Answer 1:
There are a couple of ways to answer this
question. The rotational velocity (or speed) of
the Earth is always just one revolution per day,
everywhere on Earth, since the Earth spins around
its axis once per day. This rotational speed of
one revolution per day is what gives us day and
night on a consistent 24hour cycle (unless you
are inside the Arctic or Antarctic Circles, in
which case the Earth still rotates at a speed of
one revolution per day, but day and night are not
always on 24hour cycles because you can see the
sun for multiple days in the summer and the sun is
hidden from view below the horizon for multiple
days in the winter).
However, the speed of
the surface of the Earth at Santa Barbara as it
rotates around its axis is a little more
complicated. This speed is called the tangential
velocity because it describes the speed of a
straight line that is touching the surface of the
Earth (a tangent line) at Santa Barbara. To find
this speed, you only need to know three things:
1) the latitude of Santa Barbara, and 2) the
distance around the Earth at this latitude, and 3)
the amount of time it takes for the Earth to
rotate once around its axis.
Therefore, the
short answer to your question is this: 1) the
latitude of Santa Barbara is about 34.42 degrees
north. 2) At this latitude, the distance around
the Earth is approximately 33,020 km. 3) The
amount of time it takes for the Earth to rotate is
24 hours, or 1 day. Therefore, at Santa Barbara,
the Earth rotates 33,020 km in 24 hours. The speed
at which the Earth rotates at any given latitude
is equal to the distance around the Earth at that
latitude divided by 24 hours. At Santa Barbara,
the Earth rotates at a speed of 33,000 km / 24
hours, which equals about 1376 km / hour, which is
855 mph!
Here is the long answer, showing
the calculations that I used (this will probably
be too complicated for you if you havent had any
geometry, algebra, or trigonometry lessons yet, so
dont worry if you get confused). The latitude of
Santa Barbara is approximately 34.42 degrees
north. So to figure out how fast were rotating
here, we need to find out how far it is around the
Earth at the latitude of 34.42 degrees and then
divide that by one day, or 24 hours. To find out
how far it is around the Earth at this latitude,
we need to use the equation for the circumference
of a circle. The equation is:
C = 2 x π x
R
Read aloud, this equation says the
circumference of a circle (C) equals two
multiplied by π multiplied by the radius of the
circle (R), where π is a number that equals
approximately 3.14159
The circumference is
the distance all the way around the circle. The
radius of a circle is the distance from the center
of the circle to its edge.
However, it is a
bit difficult to find the radius of the Earth at
the latitude of Santa Barbara. Using trigonometry,
we can determine the equation to find the radius
of the Earth at any given latitude. This equation
is:
Latitude = Equator*COS (Latitude)
Read aloud, this equation says the radius
of the circle circumscribing the Earth at a
specific latitude (Latitude) equals the radius of
the Earth at the equator (Equator) multiplied by
the cosine of the angle of latitude (COS
(latitude)). You probably havent seen the word
cosine before, but it is a neat mathematical
function that describes a relationship between two
sides of a triangle and one of the angles. The
derivation for this equation is a bit tricky, but
I would be happy to show you if you are
curious.
At the equator, the Earths radius
(the distance from the center to the edge of he
Earth) is approximately 6371 km (the actual radius
at the equator is about 7 km greater than this due
to the bulge that forms as a result of the
centripetal force from the Earth spinning, but we
can ignore this bulge for simplicity). The
latitude of Santa Barbara is about 34.42 degrees.
Using thisequation, we find that the radius of
the Earth at Santa Barbaras latitude is about 5256
km. Here is the calculation for this:
Latitude = Equator*COS (latitude) = 6371
km * COS (34.42) = 5256 km
So, now we know
that the radius of the Earth at Santa Barbaras
latitude is 5256 km. We can now use the equation
for the circumference of a circle to find out how
far it is around the Earth at this latitude.
Recall that the equation for the circumference of
a circle is:
C = 2 x π x R. Using this
equation and the radius of the Earth at Santa
Barbara, we find that the circumference of the
Earth at Santa Barbaras latitude is about 33,020
km. Here is the calculation for this:
C =
2 x π x R = 2 * 3.14159 * 5256 km = 33,020
km
Now we know that at Santa Barbara, the
circumference of the Earth is 33,020 km.
Therefore, here the Earth rotates a total of
33,020 km in each day, or 24 hours. The speed of
the Earths rotation in Santa Barbara is 33,020 km
/ 24 hours, which
