Honors Physics

Vectors and Scalars

Scalar Quantity

What does it mean to be a Scalar Quantity?

Examples?

Units of measure must be included with the magnitude

Vector Quantities

So what is a Vector Quantity?

Examples?

Units are again very important

Describing Direction

Many methods We will primarily use

these two methods: xy coordinate system Compass Headings

+x+y

N

E

Adding Scalars

Scalars can be added using simple rules of arithmetic

Scalars must represent the same quantity to be added or subtracted

The Units of measure must be exactly the same

Adding Vectors

Adding vectors involves adding magnitude AND direction

The means of addition depends upon the type of vectors being combined.

Three Types of Vectors Colinear Perpendicular Neither Colinear nor Perpendicular

CoLinear Vectors

Vectors which are in exactly the same or opposite directions.

Two Methods of Addition1. Arithmetic

2. Graphically This is a method of drawing the vectors commonly

called the Head-to-Tail Method.

Head-To-Tail Method

Vectors are Drawn as Arrows The length represents the Magnitude The arrow designates the direction

How to Do It Draw the first vector to some convenient scale and in the

proper direction. Draw the next vector to the same scale, starting at the

head of the first vector, and in the proper direction. Continue until all vectors have been added.

Demonstration of Head-To-Tail

The Resultant Vector This is the answer Draw a vector from the tail of the first to the head of the last. Measure its length and direction.

E100m 100m

200m

Adding Perpendicular Vectors

Can be Added using Head-To-Tail Same steps as for Colinear Vectors

Can be added Mathematically We will look at this method tomorrow.

Adding Perpendicular Vectors

Head-To-Tail Draw vector 1 Draw vector 2 at head

of vector 1 Draw and measure

resultant vector

3m

4m5m

53

Neither Colinear nor Perpendicular

Presently these can only be added using the Head-To-Tail Method

We will discuss a mathematical solution for these soon.

Vector Map Activity

Draw each supplied vector to scale and in its proper direction.

Starting Point is downtown Pittsburgh.1. 6.0km East2. 2.5km 30 degrees North West3. 4.0km West4. 7.5km South5. Draw and measure the Resultant Vector