PHY 113 C General Physics I 11 AM-12:15 PM TR Olin 101 Plan for Lecture 3: Chapter 3 – Vectors

1. PHY 113 C General Physics I • 11 AM-12:15 PM TR Olin 101 • Plan for Lecture 3: • Chapter 3 – Vectors • Abstract notion of vectors • Displacement vectors • Other examples PHY 113 C Fall 2013 -- Lecture 3

2. PHY 113 C Fall 2013 -- Lecture 3

3. PHY 113 C Fall 2013 -- Lecture 3

4. iclicker question • Have you attended a tutoring session yet? • Have you attended a lab session yet? • Have you attended both tutoring and lab sessions? PHY 113 C Fall 2013 -- Lecture 3

5. iclicker question • Have you changed your webassign password yet? • yes • no Mathematics Review -- Appendix B Serwey & Jewett • iclicker question • Have you used this appendix? • Have you used the appendix, and find it helpful? • Have you used the appendix, but find it unhelpful? PHY 113 C Fall 2013 -- Lecture 3

6. Question from Webassign #2 8 6 4 2 0 -2 1 2 3 4 5 6 7 8 9 10 -4 -6 -8 PHY 113 C Fall 2013 -- Lecture 3

7. Mathematics Review -- Appendix B Serwey & Jewett c a q b PHY 113 C Fall 2013 -- Lecture 3

8. Definition of a vector • A vector is defined by its length and direction. • Addition, subtraction, and two forms of multiplication can be defined • In practice, we can use trigonometry or component analysis for quantitative work involving vectors. • Abstract vectors are useful in physics and mathematics. PHY 113 C Fall 2013 -- Lecture 3

9. Vector addition: a + b b a Vector subtraction: a a – b -b PHY 113 C Fall 2013 -- Lecture 3

10. Some useful trigonometric relations (see Appendix B of your text) c a Law of cosines: a2 = b2 + c2 - 2bc cosa b2 = c2 + a2 - 2ca cosb c2 = a2 + b2 - 2ab cosg b a b g Law of sines: PHY 113 C Fall 2013 -- Lecture 3

11. Some useful trigonometric relations -- continued (from Appendix B of your text) c a Law of cosines: a2 = b2 + c2 - 2bc cosa b2 = c2 + a2 - 2ca cosb c2 = a2 + b2 - 2ab cosg b a b g PHY 113 C Fall 2013 -- Lecture 3

12. Some useful trigonometric relations -- continued Example: c=? a Law of cosines: a2 = b2 + c2 - 2bc cosa b2 = c2 + a2 - 2ca cosb c2 = a2 + b2 - 2ab cosg b 10 15 20o PHY 113 C Fall 2013 -- Lecture 3

13. Possible realization of previous example: Start c=? East treasure a b 10m 15m 20o A pirate map gives directions to buried treasure following the indicated arrows. A wily physics students decides to take the easterly direct route after computing the distance c. South PHY 113 C Fall 2013 -- Lecture 3

14. Quantitative representation of a vector Cartesian coordinates A Ay Ax PHY 113 C Fall 2013 -- Lecture 3

15. Quantitative representation of a vector Polar coordinates q reference direction Note: q can be specified in degrees or radians; make sure that your calculator knows your intentions! PHY 113 C Fall 2013 -- Lecture 3

16. Quantitative representation of a vector Polar & cartesian coordinates q PHY 113 C Fall 2013 -- Lecture 3

17. Vector components: ay ax PHY 113 C Fall 2013 -- Lecture 3

18. Suppose you are given the length of the vector a as shown. How can you find the components? iclicker question y ax=a cosq, ay=a sin q ax=a sin y, ay=a cosy Neither of these Both of these a = 1 m q ay ax PHY 113 C Fall 2013 -- Lecture 3

19. Vector components; using trigonometry A An orthogonal coordinate system PHY 113 C Fall 2013 -- Lecture 3

20. Vector components: by bx ay ax PHY 113 C Fall 2013 -- Lecture 3

21. Examples PHY 113 C Fall 2013 -- Lecture 3

22. Vector components Vector multiplication “Dot” product “Cross” product PHY 113 C Fall 2013 -- Lecture 3

23. Example of vector addition: b a + b a PHY 113 C Fall 2013 -- Lecture 3

24. b a + b g a PHY 113 C Fall 2013 -- Lecture 3

25. Webassign version: Note: In this case the angle f is actually measured as north of east. f PHY 113 C Fall 2013 -- Lecture 3

26. Another example: PHY 113 C Fall 2013 -- Lecture 3

27. iclicker question Why are we spending 75 minutes discussing vectors Because physics professors like to confuse students Because physics professors like to use beautiful mathematical concepts if at all possible Because all physical phenomena can be described by vectors. Because there are some examples in physics that can be described by vectors PHY 113 C Fall 2013 -- Lecture 3

28. Example: Vector addition of velocities Vb Vw Vtotal PHY 113 C Fall 2013 -- Lecture 3

29. Example: Displacement in two dimensions (8,5) (0,0) PHY 113 C Fall 2013 -- Lecture 3