1. Which of the following is
the odd one out?
Mass
Speed
Force
Temperature
Distance
Elephant
DO NOW!

2. Which of the following is
the odd one out?
Mass
Speed
Force
Temperature
Distance
Elephant
DO NOW!

3. Scalars and vectors

4. Scalars
Scalar quantities have a magnitude (size)
only.
For example:
Temperature, mass, distance, speed, energy.

5. Vectors
Vector quantities have a magnitude (size)
and direction.
For example:
Force, acceleration, displacement, velocity,
momentum.

6. Scalars and Vectors
scalars
vectors
Magnitude (size)
No direction
Magnitude and direction
temperature mass
speed
velocity
force
acceleration

7. Representing vectors
Vectors can be represented by arrows. The
length of the arrow indicates the magnitude,
and the direction the direction!

8. Representing velocity
Velocity can also be represented by an
arrow. The size of the arrow indicates the
magnitude of the velocity, and direction the
direction!
When discussing velocity or answering a
question, you must always mention the
direction of the velocity (otherwise you are
just giving the speed).

9. 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.

10. Adding vectors
For example;
6 m/s 4 m/s 2 m/s
4 N
4 N 5.7 N
Resultant force
Resultant force

11. How did we do that?

12. How did we do that?
4 N
4 N
5.7 N
4 N
4 N

13. Scale drawing
You can either do a
scale drawing
4 cm
4 cm
1 cm = 1N
θ = 45°
θ

14. Or by using pythagorous and
trigonometry
4 N
4 N
Length of hypotenuse = √42
+ 42
= √32 = 5.7 N
Tan θ = 4/4 = 1, θ = 45°

15. Subtracting vectors
For example;
6 m/s 4 m/s 10 m/s
4 N
4 N 5.7 N
Resultant velocity
Resultant force

16. Subtracting vectors
For example;
4 N
4 N
5.7 N

17. An interesting example
Think of a dog (dead) orbiting the earth with
constant speed (in a circle).

18. An interesting example
At this point, what is its velocity?
velocity?

19. An interesting example
velocity

20. An interesting example
velocity?
What is its velocity here?

21. An interesting example
velocity
As you can see the velocity has changed
as it is now going in another direction.

22. An interesting example
velocity
In uniform circular motion, we have
constant speed but changing velocity.
Of course a changing
velocity means it must
be accelerating! We’ll
come back to this next
year!

23. Resolving vectors into components

24. Resolving vectors into components
It is sometime useful to split vectors into
perpendicular components

25. Resolving vectors into components

26. A cable car question

27. Tension in the cables?
10 000 N
?? 10°

28. Vertically 10 000 = 2 X ? X sin10°
10 000 N
?? 10°
? X sin10° ? X sin10°

29. Vertically 10 000/2xsin10° = ?
10 000 N
?? 10°
? X sin10° ? X sin10°

30. ? = 28 800 N
10 000 N
?? 10°
? X sin10° ? X sin10°

31. What happens as the angle deceases?
10 000 N
?? θ
? = 10 000/2xsinθ

32. Error bars
• X = 0.6 ± 0.1
• Y = 0.5 ± 0.1

33. Gradients

34. Minimum gradient

35. Maximum gradient

36. y = mx + c

37. y = mx + c
• Ek = ½mv2

38. y = mx + c
• Ek = ½mv2
Ek (J)
V2
(m2
.s-2
)

39. Let’s try some questions!
Resultant of forces (addition of
vectors)
Page 13 Questions
1 to 6

40. Sorry, I nearly forgot!

42. Resultant force