Vectors and TwoDimensional Motion

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Vectors and Two-Dimensional Motion

• Vectors in Two Dimensions

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Adding Vectors Graphically
Place vectors head-to-tail
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Parallelogram Method

• Can move a vector parallel to itself

R A B
R B A
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Adding More Than 2 Vectors
Fig. 3.4, p. 56
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Vector Components

• Vector components related to magnitude and
  direction

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Negative Vectors

• -A has the same magnitude as A, but the opposite
  direction

A
Ay
-Ax
Ax
-Ay
-A
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Subtracting Vectors

• Subtraction is the same as adding the negative

Fig. 3.5, p. 56
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Vectors Multiplied by a Scalar

• Each component gets multiplied by scalar
• Division is the same as multiplying by 1/(scalar)
• If scalar is negative, direction is reversed

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Adding Vectors Algebraically
By
Ry
?
Ay
Ax
Bx
Rx
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Adding Vectors Algebraically
Check to make sure ? makes sense tan-1 only gives
? between -90 and 90
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Working in Two Dimensions

• Reference frame chosen for convenience
• ?r, v, and a are vectors know how to
• Break into x- and y-components
• Add/subtract components
• Convert result to magnitude and direction
• Two vectors are equal only if they have the same
  magnitude and direction

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Displacement Vector

• Point 1 is located by vector r1 with components
  x1 and y1
• It moves to point 2 via ?r with components ?x and
  ?y
• Point 2 is located by vector r2 with components
  x2 and y2

y
2
1
x
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Displacement Vector

• Vector addition holds true for displacement
  vectors and their components

y
2
?r
1
r2
r1
x
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Velocity Vectors

• Average Velocity

Components
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Acceleration Vectors

• Average Acceleration

Components
Instantaneous Acceleration