Scalars and vectors
Which of the following is
the odd one out?
Mass
Speed
Force
Temperature
Distance
Elephant
Which of the following is
the odd one out?
Mass
Speed
Force
Temperature
Distance
Elephant
Scalars
Scalar quantities have a magnitude (size)
only.
For example:
1 kg
Temperature, mass, distance, speed, energy.
Vectors
Vector quantities have a magnitude (size)
and direction.
For example:
10 N
Force, acceleration, displacement, velocity,
momentum.
Scalars and Vectors
No direction
vectors
scalars
Magnitude (size)
temperature
mass
Magnitude and direction
velocity
force
speed
acceleration
Scalars and Vectors
No direction
vectors
scalars
Magnitude (size)
temperature
mass
Magnitude and direction
velocity
force
speed
acceleration
Representing vectors
Vectors can be represented by arrows. The
length of the arrow indicates the magnitude,
and the direction the direction!
Adding vectors
When adding vectors (such as force or
velocity) , it is important to remember they
are vectors and their direction needs to be
taken into account.
The result of adding two vectors is called
the resultant.
Adding vectors
For example;
6N
Resultant force
2N
4N
4 m/s
5.7 m/s
4 m/s
Resultant velocity
Adding vectors
For example;
6N
Resultant force
4N
2N
An interesting example
Think of a dog orbiting the earth with constant
speed (in a circle).
An interesting example
At this point, what is its velocity?
velocity?
An interesting example
velocity
An interesting example
What is its velocity here?
velocity?
An interesting example
As you can see the velocity has changed
as it is now going in another direction.
velocity
An interesting example
We have constant speed but changing
velocity.
Of course a changing
velocity means it must
be accelerating! We’ll
come back to this in
year 12!
velocity
Question
• Suppose you lay 3 metre rulers on the floor
end-to-end to represent 3 vectors of equal
magnitude. How could you produce a final
vector of
• A) the largest magnitude
• B) the smallest magnitude
• C) a magnitude of the length of 1 ruler
• A) end to end = 3m
• B) in a triangle = 0m
• C) on top of each other, or 2 end to end with
another on top
Flying in a side wind
• A bird flies at a steady speed of 3 m s–1 through the air. It
is pointing in the direction due north. However, there is a
wind blowing from west to east at a speed of 2 ms–1.
• 1. What is the velocity of the bird relative to the ground?
• 2. What is the displacement of the bird, relative to its
starting point, after it has flown for20 seconds?
• 3. In what direction should the bird point if it is to travel
in a northerly direction?