# lecture4 - Chapter 3 Vectors and Two-Dimensional Two...

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Chapter 3 Vectors and wo- imensional Motion Two Dimensional Motion 1

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Two Dimensional Motion y x An object may move in both the x and y directions simultaneously O It moves in two dimensions 2
Vector vs. Scalar Review All physical quantities encountered this text will be either a scalar in this text will be either a scalar or a vector ector uantity has both A vector quantity has both magnitude (size) and direction calar completely specified by A scalar is completely specified by only a magnitude (size) 3

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Vector Notation When handwritten, use an arrow: Ā When printed, will be in bold print p, p with an arrow: Ā , When dealing with just the A magnitude of a vector in print, an italic letter will be used: A Italics will also be used to represent scalars 4
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 oved parallel to moved parallel to itself without being affected 5

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Properties of Vectors, cont. Negative Vectors Vector Ē is the negative of Ā if it has the same magnitude but is 180° apart (opposite directions) y Ē =- Ā ; Ā +( - Ē )=0 Ā x Ē 6
Adding Vectors When adding vectors, their irections ust be taken into directions must be taken into account nits ust be the same Units must be the same Methods Geometric Methods Algebraic Methods 7

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dding Vectors eometrically Adding Vectors Geometrically (Triangle or Polygon Method) Choose a scale y x 8
dding Vectors eometrically Adding Vectors Geometrically (Triangle or Polygon Method) Choose a scale raw the first vector y Draw the first vector with the appropriate length and in the direction specified A (Magnitude of Ā )=3.0 Angle = 0° x 9

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dding Vectors eometrically Adding Vectors Geometrically (Triangle or Polygon Method) Draw the next vector with origin at the end y of vector Ā and the appropriate angle lative to the relative to the coordinate system 40 x B= 4.0 Angle = 49° 10
Graphically Adding Vectors, cont. The resultant is drawn from the y R= 6.3 Angle = 28° origin of Ā to the end of the last vector Measure the length of and its angle R Use the scale factor to convert length to actual magnitude x 11

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Graphically Adding Vectors, cont. When you have many vectors, just eep repeating the keep repeating the process until all are included The resultant is still drawn from the rigin of the first origin of the first vector to the end of the last vector 12
Notes about Vector Addition Vectors obey the Commutative Law of Addition The order in which the vectors are added doesn’t affect the result  AB BA  13

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Vector Subtraction Special case of vector addition Add the negative of the subtracted ector vector    AB A B  14
Vector Subtraction Special case of vector addition Add the negative of the subtracted ector vector    AB A B  15

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## This note was uploaded on 10/05/2009 for the course PHY 1603 taught by Professor Boudreaux during the Spring '08 term at The University of Texas at San Antonio- San Antonio.

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lecture4 - Chapter 3 Vectors and Two-Dimensional Two...

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