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# Physics 504 chapter 8 vectors

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### Physics 504 chapter 8 vectors

1. 1. Chapter 8 Vectors Physics 504
2. 2. Scalars and Vectors A scalar quantity has a size and unit. E.g. 16 N (Newtons) A vector quantity has a size, unit and direction. E.g. 5 km/h [N] (North)
3. 3. Distance and Displacement Distance travelled depends on position. Distance is a scalar quantity. It is always positive. E.g. d = 5 km
4. 4. Distance and Displacement Displacement depends on the new position compared to the old position. Displacement is a vector quantity. E.g. Δd or đ = 5 km North
5. 5. Exam QuestionThe following graph represents the trail followed by a hiker going from A to F (A –> B –> C –> D –> E –> F). One centimetre represents 100 metres.What is the displacement of the hiker? A) 1 700 m B) 700 m C) 500 m D) 200 m
6. 6. The Cardinal Points
7. 7. Cardinal Points II Never Eat Slimey Worms ½ way between North [N] andWest [W] is NorthWest [NW] ½ way between NW and N is NNW
8. 8. Trigonometric Direction [East] = 0° [North] = 90° [West] = 180° [South] = 270°
9. 9. Cardinal and Degrees [N 45 ° E] means you start at North and turn 45 ° East. It is also known as NE. Or as 45 °
10. 10. Vector Addition We can show vectors as arrows in diagrams. We add vectors tip to tail. Vector Ả +Vector B = Vector B + Vector Ả The result of adding two or more vectors is the RESULTANT VECTOR. Vectors are written with little arrows on top.
11. 11. Vector Diagrams
12. 12. Vector Subtraction To subtract a vector from another, you add the opposite. Vector A – Vector B = Vector A + (-Vector B)
13. 13. Activity Page 189, Q 1 – 6 Page 192, Q 1 – 3 Page 195, Q 1 – 4 Page 197, Q. 1 - 2
14. 14. Multiplying Vectors Multiplying vectors only changes magnitude not direction (if positive). ā = (1,2); 3 ā = (3,6) đ = 5 km 45°; 2đ = 10 km 45°
15. 15. Vector Division It is just like vector multiplication, but with a fraction. N.B. multiplying by a negative ř = (3,2); - ř = (-3,-2) Ŝ = 2 m [N]; -ŝ = 2m [S]
16. 16. x-Component of a Vector ā-hyp opp Θ y-part adj x – parts Cos θ = adj/hyp = x/ā Thus, x = ā cos θ
17. 17. y-Component of a Vector ā-hyp opp Θ y-part adj x – parts sin θ = opp/hyp = x/ā Thus, y = ā sin θ
18. 18. Addition of Vectors: Component Method Add the x-components of the vectors together. Add the y-components of the vectors together. Add the total x vector to the total y vector tip to tail.
19. 19. Tools for Solving You can use diagrams; Pythagoras c2 = a2 + b2; Sine Law Cosine Law SOHCAHTOA
20. 20. Summary Some motions can be seen easily; other motions must be observed using other senses or devices. The trajectory is the path of a moving object.
21. 21. Summary Vector quantities have magnitude and direction. Scalar quantities only have magnitude. Displacement, or change in position, is a vector quantity.
22. 22. Summary Distance, the path length, is a scalar quantity. Add vectors tip to tail. Page 199, Q 1 - 5
23. 23. Activity Design an Amazing Race
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