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Vectors

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Vectors An essential component of your physics toolbox. Vectors vs. Scalars Vector: physical quantity that has both magnitude and direction Examples: displacement ... – PowerPoint PPT presentation

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Title: Vectors


1
Vectors
  • An essential component of your physics toolbox.

2
Vectors vs. Scalars
  • Vector physical quantity that has both magnitude
    and direction
  • Examples displacement, velocity, acceleration
  • Scalar physical quantity that has magnitude but
    no direction
  • Examples distance, speed, time, mass

3
Vectors vs. Scalars
4
Representing Vectors
  • Symbols in text
  • boldface
  • Symbols on paper/board
  • arrow above symbol
  • Graphically
  • draw an arrow
  • length represents magnitude
  • angle and head of arrow shows direction (angle)
  • label vector with quantity and/or value

v1 3 m/s
5
Adding and Subtracting Vectors
  • Only vectors of the same quantity and units may
    be added or subtracted
  • You cant add a velocity vector and a
    displacement vector
  • You cant add a velocity in m/s with a velocity
    in mph
  • Resultant vector that represents the sum of two
    or more vectors

6
Graphical Addition of Vectors
  • Draw all vectors to scale.
  • Add vectors using Head-To-Tail Method
  • Draw 1st vector
  • Begin tail of 2nd vector at head of 1st vector
  • Lather, rinse, repeat
  • Draw resultant vector from tail of 1st vector to
    head of last vector. Label resultant.

7
Resultant of Collinear Vectors
8
Resultant of Perpendicular Vectors
9
Properties of Vector Addition
  • Vectors can be moved parallel to themselves in a
    diagram.
  • Useful for switching from Head-To-Tail Method to
    Parallelogram Method
  • Vectors can be added in any order
  • Resultant will always be the same.
  • To subtract a vector, add its opposite.
  • Multiplying or dividing vectors by scalars
    results in vectors.
  • velocity (vector) displacement (vector) / time
    (scalar)
  • accel (vector) change in velocity (vector) /
    time (scalar)

10
Vectors Can Be Added In Any Order
11
Vectors Can Be Added In Any Order
12
Vectors Can Be Added In Any Order
13
Vector ComponentsGraphical Representation
  • projection of vector along x y axes
  • how much in the x direction, how much in the y
    direction
  • drop projection lines to x y axes
  • draw components along axes

14
Resultant of Two Non-90? Vectors
  • USE THE COMPONENT METHOD
  • Add x components
  • Add y components

15
Trigonometry Primer
  • Trigonometric functions relate measurements in
    right triangles.
  • Much of our work with vectors can be visualized
    with right triangles, so we need to know how to
    do trigonometry.

16
Trig Primer Pythagorean Thm.
  • The Pythagorean Theorem relates the lengths of
    the sides of a right triangle.

c
b
a
17
Trig Primer SOH CAH TOA
hyp
opp
?
adj
18
Vector ResolutionFinding Vector Components
  • Trigonometric Method
  • Visualize vector and its components as a right
    triangle
  • Apply Pythagorean Theorem SOHCAHTOA to find
    components (missing sides)

19
Vector AdditionFinding a Resultant Vector
  • Magnitude
  • Find the sum of all x-components and all
    y-components
  • Use Pythagorean Theorem to find resultant from
    components.

20
Vector AdditionFinding a Resultant Vector
  • Direction
  • Apply inverse trig functions to find angle
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