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 AxAx AyAy θ

y x A x < 0 AyAy θ φ

y x AyAy AxAx θ Given A and θ we found A x and A y Given A x and A y, find A and θ

Given A and θ we found A x and A y Given A x and A y, find A and θ Cx = C sin φ φ C y = C cos φ

Adding vectors numerically Also called algebraic addition What 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, 2 B.2, 3 C.-3, 2 D.2, -3 E.-3, -2 Slide 3-19

What are the x- and y-components of these vectors? A.3, -4 B.4, 3 C.-3, 4 D.4, -3 E.-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, 2.0 B.-2.0, 3.5 C.-3.5, 2.0 D.2.0, -3.5 E.-3.5, -2.0 Slide 3-23

A x is the __________ of the vector A. 1.Magnitude 2.X-component 3.Direction 4.Size 5.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