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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Chapter 3. Vectors and Coordinate SystemsChapter 3. Vectors and Coordinate SystemsOur universe has three dimensions, so some quantities also need a direction for a full description. For example, wind has both a speed and a direction; hence the motion of the wind is described by a vector.Chapter Goal: To learn how vectors are represented and used.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Student Learning Objectives – Ch. 3
• To understand the basic properties of vectors.• To add and subtract vectors both graphically and
using components.• To be able to decompose a vector into its
components and to reassemble vector components into a magnitude and a direction.
• To recognize and use the basic unit vectors.• To work with tilted coordinate systems.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Graphical Vector Addition
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Tip to Tail Method
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Parallelogram Method
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Vector Addition Problem
• Which figure shows A1 + A2 + A3?
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Which figure shows ? A A A1 2 3
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Multiplication by a scalar
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Vector Subtraction
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Vector Subtraction
• Which figure shows 2A – B?
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Which figure shows 2 − ?A
B
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Components of vectors
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Magnitude of A:
A = (Ax2 + Ay
2)1/2
Direction of A:
θ = tan-1 (Ay/Ax)
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What are the x- and y-components Cx and Cy of vector ?
C
A. Cx = 1 cm, Cy = –1 cmB. Cx = –3 cm, Cy = 1 cmC. Cx = –2 cm, Cy = 1 cmD. Cx = –4 cm, Cy = 2 cmE. Cx = –3 cm, Cy = –1 cm
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
What are the x- and y-components Cx and Cy of vector ?
C
A. Cx = 1 cm, Cy = –1 cmB. Cx = –3 cm, Cy = 1 cmC. Cx = –2 cm, Cy = 1 cmD. Cx = –4 cm, Cy = 2 cmE. Cx = –3 cm, Cy = –1 cm
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Workbook problems 12, 13, 15, 16, 18
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Workbook problems 12, 13, 15, 16, 18 - answers
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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Workbook exercises 25-29
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Workbook exercises 25-29 - answers
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Tilted axes• Often is it convenient to tilt
the coordinate axes (to represent an object on an incline for example).
• The axes stay perpendicular to each other.
• The unit vectors corespond to axes, not to “horizontal and vertical” so they are also tilted.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Tilted axes• Cx = C cos θ
• Cy = C sin θ
• Note that θ is defined relative to the tilted x-axis and not to “horizontal”
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE 3.7 Finding the force perpendicular to a surface
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EXAMPLE 3.7 Finding the force perpendicular to a surface
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EXAMPLE 3.7 Finding the force perpendicular to a surface
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Workbook problems 26, 27,28,30, 31
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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Chapter 3. Summary SlidesChapter 3. Summary Slides
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Important Concepts
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Important Concepts
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Using Vectors
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Using Vectors
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Using Vectors
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Using Vectors
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Chapter 3. Clicker QuestionsChapter 3. Clicker Questions
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Which figure shows ? A A A1 2 3
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Which figure shows 2 − ?A
B
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A. tan–1(Cy /Cx)B. tan–1(Cx /|Cy|)C. tan–1(Cy /|Cx|)D. tan–1(Cx /Cy)E. tan–1(|Cx |/|Cy|)
Angle φ that specifies the direction of is given by
C
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
A. tan–1(Cy /Cx)B. tan–1(Cx /|Cy|)C. tan–1(Cy /|Cx|)D. tan–1(Cx /Cy)E. tan–1(|Cx |/|Cy|)
Angle φ that specifies the direction of is given by
C
