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Vectors
2 Kinds of Physical    Quantities:
2 Kinds of Physical    Quantities:Scalar quantities
2 Kinds of Physical    Quantities:Scalar quantitiesVector quantities
Scalar Quantities:
Scalar Quantities:Scalar quantities have magnitude   (numerical value) and unit.          mass = 75Kg
Vector Quantities:
Vector Quantities:   Vector quantities have magnitude(numerical value), direction (+-) and                 unit.        Fo...
Examples:
Examples:Scalar
Examples:Scalar         Vector
Examples:Scalar         VectorMass
Examples:Scalar         VectorMassTemperature
Examples:Scalar         VectorMassTemperatureVolume
Examples:Scalar         VectorMassTemperatureVolumeDensity
Examples:Scalar         VectorMassTemperatureVolumeDensityWork
Examples:Scalar         VectorMassTemperatureVolumeDensityWorkSpeed
Examples:Scalar         VectorMassTemperatureVolumeDensityWorkSpeedDistance
Examples:Scalar         VectorMassTemperatureVolumeDensityWorkSpeedDistancePower
Examples:Scalar         VectorMassTemperatureVolumeDensityWorkSpeedDistancePowerHeat
Examples:Scalar         VectorMassTemperatureVolumeDensityWorkSpeedDistancePowerHeatEnergy
Examples:Scalar         VectorMassTemperatureVolumeDensityWorkSpeedDistancePowerHeatEnergy
Examples:Scalar         VectorMass           Force and weightTemperatureVolumeDensityWorkSpeedDistancePowerHeatEnergy
Examples:Scalar         VectorMass           Force and weightTemperature    PositionVolumeDensityWorkSpeedDistancePowerHea...
Examples:Scalar         VectorMass           Force and weightTemperature    PositionVolume         AccelerationDensityWork...
Examples:Scalar         VectorMass           Force and weightTemperature    PositionVolume         AccelerationDensity    ...
Examples:Scalar         VectorMass           Force and weightTemperature    PositionVolume         AccelerationDensity    ...
Examples:Scalar         VectorMass           Force and weightTemperature    PositionVolume         AccelerationDensity    ...
Examples:Scalar         VectorMass           Force and weightTemperature    PositionVolume         AccelerationDensity    ...
Examples:Scalar         VectorMass           Force and weightTemperature    PositionVolume         AccelerationDensity    ...
Examples:Scalar         VectorMass           Force and weightTemperature    PositionVolume         AccelerationDensity    ...
Examples:Scalar         VectorMass           Force and weightTemperature    PositionVolume         AccelerationDensity    ...
How is a vector represented?
How is a vector represented?         ( starting point               ( direction B         A )      A                     )...
How is a vector represented?                 ( starting point               ( direction B                 A )      A      ...
How is a vector represented?                   ( starting point               ( direction B                   A )      A  ...
Properties of Vectors:
Properties of Vectors:                                                    C          AD         B         C               ...
Vector Components:                                 Sin θ = Opp./Hyp.                   HypothenousOppositeside            ...
Addition and Subtraction Vectors can’t be added and subtracted the same way scalar   quantities can. Different rules apply ...
Parallelogram: (Tail to Tail)R        B                   R = A+B    A    A    R            -(B)     R = A-B
Polygon Method         (Head to Tail)                 R=A+B+CR        C                            B             B        ...
y    x
yAx              xA         Ay
Vector Components
Vector Components           A
Vector Components           A   B
Vector Components             A   B         C
Vector Components     x   yA   -4   3B    0   3                AC    2   2      BR   -2   8                      C
Vector Components     x   yA   -4   3B    0   3                AC    2   2      BR   -2   8                      C
Vector Components     x   yA   -4   3B    0   3                AC    2   2      BR   -2   8                      C
Vector Components     x   yA   -4   3B    0   3                AC    2   2      BR   -2   8                      C
Vector Components     x   yA   -4   3B    0   3                AC    2   2      BR   -2   8                      C
Vector Components     x   yA   -4   3B    0   3                AC    2   2      BR   -2   8                      C
Vector Components     x   yA   -4   3B    0   3                AC    2   2      BR   -2   8                      C
Vector Components     x   yA   -4   3B    0   3                AC    2   2      BR   -2   8                      C
Vector Components     x   yA   -4   3B    0   3                AC    2   2      BR   -2   8                      C
Vector Components     x   yA   -4   3B    0   3                AC    2   2      BR   -2   8                      C
Vector Components     x   yA   -4   3B    0   3                AC    2   2      BR   -2   8                      C
Vector Components     x   yA   -4   3B    0   3                AC    2   2      BR   -2   8                      C
Vector Components     x   yA   -4   3B    0   3                AC    2   2      BR   -2   8                      C
Vector Components     x   yA   -4   3B    0   3                AC    2   2      BR   -2   8                      C
Vector Components     x   yA   -4   3B    0   3                AC    2   2      BR   -2   8                      C
Resultant Vector     x   yA   -4   3B    0   3C    2   2R   -2   8
Resultant Vector     x   yA   -4   3B    0   3C    2   2R   -2   8
Resultant Vector     x   yA   -4   3B    0   3C    2   2R   -2   8                      R
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Vectors

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Scalar and Vector quantities.

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  • Transcript of "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
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