1. Vector Components 2-D Coordinate Systems Vector Components
2-D Vector Algebra
Outline

2. Coordinate Systems We have been using Cartesian Coordinates
In 2-D, this has x and y axes
The positive y-axis is located 90 counter-clockwise from the positive x-axis
The fact that the axes are 90 to each other allows us to have x and y components which are independent
Draw a set of non-orthogonal axes on the sympodium. Draw a path that is parallel to one of the axes. Does the value of the other coordinate change as well?

3. Component Vectors

4. How to find Component Vectorsx y 

5. Just remember: SOH CAH TOAy  x
You can always use sin() instead of cos ()  use 90 - 

6. Ratios you should know

7. Exercise Ax = __________ Bx = __________ Ay = __________
QQ29: 2-D Components
Exercise
Determine the numerical values of the x and y components of each vector: y y
120 5 x x
45 10
Ax = __________
Ay = __________
Bx = __________
By = __________
Don’t use a calculator.

8. Given and , you can find the magnitude and direction of :
Magnitudes
Given and , you can find the magnitude and direction of : y  x

9. Example: For a particle moving with vx = 5 m/s and vy = -2 m/s.
QQ30: Magnitudes
Example:
For a particle moving with vx = 5 m/s and vy = -2 m/s.
A) Draw the velocity vector on an set of x-y coordinates B) Find

10. Component notation A velocity vector has components vx , vy
“Unit vectors” i, j:
In 3-D space:
and vz .

11. Example: For a particle moving with vx = 5 m/s and vy = -2 m/s.
QQ30: Magnitudes
Example:
For a particle moving with vx = 5 m/s and vy = -2 m/s.
Express using unit vectors.

12. Worked Example: Unit Vectors
Ex. Unit Vectors
Worked Example: Unit Vectors
Two students are moving a refrigerator. One pushes with a force of 300 N along the horizontal, the other lifts with a force of 400 N along the vertical. What is the resultant force when expressed using unit vectors?

13. What if the vectors are not directed along an axis?
C=A+B
What if the vectors are not directed along an axis? By Bx Ax Ay C B A

14. Example:
A=2i+3j and B=-5i-7j What is A+B and A-B ?

15. Do for next class: Read: Sections 4.1, 4.2, 4.3
Suggested problems: 4.2, 4.3, 4.4