Lecture 8: Vector Components

Average amount spent lobbying Congress each day it was in session last year:

$16,279,069

Vector Components

y

x

A

Ax

Ay

θ

cossin

x

y

A AA A

y

xAx < 0

Ay

θ

φ

coscossin

x

y

A AA

A A

y

x

Ay

Ax

2 2

1tan

x y

y

x

A A A

AA

θ

Given A and θ we found Ax and Ay

Given Ax and Ay, find A and θ

Given A and θ we found Ax and Ay

Given Ax and Ay, find A and θ

Cx = C sin φ

φCy = C cos φ

2 2x yC C C

1tan x

y

CC

Adding vectors numerically

x x x

y y y

C A BC A BC A B

Also called algebraic additionWhat would subtraction look like?Scalar multiplication?

Slide 3-13

Which of the vectors below best represents the vector sum P + Q?

Slide 3-14

Which of the vectors below best represents the vector sum P + Q?

Answer

Slide 3-15

Which of the vectors below best represents the difference P – Q?

Slide 3-16

Which of the vectors below best represents the difference P – Q?

Answer

What are the x- and y-components of these vectors?

A. 3, 2B. 2, 3C. -3, 2D. 2, -3E. -3, -2

Slide 3-19

What are the x- and y-components of these vectors?

A. 3, -4B. 4, 3C. -3, 4D. 4, -3E. -3, -4

Slide 3-21

The following vectors have length 4.0 units.What are the x- and y-components of these vectors?

A. 3.5, 2.0B. -2.0, 3.5C. -3.5, 2.0D. 2.0, -3.5E. -3.5, -2.0

Slide 3-23

Ax is the __________ of the vector A.

Magn

itude

X-component

Directi

on Si

ze

displace

ment

20% 20% 20%20%20%1. Magnitude2. X-component3. Direction4. Size5. displacement

Monday

• Review for Exam I• Chapter 1 motion diagrams, unit conversion• Chapter 2 motion in 1-dimension, constant

velocity, constant acceleration• Chapter 3 (part) add vectors graphically,

algebraically, components