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In this chapter we will learn about vectors, properties, addition, components of vectors and multipl

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Multiplying a vector by a scalar ... 5. Express vectors in terms of unit vectors and their scalar components. ... vector and scalar quantities. Performance ... – PowerPoint PPT presentation

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Title: In this chapter we will learn about vectors, properties, addition, components of vectors and multipl


1
Chapter 3 Vectors
Things to ask the class Have you all checked
your WebCT account? Do the Quiz, participate in
the discussion and learn from the applets!
  • In this chapter we will learn about vectors,
    (properties, addition, components of vectors and
    multiplying)

2
Vectors Magnitude and direction Scalars
Only Magnitude A scalar quantity has a single
value with an appropriate unit and has no
direction.
Examples for each Vectors Scalars
Motion of a particle from A to B along an
arbitrary path (dotted line). Displacement is a
vector
3
  • Vectors
  • Represented by arrows (example displacement).
  • Tip points away from the starting point.
  • Length of the arrow represents the magnitude
  • In text a vector is often represented in bold
    face (A) or by an arrow over the letter.
  • In text Magnitude is written as A or

This four vectors are equal because they have the
same magnitude and same length
4
Adding vectors
Graphical method (triangle method)
Draw vector A. Draw vector B starting at the
tip of vector A. The resultant vector R A B
is drawn from the tail of A to the tip of B.
5
Adding several vectors together.
Resultant vector RABCD is drawn from the
tail of the first vector to the tip of the last
vector.
6
Commutative Law of vector addition
A B B A
(Parallelogram rule of addition)
7
Associative Law of vector addition
A(BC) (AB)C
The order in which vectors are added together
does not matter.
8
Negative of a vector. The vectors A and A have
the same magnitude but opposite directions. A
(-A) 0
A
-A
9
Subtracting vectors
A - B A (-B)
10
Multiplying a vector by a scalar
The product mA is a vector that has the same
direction as A and magnitude mA. The product
mA is a vector that has the opposite direction
of A and magnitude mA.
Examples 5A -1/3A
11
Components of a vector
The x- and y-components of a vector
The magnitude of a vector
The angle q between vector and x-axis
12
The signs of the components Ax and Ay depend on
the angle q and they can be positive or negative.
(Examples)
13
Unit vectors
  • A unit vector is a dimensionless vector having
    a magnitude 1.
  • Unit vectors are used to indicate a direction.
  • i, j, k represent unit vectors along the x-, y-
    and z- direction
  • i, j, k form a right-handed coordinate system

14
The unit vector notation for the vector A is OR
in even better shorthand notation
15
Adding Vectors by Components
We want to calculate R A B From diagram R
(Axi Ayj) (Bxi Byj) R (Ax Bx)i
(Ay By)j
Rx Ax Bx Ry Ay By
The components of R
16
Adding Vectors by Components
The magnitude of a R
The angle q between vector R and x-axis
17
Checkpoint 3 (page 45)
What are the signs of x components of d1 and
d2? What are the sign of the y components of d1
and d2? What are the signs of the x and y
components of d1d2
18
Sample Problem 3-4
19
Vectors and the Laws of Physics
This section will be left as a reading assignment
for the student.
20
Multiplying a vector by another vector Two types
21
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