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Lesson 2: Physics 150 / 215 2-D Motion

Lesson 2: Physics 150 / 215 2-D Motion. Coordinate Systems Vectors in general Special Vectors. Coordinate Systems. 1. Fix a reference point : ORIGIN 2. Define a set of directed lines that intersect at origin: COORDINATE AXES

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Lesson 2: Physics 150 / 215 2-D Motion

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  1. Lesson 2: Physics 150 / 2152-D Motion • Coordinate Systems • Vectors in general • Special Vectors

  2. Coordinate Systems 1. Fix a reference point : ORIGIN 2. Define a set of directed lines that intersect at origin: COORDINATE AXES 3. Instructions on how to label point with respect origin and axes. COORDINATES

  3. y p b r  x a • rectangular Cartesian coordinates of point • p=(a,b) • plane polar coordinates of point • p = (r,)

  4. Two vectors are equal if they have • same length • same direction = parallel transport is moving vector without changing length or direction

  5. V2 Addition tip + V1 tail

  6. V1 V2 V1 + V2 V2

  7. V j i V  Vx Vx j i Vy  Cos     V Vx Vy  V Sin   

  8. can always represent a vector by a directed line segment: y x • Two vectors are equal if they have • same length • same direction =

  9. Vector Addition is Commutative : a + b = b + a Associative : a + ( b + c ) = ( a + b ) + c - a = vector that has same length as a but opposite direction Multiplication by scalar : ì m > 0 vector in same direction as a ï ï but m times as long m a = í m < 0 vector in opposite direction as a ï ï î but m times as long

  10. Solving Problems Involving Vectors 1. Graphically ! Draw all vectors in pencil ! Arrange them tip to tail ! Draw a vector from the tail of the first vector to the tip of the last one.

  11. ! measure the angle the vector makes with the positive x-axis ! measure the length of the vector. ! measure the length of its X component ! measure the length of its Y component

  12. 2. Algebraically ! write all vectors in terms of their X and Y components ! The X component of the sum of the vectors is the sum of the X components ! The Y component of the sum of the vectors is the sum of the Y components

  13. coordinates of vectors (x,y) V yj xi V=xi + yj

  14. 1-1 correspondence between vectors and their coordinates V = xi + yj (x,y)

  15. Special Vectors (x,y) r d ri rf

  16. Unit vectors

  17. special unit vectors k i j

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