn’t uniform, the
result is a wobbly Polar Vortex that spreads
beyond its usual limits.

12. Polar Vortex
This isn’t just wind that’s moving into the U.S. It’s
Arctic weather that’s seeping in. This is why
temperatures have dropped so dramatically.

13. Polar Vortex
Eventually the air pressure will normalize and the
Polar Vortex will return to its usual size and
expanse.