chapter03 - Chapter 3 Vectors and Two-Dimensional Motion...

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Chapter 3 Vectors and Two-Dimensional Motion
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Vector vs. Scalar Review All physical quantities encountered in this text will be either a scalar or a vector A vector quantity has both magnitude (size) and direction A scalar is completely specified by only a magnitude (size)
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Vector Notation When handwritten, use an arrow: When printed, will be in bold print with an arrow: When dealing with just the magnitude of a vector in print, an italic letter will be used: A Italics will also be used to represent scalars A A
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Properties of Vectors Equality of Two Vectors Two vectors are equal if they have the same magnitude and the same direction Movement of vectors in a diagram Any vector can be moved parallel to itself without being affected
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More Properties of Vectors Negative Vectors Two vectors are negative if they have the same magnitude but are 180° apart (opposite directions) Resultant Vector The resultant vector is the sum of a given set of vectors ;0 A B A A R A B
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Adding Vectors When adding vectors, their directions must be taken into account Units must be the same Geometric Methods Use scale drawings Algebraic Methods More convenient
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Adding Vectors Geometrically (Triangle or Polygon Method) Choose a scale Draw the first vector with the appropriate length and in the direction specified, with respect to a coordinate system Draw the next vector using the same scale with the appropriate length and in the direction specified, with respect to a coordinate system whose origin is the end of vector and parallel to the coordinate system used for A A
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Graphically Adding Vectors, cont. Continue drawing the vectors “tip -to- tail” The resultant is drawn from the origin of to the end of the last vector Measure the length of and its angle Use the scale factor to convert length to actual magnitude A R
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Graphically Adding Vectors, cont. When you have many vectors, just keep repeating the process until all are included The resultant is still drawn from the origin of the first vector to the end of the last vector
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Notes about Vector Addition Vectors obey the Commutative Law of Addition The order in which the vectors are added doesn’t affect the result A B B A
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Vector Subtraction Special case of vector addition Add the negative of the subtracted vector Continue with standard vector addition procedure A B A B
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Multiplying or Dividing a Vector by a Scalar The result of the multiplication or division is a vector The magnitude of the vector is multiplied or divided by the scalar If the scalar is positive, the direction of
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This note was uploaded on 04/12/2011 for the course PHYS 1410 taught by Professor Staff during the Spring '08 term at North Texas.

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chapter03 - Chapter 3 Vectors and Two-Dimensional Motion...

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