Vectors Scalars

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Vectors Scalars
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Vectordefinition

• Any quantity that needs a magnitude (size) and a
  direction to completely and clearly specify it.
• Examples
• displacement
• velocity
• acceleration
• force

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Scalar.definition

• Any quantity that only needs a magnitude (size)
  to completely and clearly specify it.
• Examples
• distance
• speed
• mass
• time

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Why Vectors?

• We need vectors because how big and how much
  are not always enough
• we need more clarity
• Vector or scalar is a classification for
  concepts.
• Like hearts or spades are to a deck of cards

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Examples

• I am 50 miles from Concord
• I am 50 miles South-East of Concord.
• Run 7 m/sec
• Run 7 m/sec West
• Apply 65 N of force
• Apply 65 N of force toward the right

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Graphic representations of vectors...

• We use arrows to represent vectors
• length tells about magnitude
• specific direction given by an angle with an axis

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Graphic addition of Vectors

• Vectors (arrows) are always added head to tail!

Does order of vector addition matter?
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A B C
C A B
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• What do you get when you add?
• a sum.
• What do you get when you add vectors?
• vectors
• What do you get when you add vectors together?

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• The sum of vectors added together is called the
  RESULTANT. (or resultant vector)
• The Resultant is always from where you start to
  where you end.

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End
Start
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• How many vectors could we add together to get
  resulting vector R?
• 2.
• 5..
• 40..
• infinite ?
• Infinite
• Would this be helpful?
• NO, its useless!

R
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Components

• A component is any vector you add to one or more
  other vectors to get a resultant.
• We care about the components that run along the x
  axis and y axis.
• Components are the Fll, the Fin, Fpulling,
  Flifting

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Direction of components count!
What kind of triangle!
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• What vector would be needed to cancel out the
  resultant?
• Wouldnt it be
• equal in magnitude
• and opposite
• in direction?

Equilibrant
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So what a quantity is a vector?!

• Direction matters.
• It can be canceled out.

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• Which vector is at 30?

Directions have to be more specific than an
angle.
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Or
20 N _at_
30 E of N
30
10 N of W
2 m/sec2_at_
1
4
10
50
2
45
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75 m _at_
45 W of S
or 45 SW
15 m/sec _at_
50 S of E