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# Vectors

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Scalar and Vector quantities.

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• ### Vectors

1. 1. Vectors
2. 2. 2 Kinds of Physical Quantities:
3. 3. 2 Kinds of Physical Quantities:Scalar quantities
4. 4. 2 Kinds of Physical Quantities:Scalar quantitiesVector quantities
5. 5. Scalar Quantities:
6. 6. Scalar Quantities:Scalar quantities have magnitude (numerical value) and unit. mass = 75Kg
7. 7. Vector Quantities:
8. 8. Vector Quantities: Vector quantities have magnitude(numerical value), direction (+-) and unit. Force = 55N due east
9. 9. Examples:
10. 10. Examples:Scalar
11. 11. Examples:Scalar Vector
12. 12. Examples:Scalar VectorMass
13. 13. Examples:Scalar VectorMassTemperature
14. 14. Examples:Scalar VectorMassTemperatureVolume
15. 15. Examples:Scalar VectorMassTemperatureVolumeDensity
16. 16. Examples:Scalar VectorMassTemperatureVolumeDensityWork
17. 17. Examples:Scalar VectorMassTemperatureVolumeDensityWorkSpeed
18. 18. Examples:Scalar VectorMassTemperatureVolumeDensityWorkSpeedDistance
19. 19. Examples:Scalar VectorMassTemperatureVolumeDensityWorkSpeedDistancePower
20. 20. Examples:Scalar VectorMassTemperatureVolumeDensityWorkSpeedDistancePowerHeat
21. 21. Examples:Scalar VectorMassTemperatureVolumeDensityWorkSpeedDistancePowerHeatEnergy
22. 22. Examples:Scalar VectorMassTemperatureVolumeDensityWorkSpeedDistancePowerHeatEnergy
23. 23. Examples:Scalar VectorMass Force and weightTemperatureVolumeDensityWorkSpeedDistancePowerHeatEnergy
24. 24. Examples:Scalar VectorMass Force and weightTemperature PositionVolumeDensityWorkSpeedDistancePowerHeatEnergy
25. 25. Examples:Scalar VectorMass Force and weightTemperature PositionVolume AccelerationDensityWorkSpeedDistancePowerHeatEnergy
26. 26. Examples:Scalar VectorMass Force and weightTemperature PositionVolume AccelerationDensity VelocityWorkSpeedDistancePowerHeatEnergy
27. 27. Examples:Scalar VectorMass Force and weightTemperature PositionVolume AccelerationDensity VelocityWork MomentumSpeedDistancePowerHeatEnergy
28. 28. Examples:Scalar VectorMass Force and weightTemperature PositionVolume AccelerationDensity VelocityWork MomentumSpeed DisplacementDistancePowerHeatEnergy
29. 29. Examples:Scalar VectorMass Force and weightTemperature PositionVolume AccelerationDensity VelocityWork MomentumSpeed DisplacementDistance Magnetic fieldPowerHeatEnergy
30. 30. Examples:Scalar VectorMass Force and weightTemperature PositionVolume AccelerationDensity VelocityWork MomentumSpeed DisplacementDistance Magnetic fieldPower Electric fieldHeatEnergy
31. 31. Examples:Scalar VectorMass Force and weightTemperature PositionVolume AccelerationDensity VelocityWork MomentumSpeed DisplacementDistance Magnetic fieldPower Electric fieldHeat GravityEnergy
32. 32. Examples:Scalar VectorMass Force and weightTemperature PositionVolume AccelerationDensity VelocityWork MomentumSpeed DisplacementDistance Magnetic fieldPower Electric fieldHeat GravityEnergy Impulse
33. 33. How is a vector represented?
34. 34. How is a vector represented? ( starting point ( direction B A ) A )B Y X ( line of action XY ) (the length of AB line segment
35. 35. How is a vector represented? ( starting point ( direction B A ) A )B Y X ( line of action XY ) (the length of AB line segmentVectors are usually bold typed and represented by an arrow above the letter. For instance: Force ( F )
36. 36. How is a vector represented? ( starting point ( direction B A ) A )B Y X ( line of action XY ) (the length of AB line segment Vectors are usually bold typed and represented by an arrow above the letter. For instance: Force ( F )The magnitude of a vector is represented by the absolute value of the vector and it doesn’t have the arrow above the letter. F =F
37. 37. Properties of Vectors:
38. 38. Properties of Vectors: C AD B C D X A F E B G Fig.1.2.1 Fig.1.2.2
39. 39. Vector Components: Sin θ = Opp./Hyp. HypothenousOppositeside Cos θ = Adj./Hyp. Adjacent side Tan θ = Opp./Adj. 20m/s 60º
40. 40. Addition and Subtraction Vectors can’t be added and subtracted the same way scalar quantities can. Diﬀerent rules apply because vectors involve direction. There are 2 diﬀerent methods for graphically adding orsubtracting vectors. Either one will produce the same results. •Parallelogram •Polygon MethodThe new vector formed from the vectors added or subtracted is called the resultant vector.
41. 41. Parallelogram: (Tail to Tail)R B R = A+B A A R -(B) R = A-B
42. 42. Polygon Method (Head to Tail) R=A+B+CR C B B -C A A R1 R1=A+B-C
43. 43. y x
44. 44. yAx xA Ay
45. 45. Vector Components
46. 46. Vector Components A
47. 47. Vector Components A B
48. 48. Vector Components A B C
49. 49. Vector Components x yA -4 3B 0 3 AC 2 2 BR -2 8 C
50. 50. Vector Components x yA -4 3B 0 3 AC 2 2 BR -2 8 C
51. 51. Vector Components x yA -4 3B 0 3 AC 2 2 BR -2 8 C
52. 52. Vector Components x yA -4 3B 0 3 AC 2 2 BR -2 8 C
53. 53. Vector Components x yA -4 3B 0 3 AC 2 2 BR -2 8 C
54. 54. Vector Components x yA -4 3B 0 3 AC 2 2 BR -2 8 C
55. 55. Vector Components x yA -4 3B 0 3 AC 2 2 BR -2 8 C
56. 56. Vector Components x yA -4 3B 0 3 AC 2 2 BR -2 8 C
57. 57. Vector Components x yA -4 3B 0 3 AC 2 2 BR -2 8 C
58. 58. Vector Components x yA -4 3B 0 3 AC 2 2 BR -2 8 C
59. 59. Vector Components x yA -4 3B 0 3 AC 2 2 BR -2 8 C
60. 60. Vector Components x yA -4 3B 0 3 AC 2 2 BR -2 8 C
61. 61. Vector Components x yA -4 3B 0 3 AC 2 2 BR -2 8 C
62. 62. Vector Components x yA -4 3B 0 3 AC 2 2 BR -2 8 C
63. 63. Vector Components x yA -4 3B 0 3 AC 2 2 BR -2 8 C
64. 64. Resultant Vector x yA -4 3B 0 3C 2 2R -2 8
65. 65. Resultant Vector x yA -4 3B 0 3C 2 2R -2 8
66. 66. Resultant Vector x yA -4 3B 0 3C 2 2R -2 8 R