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 Addition 1. 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. E 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 4m 5m 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 km East km 30 degrees North West km West km South 5. Draw and measure the Resultant Vector