Scalar and Vector quantities.

1. Vectors

2. 2 Kinds of Physical
Quantities:

3. 2 Kinds of Physical
Quantities:
Scalar quantities

4. 2 Kinds of Physical
Quantities:
Scalar quantities
Vector quantities

5. Scalar Quantities:

6. Scalar Quantities:
Scalar quantities have magnitude
(numerical value) and unit.
mass = 75Kg

7. Vector Quantities:

8. Vector Quantities:
Vector quantities have magnitude
(numerical value), direction (+-) and
unit.
Force = 55N due east

9. Examples:

10. Examples:
Scalar

11. Examples:
Scalar Vector

12. Examples:
Scalar Vector
Mass

13. Examples:
Scalar Vector
Mass
Temperature

14. Examples:
Scalar Vector
Mass
Temperature
Volume

15. Examples:
Scalar Vector
Mass
Temperature
Volume
Density

16. Examples:
Scalar Vector
Mass
Temperature
Volume
Density
Work

17. Examples:
Scalar Vector
Mass
Temperature
Volume
Density
Work
Speed

18. Examples:
Scalar Vector
Mass
Temperature
Volume
Density
Work
Speed
Distance

19. Examples:
Scalar Vector
Mass
Temperature
Volume
Density
Work
Speed
Distance
Power

20. Examples:
Scalar Vector
Mass
Temperature
Volume
Density
Work
Speed
Distance
Power
Heat

21. Examples:
Scalar Vector
Mass
Temperature
Volume
Density
Work
Speed
Distance
Power
Heat
Energy

22. Examples:
Scalar Vector
Mass
Temperature
Volume
Density
Work
Speed
Distance
Power
Heat
Energy

23. Examples:
Scalar Vector
Mass Force and weight
Temperature
Volume
Density
Work
Speed
Distance
Power
Heat
Energy

24. Examples:
Scalar Vector
Mass Force and weight
Temperature Position
Volume
Density
Work
Speed
Distance
Power
Heat
Energy

25. Examples:
Scalar Vector
Mass Force and weight
Temperature Position
Volume Acceleration
Density
Work
Speed
Distance
Power
Heat
Energy

26. Examples:
Scalar Vector
Mass Force and weight
Temperature Position
Volume Acceleration
Density Velocity
Work
Speed
Distance
Power
Heat
Energy

27. Examples:
Scalar Vector
Mass Force and weight
Temperature Position
Volume Acceleration
Density Velocity
Work Momentum
Speed
Distance
Power
Heat
Energy

28. Examples:
Scalar Vector
Mass Force and weight
Temperature Position
Volume Acceleration
Density Velocity
Work Momentum
Speed Displacement
Distance
Power
Heat
Energy

29. Examples:
Scalar Vector
Mass Force and weight
Temperature Position
Volume Acceleration
Density Velocity
Work Momentum
Speed Displacement
Distance Magnetic field
Power
Heat
Energy

30. Examples:
Scalar Vector
Mass Force and weight
Temperature Position
Volume Acceleration
Density Velocity
Work Momentum
Speed Displacement
Distance Magnetic field
Power Electric field
Heat
Energy

31. Examples:
Scalar Vector
Mass Force and weight
Temperature Position
Volume Acceleration
Density Velocity
Work Momentum
Speed Displacement
Distance Magnetic field
Power Electric field
Heat Gravity
Energy

32. Examples:
Scalar Vector
Mass Force and weight
Temperature Position
Volume Acceleration
Density Velocity
Work Momentum
Speed Displacement
Distance Magnetic field
Power Electric field
Heat Gravity
Energy Impulse

33. How is a vector represented?

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. 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 )

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. Properties of Vectors:

38. Properties of Vectors:
C
A
D B C D X
A
F
E B
G
Fig.1.2.1 Fig.1.2.2

39. Vector Components:
Sin θ = Opp./Hyp.
Hypothenous
Opposite
side
Cos θ = Adj./Hyp.
Adjacent
side
Tan θ = Opp./Adj.
20m/s
60º

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 or
subtracting vectors. Either one will produce the same results.
•Parallelogram
•Polygon Method
The new vector formed from the vectors added or subtracted
is called the resultant vector.

41. Parallelogram:
(Tail to Tail)
R
B
R = A+B
A
A
R
-(B) R = A-B

42. Polygon Method
(Head to Tail)
R=A+B+C
R C
B
B -C
A A
R1
R1=A+B-C

43. y
x

44. y
Ax
x
A
Ay

45. Vector Components

46. Vector Components
A

47. Vector Components
A
B

48. Vector Components
A
B
C

49. Vector Components
x y
A -4 3
B 0 3 A
C 2 2 B
R -2 8
C

50. Vector Components
x y
A -4 3
B 0 3 A
C 2 2 B
R -2 8
C

51. Vector Components
x y
A -4 3
B 0 3 A
C 2 2 B
R -2 8
C

52. Vector Components
x y
A -4 3
B 0 3 A
C 2 2 B
R -2 8
C

53. Vector Components
x y
A -4 3
B 0 3 A
C 2 2 B
R -2 8
C

54. Vector Components
x y
A -4 3
B 0 3 A
C 2 2 B
R -2 8
C

55. Vector Components
x y
A -4 3
B 0 3 A
C 2 2 B
R -2 8
C

56. Vector Components
x y
A -4 3
B 0 3 A
C 2 2 B
R -2 8
C

57. Vector Components
x y
A -4 3
B 0 3 A
C 2 2 B
R -2 8
C

58. Vector Components
x y
A -4 3
B 0 3 A
C 2 2 B
R -2 8
C

59. Vector Components
x y
A -4 3
B 0 3 A
C 2 2 B
R -2 8
C

60. Vector Components
x y
A -4 3
B 0 3 A
C 2 2 B
R -2 8
C

61. Vector Components
x y
A -4 3
B 0 3 A
C 2 2 B
R -2 8
C

62. Vector Components
x y
A -4 3
B 0 3 A
C 2 2 B
R -2 8
C

63. Vector Components
x y
A -4 3
B 0 3 A
C 2 2 B
R -2 8
C

64. Resultant Vector
x y
A -4 3
B 0 3
C 2 2
R -2 8

65. Resultant Vector
x y
A -4 3
B 0 3
C 2 2
R -2 8

66. Resultant Vector
x y
A -4 3
B 0 3
C 2 2
R -2 8
R