Introduction to Vectors

1
Introduction to Vectors

• Chapter 3 section 1

2
Scalar Quantity

• Scalar A quantity that can be completely
  specified by its magnitude, but NO direction.
• Examples
• Speed
• Distance
• Volume
• Energy
• Time
• Mass

3
Vector Quantity

• Vector A quantity that can be described by its
  magnitude AND its direction.
• Examples
• Displacement
• Velocity
• Acceleration
• Force
• Momentum

4
Vectors and Scalars in the Book

• Vectors quantities are indicated in Boldface by
  their variable.
• v 30 m/s
• Scalars quantities are indicated in italics by
  their variable.
• t 3.2 s

5
Vector Diagrams

• In diagrams, vectors are shown as arrows that
  point the direction of its magnitude.
• Length of arrow Magnitude of the vector
• Direction of arrow Path of vector

v 30 mi/hr
v 60 mi/hr
6
Resultant

• Resultant A vector representing the sum of two
  or more vectors.
• When adding vectors, they must have the same
  units and describe similar quantities.
• Example
• The sum of the vectors must all be velocity and
  must be in units of m/s.

7
Vector Addition in 1-Dimension
A5m
R7m
B2m
ABR 5m 2m 7m
A5m
B3m
R2m
ABR 5m (-3m) 2m
8
Head-to-Tail Method

• To add two (or more) vectors together graphically
  using the head-to-tail method you simply draw the
  first vector and then draw the second vector with
  its tail at the head of the first vector.
• If there are more vectors to be added draw each
  one with its tail at the head of the preceding
  one. The sum or resultant is a vector drawn from
  the tail of the first vector to the head of the
  last vector. It does not matter in which order
  you add them.

9
Vectors
The resultant always measures from where you
started to where you end at.
HEAD
TAIL
10
Cartesian Plane
90
0
180
270
11
Vector Angles

• When describing the direction of a vector, the
  angle always starts at the 0 degrees on the
  x-axis and moves counter-clockwise to reference
  the direction of the vector.

?300
?45
?105
12
Properties of Vectors

• Vectors can be moved parallel to themselves in a
  diagram, as long as the magnitude stays the same.
• The horizontal vector is moved and doesnt
  change the problem as long as the magnitude
  doesnt change and it remains parallel to its
  original position.

13
Properties of Vectors

• 2. Vectors can be added in any direction.
• Ex ABCDE Resultant
• BADCE Resultant

E
E
Resultant
Resultant
C
D
D
C
A
B
B
A
14
Properties of Vectors

• 3. To subtract a vector, add its opposite
• A - B A (-B)

15
Properties of Vectors

• 4. Multiplying or dividing vectors by scalars
  results in vectors.
• 3 A 3A