Degrees or radians. Let's Learn Physics.
Our students understand degrees. They can
think in degrees. They can even measure
degrees. That 360 degrees in a circle?
That's because there are exactly 30 days
in a moonth and 12 moonths in a year and
12 x 30 for 360 days in a year.
Exactly. Some old calendars even had a
leap moonth every five or six years to
catch up. Degrees are dumb. But we
understand degrees because we have
protractors and we can measure in
degrees. Compasses in degrees. And
navigation for boats and ships - heading
in degrees. But radians?
I barely understand radians and my
students have no clue. The angle swept
out by a radial line is defined as the
ratio of the arc length to the radius
for a circle. And since the units divide
out the ratio is what we call a
dimensionless unit - a simple ratio. Since
the circumference - the arc length in a
whole circle - is equal to 2 pi times the
radius there are 2 pi radians of angle
measure in a whole circle of turn.
Sounds complicated. That impression of
complicatitude is one of our impediments to
a good understanding of radians.
of course is just like X or Y in algebra.
Except it's not at all.
Pi is a number. it's a number that shows
up in our natural world again and again
and again. It's the ratio of the
circumference of every circle to its
diameter. Every circle. It's the ratio of
the surface area of every circle to the
square of its radius.
Pi is three-quarters the volume of a
sphere / the cube of its radius.
Pi shows up in
physics equations again again and again.
It's real and irrational just like all
of you. And one full circle is 2pi
radians - 6.28 blah blah blah radians.
Half a circle is 3.14 etc radians.
1 radian - 2 radians - 3 radians - 4 radians
5 radians - 6 radians. One radian is a bit
less than one-sixth of one full turn
around a circle. So why don't our
students understand those radians? or pi?
Because I've never seen - never even seen
a protractor in radians. If you look at a
math catalog you can find them. They
exist but they're really uncommon. I've
never seen a compass in radians.
So I came out here looking for some radians...
No luck. But i did find some degrees.
It's cold out here.
And I've never even considered
using radians for anything but math
class and only certain parts of math
class.
It's unused in almost everything I know.
It's just like the metric system we use
in physics class and in chemistry class.
And why would I ever need to speak a
different language? I do. I can switch
back and forth from feet and inches to
meters and centimeters when working with
my brother-in-law - my Syrian
brother-in-law on a home project.
Yo puedo contar una historia
en kilometros y kilometros por hora
a mi familia en Paraguay.
But that's only because i won't be
understood if I don't. Radians are real.
And they're better than degrees in
almost every way. Degrees are physically
smaller divisions so maybe that's why
they use degrees on protractors. But like
many things, we use degrees. We use
kilometers. We use gallons and we use
twenty four-hours-a-day and 60 minutes
in an hour and 60 seconds in
minute not because they make more sense
They often don't. But because we're used
to them and that's what we've always
done. And we won't change until we have to