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Lecture 8: Vector Components

This lecture covers the analysis of vector components and the numerical addition of vectors, along with concepts such as scalar multiplication and vector subtraction. It delves into how to determine vector sums and differences visually and algebraically. Additionally, the session provides context with an example highlighting the average amount spent on lobbying Congress, which was approximately $16,279,069 daily when it was in session last year. The material is designed to help students prepare for Exam I, covering fundamental motion concepts in physics.

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Lecture 8: Vector Components

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  1. Lecture 8: Vector Components Average amount spent lobbying Congress each day it was in session last year: $16,279,069

  2. Vector Components y A Ay θ x Ax

  3. y Ay θ φ x Ax < 0

  4. Given A and θ we found Ax and Ay Given Ax and Ay, find A and θ y Ay θ Ax x

  5. Given A and θ we found Ax and Ay Given Ax and Ay, find A and θ φ Cy = C cosφ Cx = C sin φ

  6. Adding vectors numerically Also called algebraic addition What would subtraction look like? Scalar multiplication?

  7. Which of the vectors below best represents the vector sum P + Q?   Slide 3-13

  8. Answer Which of the vectors below best represents the vector sum P + Q?   Slide 3-14

  9. Which of the vectors below best represents the difference P – Q?   Slide 3-15

  10. Answer Which of the vectors below best represents the difference P – Q?   Slide 3-16

  11. What are the x- and y-components of these vectors? 3, 2 2, 3 -3, 2 2, -3 -3, -2 Slide 3-19

  12. What are the x- and y-components of these vectors? 3, -4 4, 3 -3, 4 4, -3 -3, -4 Slide 3-21

  13. The following vectors have length 4.0 units. What are the x- and y-components of these vectors? 3.5, 2.0 -2.0, 3.5 -3.5, 2.0 2.0, -3.5 -3.5, -2.0 Slide 3-23

  14. Ax is the __________ of the vector A. • Magnitude • X-component • Direction • Size • displacement

  15. 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

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