1. Mechanics &
Materials
2015 AQA A Level Physics
Vectors
9/17/2018

2. Physical Quantities
17/09/2018
Scalars
Vectors
Physical Quantity

3. Vectors and Scalars Physical Quantity
17/09/2018
Scalars
Vectors
Scalars have magnitude (size) but no direction
Physical Quantity
Vectors have both magnitude and direction

4. Vector or scalar? Vector Scalar ?? weight velocity mass displacement
speed
acceleration
distance
energy
force

5. Vector or scalar? Vector Scalar ?? Weight velocity mass displacement
speed
acceleration
distance
energy
force

6. Resultant of two Vectors
The resultant is the sum or the combined effect of two vector quantities
Vectors in the same direction:
6 N 4 N = 10 N
6 m
= 10 m
4 m
Vectors in opposite directions:
6 m s m s-1 = 4 m s-1
6 N 10 N = 4 N

7. Combining vectors When two vectors are joined tail to tail
Complete the parallelogram
The resultant is found by drawing the diagonal
When two vectors are joined head to tail
Draw the resultant vector by completing the triangle

8. Combining perpendicular Vectors
17/09/2018
15km
10km
100ms-1
6ms-1
100.1ms-1

9. Combining Vectors 15km 10km 100ms-1 6ms-1
17/09/2018
15km
10km
100ms-1
6ms-1
Find the magnitude of the resultant vectors using PYTHAGARUS
100.1ms-1

10. Combining Vectors 15km 10km 18km 100ms-1 6ms-1
17/09/2018
15km
10km
18km
100ms-1
6ms-1
Find the magnitude of the resultant vectors using PYTHAGARUS
100.1ms-1
100.2ms-1

11. Resolving Vectors θ Consider a diagonal push: This force is given by:
17/09/2018
Consider a diagonal push:
This force is given by:
F1 = F sin θ F1 F θ θ F2
This force is given by:
F2 = F cos θ

12. Resolving Vectors – example questions
17/09/2018
Calculate the horizontal and vertical components
of the following: 1) 2)
20N
10N
35O
45O
Work out the size and direction of the resultant force: 3) 4) 8N
12N
40O
80O

13. Resolving Vectors – example questions
17/09/2018
Calculate the horizontal and vertical components
of the following:
20sin45 =14.12N 1) 2)
20N
10N
5.74N
35O
45O
20cos45 =14.12N
8.19N
Work out the size and direction of the resultant force: 3) 4) 8N
12N
40O
80O

14. Resolving Vectors – example questions
17/09/2018
Calculate the horizontal and vertical components
of the following:
20sin45 =14.12N 1) 2)
20N
10N
5.74N
35O
45O
20cos45 =14.12N
8.19N
Work out the size and direction of the resultant force: 3) 4)
16.94N
11.8N 8N
17.41N
5.14N
tan θ = 4.05/16.94
θ = 13.40
12N θ
40O
80O
6.13N
4.05N
2.08N

15. More questions on vectors
17/09/2018
Joe hikes 5km north and then 9km east. This journey takes him 2 hours. Draw, on graph paper, a scale diagram to show this movement and calculate:
The displacement at the end of the journey
His average speed
His average velocity
An aeroplane takes off with a velocity of 110ms-1 at an angle of 25O to the horizontal runway. Calculate the horizontal and vertical components of the plane’s velocity.
A coin is flicked off a table with a horizontal speed of 2ms-1. Calculate its new speed 1 second later.