3.0 - Introduction

Knowing “how far” or “how fast” can often be useful, but “which way” sometimes

proves even more valuable. If you have ever been lost, you understand that

direction can be the most important thing to know.

Vectors describe “how much” and “which way,” or, in the terminology of physics,

magnitude and direction. You use vectors frequently, even if you are not familiar

with the term. “Go three miles northeast” or “walk two blocks north, one block east”

are both vector descriptions. Vectors prove crucial in much of physics. For example,

if you throw a ball up into the air, you need to understand that the initial velocity of

the ball points “up” while the acceleration due to the force of gravity points “down.”

In this chapter, you will learn the fundamentals of vectors: how to write them and

how to combine them using operations such as addition and subtraction.

On the right, a simulation lets you explore vectors, in this case displacement

vectors. In the simulation, you are the pilot of a small spaceship. There are three

locations nearby that you want to visit: a refueling station, a diner, and the local

gym. To reach any of these locations, you describe the displacement vector of the

spaceship by setting its x (horizontal) and y (vertical) components. In other words, you set how far horizontally you want to travel, and how far

vertically. This is a common way to express a two-dimensional vector.

There is a grid on the drawing to help you determine these values. You, and each of the places you want to visit, are at the intersection of two

grid lines. Each square on the grid is one kilometer across in each direction. Enter the values, press GO, and the simulation will show you

traveling in a straight line í along the displacement vector í according to the values you set. See if you can reach all three places. You can do

this by entering displacement values to the nearest kilometer, like (3, 4) km. To start over at any time, press RESET.

3.1 - Scalars

Scalar: A quantity that states only an amount.

Scalar quantities state an amount: “how much” or “how many.” At the right is a picture of

a dozen eggs. The quantity, a dozen, is a scalar. Unlike vectors, there is no direction

associated with a scalar í no up or down, no left or right í just one quantity, the

amount. A scalar is described by a single number, together with the appropriate units.

Temperature provides another example of a scalar quantity; it gets warmer and colder,

but at any particular time and place there is no “direction” to temperature, only a value.

Time is another commonly used scalar.

Speed and distance are yet other scalars. A speed like 60 kilometers per hour says how

fast but not which way. Distance is a scalar since it tells you how far away something is,

but not the direction.

Scalars

Amount

Only one value

Examples of scalars

12 eggs

Temperature is í5º C

(^52) Copyright 2000-2007 Kinetic Books Co. Chapter 03