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 24-hour 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 24-hour 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 haven't had any geometry, algebra, or trigonometry lessons yet, so don't 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 haven't 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 this equation, we find that the radius of the Earth at Santa Barbara's latitude is about 5256km. 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 Barbara's 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 Barbara's 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.

What a great question! Let's start with the equator first. An object on the equator travels a distance that is equal to the Earth's circumference (40,075.036 km) every day (24 hours). This gives us a speed of 1669.79 km/hr (kilometers each hour) at the equator. To find the speed here in Santa Barbara, we need to multiply this number by the cosine of the latitude of Santa Barbara (34.45 degrees). Latitude is a measure of the angle between two points on the earth's surface. The final answer gives us a speed of 1376.95 km/hr.