1. SCALAR QUANTITIES AND VECTOR QUANTITIES
Sumber Gambar
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SCALAR QUANTITIES AND VECTOR QUANTITIES

2. Scalar
Scalar quantities is a value without a direction, such as: density, volume, temperature
Length
Time
Energy
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scalar

3. Scalar
The scalar quantities comply with all rules of mathematical algebra
Example:
1) Temperature: (300 K K) = 500 K
2) Power: 200 J + (-50 Joule ) = 150 Joule.
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scalar

4. Vector Vector quantities is a value with a direction
Example: displacement, velocity, acceleration, force
Vector is expressed in a straight line with an arrow. The length of line shows the value of vector and the arrow direction shows the vector direction B AB b A
vector AB
vector b
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vector

5. Vector Components
Vector can be subdivided into 2 vector components, each of them has the same direction as X axis and Y axis in cartesian coordinate b b x y θ =
b cos θ
b sin θ
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vector

6. ˆ ˆ ˆ Unit Vector Vector can be expressed as a unit vector b
Unit Vector is a one unit vector and has the same direction with the vector component
Vector can be expressed as a unit vector b b ˆ b = a
Example 5 ˆ
a = magnitude (value) b ˆ
= unit vector
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Unit vector

7. ˆ ˆ ˆ ˆ Unit Vector i = unit vector in the same direction as X axis j
= unit vector in the same direction as Y axis y z x ˆ i k j k ˆ
= unit vector in the same direction as Z axis
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unit vector

8. Unit Vector ˆ i ˆ j ˆ c = 4 + 5 + 8 k
Vector can be expressed by unit vector as follows: c ˆ i ˆ j ˆ c = k
It means that vector has:
4 unit vector in the same direction as X axis, 5 unit vector in the same direction as Y axis,
8 unit vector in the same direction as Z axis c
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unit vector

9. ˆ ˆ Unit Vector c = 4 + 5 + 8 i j k z 8 k 5 y 4 j i x page: 9= ˆ i j k y z x ˆ i k j 4 5 8
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unit vector

10. Addition of Vector Example: c b d = + b
Vector can be result from 2 methods: d
1. Geometrical method
2. Analytical method c
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addition of vector

11. Geometrical Method
1. Poligon b c b d c
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Geometrical method

12. according cosinus rule:
Geometrical Method
2. Paralellogram b c d θ b c
according cosinus rule:
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Geometrical method

13. Disruption of vector in cartesian coordinate
Analytical Method
Disruption of vector in cartesian coordinate b c x y α β bx cx cy by b c
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analytical method

14. Disruption of vector in cartesian coordinate
Analytical Method
Disruption of vector in cartesian coordinate
by = b sin α
cy = c sin β b c x y α β bx cx cy by
bx = b cos α
cx = c cos β
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analytical method

15. ˆ Analytical Method The direction of can be determined as : d d
= dx + dy ˆ i j If  d dx dy
dy = by + (-cy)
dx = bx + cx
The direction of can be determined as : d or
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analytical method