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CHAPTER 1 Mathematics
We use math to quantify all sorts of things around us. The architects of a building have to consider the total surface area of glass and its effect on the heating and cooling needs of the building. The building design would detail heights, lengths, temperatures, volumes, thicknesses, flow rates, currents, wattages, energy use, etc. Such quantities are members of a class called scalars.
Any quantity that can be described entirely in terms of its magnitude is called a scalar.
When we travel on the highway we are concerned with such scalar quantities as speed, time, and distance. But we're also concerned with the direction of our travel. Traveling across New Mexico, where the roads are straight, we might travel 5 miles in the northwest direction. We could cover this distance in 6 minutes if we traveled 50 miles per hour in a northwest direction. We call these directed quantities our displacement and velocity, respectively. They are members of a class called vectors
We call any quantity that specifies both magnitude and direction a vector.
The math of scalars is generally no more mysterious than balancing a checkbook. You add what comes in and subtract what goes out. If you get overdrawn, it must be the bank's error.
Then of course there's multiplication, etc.
The math of vectors is different in that we have to account for direction.
Let's get the low-down this important distinction between scalars and vectors. As usual, explore around a bit, then watch the video.
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In summary:
To add several vectors together, connect them tail to head, in any order. The vector sum or resultant is a vector from the tail of the first to the head of the last.
The resultant of several vectors is a vector indicating the net effect of those vectors.
When vectors are actually drawn to scale and the magnitude and direction of their resultant is determined from the scale of the drawing and a protractor measurement, we call this graphical addition. We will develop more analytical methods but any method of addition will have this at its core.
Let's develop this further with some examples.
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