1. Vectors

2. Cartesian vs. Polar Coordinates
Polar coordinates  (r, theta) are measured by how far away (r) and at what angle (theta) a point is.
Converting from polar to cartesian:  
to X uses cosine function x=rcos(theta)
 to Y uses sine function y=rsin(theta)
Cartesian points (x,y) are measured in how far along (X) and how far up (Y) a point is. 
Converting from cartesian to polar
to R uses Pythagorean theorem
r= sqrt(x2 + y2)
to theta uses tangent function
Tan(theta)= y/x
Quadrant
Value tan-1 I
Calculator Value II
Add 180*
III IV
Add 360*

4. Practice 
Convert between cartesian and polar coordinates: (13, 22.6*) (6, 3)
(13, 22.6*)= (12,5)

5. Vectors Vectors represent a magnitude & direction
Vector quantities: displacement, velocity, acceleration, & force
Free Body Diagrams 
Scale
Arrow with head (point) & tail
Magnitude & direction are clearly labeled

6. Vector Direction & Magnitude
Described by the angle of rotation of the vector tail from: E, N, W, or S.
Can be described as 40* North of East 
The vector pointing east has been rotated 40* toward the northerly direction
Can be described as 40* C-C from East
The vector is described as an angle value counter-clockwise (up to 359*) from due east
Magnitude in a scaled diagram is depicted by the length of the arrow.

7. Vector Addition
Simple Addition for vectors pointing in the same or opposite directions
When vectors are point in non-vertical/horizontal orientation
Calculating displacement using Pythagorean theorem, head to tail method, & parallelograms

8. Resultant
The resultant (R) represents a displacement equal to that of a scaled vector diagram

9. Practice What is the magnitude and direction of the resultant vector?9 6 12

10. Activity: String Writing
Your group must write the complete FIRST NAME of every person in the group on a standard piece of paper. However, nobody may touch the pen! You must attach the strings to the pen and write your names by pulling on the strings.
Materials:
4 strings
Blank sheet of paper taped to desk
Ink Pen

11. Requirements Keep at least 8 inches from pen at all times.
Each person can only use 1 string
The paper cannot be moved, tape it down to the desk.
Must write complete first names of each student in the group

12. Reflection Questions What was challenging about this activity?
What were some ways that you group worked to overcome these challenges?
What were the forces that your group worked with?

13. Practice
ADD EM UP!