Vectors

1
Vectors

• Represent magnitude and direction
• Example Displacement
• go 2 miles East

2
Vector Quantities

• Force
• Velocity
• Magnetic Field

3
Vector Notation

• Vector Bold or arrow over

Scalar Italic, no arrow
4
Numerical Description

• Polar Form
• Magnitude and angle
• Rectangular Form
• x- and y-components

5
Polar Form
V
Magnitude
Angle
V (r, q ) V (53, 65)
V r?q V 53?65
6
Rectangular Form
V
VxV cos q
V
VyV sin q
Vy
q
Vx
7
Rectangular to Polar
8
Vector Addition

• Resultant vector
• Not the sum of the magnitudes
• Vectors add head-to-tail

9
Vector Addition Example

• Go 3 miles East,
• then 4 Miles North

R
4
R 5 miles at 53
3
10
Adding Nonperpendicular Vectors

• x-components add to givex-component of resultant
• y-components add to givey-component of resultant

11
Adding Nonperpendicular Vectors
R
R A B
B
A
Rx Ax Bx
Ry Ay By
12
Adding Nonperpendicular Vectors
By
Ry
Ay
Ax
Bx
Rx