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Vectors and Two-Dimensional Motion

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Vectors and Two-Dimensional Motion Vectors in Two Dimensions Adding Vectors Graphically R A B R A B Place vectors _____ Parallelogram Method Can move a vector ... – PowerPoint PPT presentation

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Title: Vectors and Two-Dimensional Motion


1
Vectors and Two-Dimensional Motion
  • Vectors in Two Dimensions

2
Adding Vectors Graphically
Place vectors ____________
3
Parallelogram Method
  • Can move a vector parallel to itself

R A __
R B __
4
Adding More Than 2 Vectors
Fig. 3.4, p. 56
5
Vector Components
  • Vector components related to ________ and
    _________

6
Negative Vectors
  • -A has the same magnitude as A, but the
    __________ direction

A
Ay
-Ax
Ax
-Ay
-A
7
Subtracting Vectors
  • Subtraction is the same as ________ the ________

Fig. 3.5, p. 56
8
Vectors Multiplied by a Scalar
  • Each ___________ gets multiplied by scalar
  • Division is the same as ___________ by 1/(scalar)
  • If scalar is negative, direction is _______

9
Adding Vectors Algebraically
By
Ry
?
Ay
Ax
Bx
Rx
10
Adding Vectors Algebraically
Check to make sure __ makes sense tan-1 only
gives ? between ____ and ____
11
Working in Two Dimensions
  • Reference frame chosen for convenience
  • ?r, v, and a are vectors know how to
  • Break into x- and y-components
  • Add/subtract components
  • Convert result to magnitude and direction
  • Two vectors are equal only if they have the same
    __________ and __________

12
Displacement Vector
  • Point 1 is located by vector ___ with components
    ___ and ___
  • It moves to point 2 via ___ with components ___
    and ___
  • Point 2 is located by vector ___ with components
    ___ and ___

y
2
1
x
13
Displacement Vector
  • Vector addition holds true for displacement
    vectors and their components

y
2
?r
1
r2
r1
x
14
Velocity Vectors
  • Average Velocity

Components
15
Acceleration Vectors
  • Average Acceleration

Components
Instantaneous Acceleration
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