chapter3 - Chapter3 Vectorsand TwoDimensionalMotion...

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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 vector  quantity has both magnitude  (size) and direction 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 r A r
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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   ( 29 ; 0 = - + - = A B A A r r r r = + R A B r r r
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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 r A r
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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 R 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 r r r r
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    Vector Subtraction Special case of  vector addition Add the negative of  the subtracted vector    Continue with  standard vector  addition procedure ( 29 - = + - A B A B r r r r
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chapter3 - Chapter3 Vectorsand TwoDimensionalMotion...

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