Relative Motion by fhSiUpI

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									AP Physics C
 Mrs. Coyle
• Coordinate Systems
• Vectors and Scalars
• Properties of Vectors
• Unit Vectors
Coordinate Systems

• Cartesian (rectangular) Coordinates
                           (x,y)


• Polar Coordinates          (r, θ)
  – θ is taken to be positive
    counterclockwise from the +x axis.
     Vectors and Scalars
• Scalars- magnitude only

• Vectors- magnitude and direction
      Equality of Vectors
• Two vectors are equal if they have
  the same magnitude and direction.
      Addition of Vectors
• Graphical
• Algebraic



• Resultant: sum of vectors
   Properties of Vector
        Addition

–Commutative Property of Addition
  •A + B = B + A


–Associative Property of Addition
  •(A + B) + C = A + (B + C)
     Graphical Addition of
           Vectors
• Head-to-Tail Method

• Parallelogram Method
    Graphical Addition of
          Vectors
Head-to-Tail Method
   • Vectors are moved parallel to themselves so
     that they are positioned in such a way that
     the head of one is adjacent to the tail of the
     other.
   • The resultant is drawn by starting at the
     first tail (loose tail) and ending (arrow head
     pointed) at the last head (loose head).
                                   B
             A



                       Resultant
Graphical Addition of Vectors


• Parallelogram Method
    • The vectors are placed tail to tail forming a
      rectangle.
    • The diagonal that starts at the joint tails
      has its tail at the joint tails) is the
      resultant.
               A
                           Resultant



                       B
        Graphical Vector
          Subtraction
When subtracting A-B :

• Invert vector B to get -B
• Add A+(-B) normally
  Algebraic Addition of Vectors-
       Component Method
1)Find x and y components of each
 vector.
                        ax = acosθ

                        ay = a sinθ
  Component Method Cont’d
2)Add x and y components.

3)Use the Pythagorean Theorem to find
 the magnitude of the resultant.

4)Use q=tan-1 |Y | to find the direction
                X
 with respect to the x-axis.
     Unit Vectors:         î, ĵ, k
• Dimensionless vector with a
  magnitude of 1.

• They specify direction x, y, z

• Example: A= 2 î + 3 ĵ - 6k
            Example 1
• Add the vectors:
 A= 10 î - 1 ĵ - 6k
 B= - 6î + 5 ĵ + 6k
   Give the components of the
  resultant vector, its magnitude and
  its direction with respect to the x-
  axis.

Answer: R= 4î + 4ĵ, 5.7, 45 deg above +x
 axis
            Example 2
The position vector as a function of
time for an object is given by
r(t)= 2 î + 3t ĵ - 6k,
r is in meters and t is in seconds.

Evaluate dr/dt and explain what is its
significance?
            Example 3
• These are instructions for finding a
  treasure : Go 75.0 paces at 240°,
  turn to 135° and walk 125 paces,
  then travel 100 paces at 160°. The
  angles are measured ccw from the
  east, the +x direction. Determine the
  resultant displacement from the
  starting point.

• Answer: 227 paces at 165°
           Useful Link
• http://hyperphysics.phy-
  astr.gsu.edu/hbase/vect.html#vecco
  n

								
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