Vectors & Scalars
IB Core
Scalars
Quantities that can
be completely
specified by
magnitude (and
unit).
Eg temperature,
mass, number of
objects.
Vectors
Has both
magnitude and
direction.
Eg weight (a
force), velocity.
Some Properties of
Vectors
Can be
manipulated
algebraically
Can be combined
graphically or by
calculation
Eg sailing
Equality of 2 Vectors
Magnitude and
direction equal
Can be
“translated”
Adding Vectors
Triangle Method
Parallelogram Method
B
B
A
A
Shock Wave Flash
Demos
Adding 2 Vectors
(add2vectors.swf)
Adding 3 Vectors
(add3vectors.swf)
Negative of a Vector
+
=0
Opposite direction
A + -A = 0
Vector Subtraction
B
A
A-B
Special case of
vector addition
-B
Reverse direction
of B then add to A
Shock Wave Flash
Demos
Subtracting 2 Vectors (subtract2vectors.swf)
Multiplication of
Vectors by scalars
A
-2A
Gives another
vector
Magnitude
changes
Division of Vectors by
Scalars
A
0.5A
Division alters
magnitude
Direction may
reverse
y component = A sin = Ay
Components of a
Vector
angle 
x component = A cos =
Ax
Angle Determination using the UNIT Circle
90 degrees

degrees
180 degrees
0 degrees
270 degrees
Angle Determination using the UNIT Circle
90 degrees
180 degrees

 
degrees
  degrees
Resultant Vector
‘C’
270 degrees
0 degrees
Problem-solving
Strategy for Adding
Select coordinate
system
Vectors
Draw a sketch of the vectors & label
them
Find x and y components of all vectors
Find resultants separately for x & y
Use Pythagoras to find magnitude
Use trig function to get direction
More questions
Your turn
pictures below are not to scale)
1 cm to 0.5 N
Step 1: Choose a suitable scale, e.g. 1 cm to 0.5 N.
Remember to make your scale big enough - big
is beautiful!!
Questions
1. Add the following vectors and determine the
resultant. 3.0 m/s, 45o from x axis and 5.0 m/s,
135o from the x axis.
3.0 m/s, 45 deg + 5.0 m/s, 135 deg = 5.83 m/s, 104 deg (Note: the
resultant is drawn in red.)
Questions
2. Add the following vectors and determine the resultant:
3.0 m/s, 45o from x axis and 5.0 m/s, 135o from x axis
and 2.0 m/s, 60o from x axis.
3.0 m/s, 45 deg+ 5.0 m/s, 135 deg+ 2.0 m/s, 60 deg=
7.40m/s, 93.2 deg (Note: the resultant is drawn in red).