1. FRIDAY(09/04): Coordinate Systems, Properties of Vectors, Scalars.

HW: Read Ch.3, pages 59-65 and solve prob. 4, 7, 14, 18, & 27 on

pages 71-2.

2. TUESDAY(09/08): Lab on Addition of Vectors.

HW: Complete lab report and write Abstract, due Friday.

3. WEDNESDAY(09/09): The Mathematics of Vectors.

HW: Read pages 65-70 and solve prob. 29, 31, 33, 49, & 59 on pages 72-4.

4. THURSDAY(09/10): Review for Ch.3. All completed homework must

be brought to class today in your binder to be checked. HW: Complete

Review Handout.

5. FRIDAY(09/11): TEST on Ch.3 - Vectors. HW: Go to web-site for

notes on Ch.4 - Motion in Two Dimensions.

I. Vectors.

Vectors are used to describe multi-dimensional quantities. Multi-dimensional

quantities are those which require more than one number to completely

describe them. Vectors, unlike scalars, have two characteristics, magnitude

and direction. A vector is indicated by an uppercase letter either in boldface

or with an arrow over the top.  For example,  A or  Â . Examples of vector

quantities are: position in a plane, position in space, velocity, acceleration,

and force.

II. Scalars.

Scalars are used to describe one- dimensional quantities, that is, quantities

which require only one number to completely describe them. They have

magnitude only. Direction does not apply. There are cases where scalars can

be combined mathematically, but we will save that for later. Some examples

of scalar quantities are: temperature, mass, time, volume, density, length,

area, and energy.

III. Vector Diagrams.

Any vector can be resolved into perpendicular component vectors using sine

and cosine functions. Actually, for all vector problems just remember

SOHCAHTOA.

IV. Some Properties of Vectors.

Two vectors are equal only if they have the same magnitude and

direction. To find the opposite of a given vector just keep the same

magnitude but point it in the opposite direction.  ex. A - B = A + (-B)

Vectors can also be expressed using polar coordinates (r , θ) specifying

the length of the radius vector r , and the angle of rotation, Ø ("Phi"),

from the positive x-axis.

Additionally, in a two-dimensional coordinate system, vectors can be

denoted using the unit vectors î and ĵ. Each unit vector has magnitude

equal to 1, and they point in the x and y directions, respectively. We

can easily add the third dimension, or z direction using unit vector k.

V. Addition of Vectors

Vectors can be added graphically using the head-to-tail method. You

begin by drawing the first vector in a coordinate system, and then

drawing the second vector from the endpoint of the first, and so on.

Then you draw a single vector from the origin to the head of the last

vector.

The vector difference works the same as vector addition except that

we multiply the vector we are subtracting by -1. It is much like

subtracting two numbers: A - B = A + (-B). The diagram below

illustrates vector subtraction in the tip-to-tail style. The original B

vector is shown as a dotted line.