1. Starter

2. Extra question

3. What are scalars and vectors?

4. Scalars & Vectors Lesson Goals:
Be able to identify scalar and vector quantities
Be able to determine a resultant vector using the parallelogram or triangle rule
Be able to resolve a vector into perpendicular components

5. Khan Academy
One resource you can use outside the classroom to help consolidate work.
Also:

6. Antonine Education

7. Scalar Quantity – A quantity which has a magnitude but not a direction
Vector Quantity – A quantity with both magnitude and direction

8. Scalar or Vector? Distance Mass Velocity Displacement Energy
Force Acceleration
Speed Density
Power Current
Momentum Frequency
Scalar or
Vector?

9. Parallel Vectors If they point in the same direction, add them
If they point in opposite directions, add them with one direction taken to be negative (normally left).

10. Taking into account their direction
How do we combine scalar quantities?
Add them together
How do we combine vector quantities?
Carefully!
Taking into account their direction

11. Perpendicular Vectors –
The Triangle Rule
This is a geometric construction that can be used to determine the resultant of two vectors. In this construction the arrows must be drawn tip to tail.
If right-angles triangle then use Pythagoras R b a
Resultant Vector
R2 = a2 + b2

12. Trigonometry recap - V.Important!!!
sin θ = opposite ÷ hypotenuse
cos θ = adjacent ÷ hypotenuse
tan θ = opposite ÷ adjacent

13. Calculate the missing side or angle? ? 3 B 6
30°
Calculate the missing side or angle 4 7 ? C 9
15° ? D 10

14. What about when the vectors are at a random angle?

15. Resolving Vectors into Perpendicular ComponentsF θ
Horizontal component, Fx = F cos θ
Vertical component, Fy = F sin θ

16. Resolve the following forces into perpendicular componentsB A 8N 4N
30°
50° D C
17N
12N
40°
15°

17. How do we combine two or more non-perpendicular vectors ?

18. The Parallelogram Rule
This is a geometric construction that can be used to determine the resultant of two vectors
E.g. What is the resultant of the following? 8N B A 5N
45°
20°

19. But - Let’s just use the triangle rule from now on!
What is the resultant magnitude and direction of the following? 8N B A 5N
45°
20°

20. How would you tackle this???8N B 3N A
70°
80°
60°
70°
50°
30° D C 7N 5N

21. What is the resultant force? Step 1 Draw resolved vector arrows.
Calculate the horizontal and vertical components of each vector
60°
50°
70°
80° 3N 8N 5N 7N
30° B A D C

22. A What is the resultant force? Horizontally: - 3 cos 10 = - 2.95NB
60°
50°
70°
80° 3N 8N 5N 7N
30° A
Horizontally:
- 3 cos 10 = N
Vertically:
3 sin 10 = 0.52N D C

23. B What is the resultant force? Horizontally: 8 cos 20 = 7.52N
60°
50°
70°
80° 3N 8N 5N 7N
30° A
Horizontally:
8 cos 20 = 7.52N
Vertically:
8 sin 20 = 2.74N D C

24. C What is the resultant force? Horizontally: 7 cos 40 = 5.36N
60°
50°
70°
80° 3N 8N 5N 7N
30° B
Horizontally:
7 cos 40 = 5.36N
Vertically:
-7 sin 40 = -4.50N A D C

25. D What is the resultant force? Horizontally: -5 cos 60 = -2.5N
60°
50°
70°
80° 3N 8N 5N 7N
30° B
Horizontally:
-5 cos 60 = -2.5N
Vertically:
-5 sin 60 = -4.33N A D C

26. What is the resultant force?B
60°
50°
70°
80° 3N 8N 5N 7N
30° A
Step 2
Add horizontal and vertical components D C

27. What is the resultant force?
60°
50°
70°
80° 3N 8N 5N 7N
30° B
Horizontally:
– 2.5
= 7.43N
Vertically:
– 4.50 – 4.33
= N A C D

28. Find the resultant of this pair of perpendicular vectors
Step 3
Find the resultant of this pair of perpendicular vectors
7.43N
5.57N
We could use scale diagrams…
I vote for Pythagoras

29. Tan θ = opp / adj R2 = 7.432 + 5.572 = 5.57 / 7.43 = 86.23 θ = 36.86°
R = 9.29N