Vector Mathematics

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Vector Mathematics
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Why?

• One can add 23 kg and 42 kg and get 65 kg.
• However, one cannot add together 23 m/s south and
  42 m/s southeast and get 65 m/s south-southeast.
• Vectors addition takes into account adding both
  magnitude and direction

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Words

• Vector A measured quantity with both magnitude
  and direction
• Scalar A measured quantity with magnitude only
• Resultant Vector The final vector of a vector
  math problem

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Vector addition

• Two Ways
• Graphically Draw vectors to scale, Tip to Tail,
  and the resultant is the straight line from start
  to finish
• Mathematically Employ vector math analysis to
  solve for the resultant vector

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Graphically 1-D

• A 5.0 m east
• B 2.0 m east
• Solve A B

Start
R
R 7.0 m east
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Graphically 2-D Right

• A 5.0 m East
• B 5.0 m North
• Solve A B

R
R7.1 m Northeast
Start
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But what if

• the vectors are not equal in length initially
  and not at right angles. NE would not make
  sense. Therefore we need a better coordinate
  system!

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Compass Coordinate System
N 0º
E 90º
W 270º
S 180º
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Math (general) Coordinate System
90º
180º
0º
270º
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Polar Coordinate System
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Polar ?? Math
r
y
?
x
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Lets get back to adding

• Go back to the previous examples and assign
  general angle (math) and polar directions then
  solve mathematically

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Important

• You can add vectors in any order and yield the
  same resultant.

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Try this one
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What?!?

• The math you used previously doesnt work (and I
  wont let you use the Law of Sines or Cosines) or
  does it???
• What we will do is break each vector into
  components
• The components are the x and y values of the
  polar coordinate (go back 6 slides)
• Check out the next slide

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The Table Method

• We will organize these components in a table.
• See the board for this part.

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Subtracting Vectors

• Simply add or subtract 180 (keep ? between 0
  and 360) to the direction of the vector being
  subtracted
• You just ADD the OPPOSITE vector (there is no
  subtraction in vector math)
• Or subtract the proper component in the table

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Subtracting Vectors
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Relative Velocity
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• Read Ch 3
• pp 81 - 94

• HW due on test day
• P 85 1, 5
• P 89 1 4
• P 92 3, 4
• P 94 C 1 - 4