2. Vectors and scalars LOs
To do - in pairs
1. Explain the difference between speed and velocity.
2. Write definitions for vector and scalar.
3. Give two examples of vector and scalar quantities.
Extension
Give another pair of quantities that have the same relationship as
speed and velocity.
Module 1: Motion LO1: define scalar and vector quantities and give examples
3. Lesson focus
• An introduction to vectors
Learning objectives
At the end of the lesson you will be able to:
• define scalar and vector quantities and give examples;
• draw and use a vector triangle to determine the resultant of
two coplanar vectors such as displacement, velocity and force;
• calculate the resultant of two perpendicular vectors such as
displacement, velocity and force.
Module 1: Motion
4. Learning outcomes
All can
• explain the difference between a scalar and a vector quantity;
• give two examples each of scalars and vectors;
• add two vectors using a scale drawing;
• add two vectors at right angles using Pythagoras’s theorem.
Some can
• add components to sum vectors
Module 1: Motion
5. Vectors and scalars LOs
A scalar quantity (‘scalar’) is a physical quantity that can be completely
specified by a single number together with an appropriate unit.
A vector quantity (‘vector’) is a physical quantity that is completely specified
by a magnitude (size) and a direction.
Question
Which of these quantities are scalars?
displacement / kinetic energy / mass / power / velocity / weight
Module 1: Motion LO1: define scalar and vector quantities and give examples
7. How to show and notate a vector LOs
E.g. In a diagram B
a
‘The vector AB … ’
A
Vectors are shown in diagrams as arrows (‘directed line segments’).
Vectors are written as
a bold, lower case letters in printed text
~ or AB
a in handwritten text
|a| means the magnitude of a.
Module 1: Motion
8. How to add two vectors: method 1 LOs
1. parallelogram rule
a
a+b
resultant vector
b
The two vectors are drawn from a common point. The diagonal of the
resulting parallelogram is the vector sum (resultant).
Module 1: Motion LO 2 & 3: draw and use a vector triangle to find a resultant
9. How to add two vectors: method 1 LOs
To do - pairs
Work out a method
for finding the
displacement
(distance and angle
θ) of the spider.
Module 1: Motion
10. How to add two vectors: method 1 LOs
Question How should these vectors
be added?
Answer Use Pythagoras’s theorem
and trigonometry.
OB2 = OA2 + AB2
= 0.82 + 1.22
= 2.08 m
OB = 1.4 m
tanθ = 0.8 / 1.2 = 0.67
θ = 37.4
‘The spider undergoes a displacement of 1.4 m along a
bearing of 37.4 N of east.’
Module 1: Motion
11. 2861 June, 2002 Adding vectors using Pythagoras and trig. LOs
Module 1: Motion
12. Adding vectors by drawing LOs
Module 1: Motion LO 2 & 3: draw and use a vector triangle to find a resultant
13. Adding vectors LOs
Choose appropriate methods to answer these questions.
1. Two forces act on a wooden block, one to the right of 3 N and the other, to
the left, of 5 N. Draw a scale diagram of these vectors. What are the
magnitude and direction of the resultant force on the block measured from
the diagram?
2. A boat leaves harbour and travels due north for a distance of 3 km and then
due west for a distance of 8 km. What is the final displacement of the boat
with respect to the harbour? The boat then travels a further 1 km due
south. What is the new displacement with respect to the harbour?
3. A helicopter rises vertically from the ground for a distance of 600 m and
then moves horizontally for a distance of 1.6 km. Draw a scale diagram to
calculate the displacement of the helicopter from its starting point.
Module 1: Motion LO 2 & 3: draw and use a vector triangle to find a resultant
14. Vectors and scalars LOs
Module 1: Motion LO1: define scalar and vector quantities and give examples
15. Adding vectors by drawing LOs
Methods for adding vectors:
1. Pythagoras theorem & trigonometry 2. scale diagram
Which is most appropriate for each of these?
Calculate the magnitude and direction of An aircraft has a speed relative to still air
the resultant of 55 N and 25 N acting at of 150 ms-1. The pilot wishes to fly due
right-angles on a small object. north when the wind velocity is 20 ms-1
towards the north-east. On what bearing
should the pilot fly?
Two ships, A and B, leave port P at the
same time. Ship A travels due north at a A helicopter rises vertically from the
steady speed of 15 km h-1 and ship B ground for a distance of 600 m and then
travels N 60 E at a steady speed of 10 moves horizontally for a distance of 1.6
km h-1. What is the distance and km. Find the displacement of the
direction from A to B after one hour? helicopter from its starting point.
Module 1: Motion LO 2 & 3: draw and use a vector triangle to find a resultant
