Textbook: Moment of a Force | Technical Science for Grade 10 PDF Download

 Page 1


 technical science GRADE 10 103
chapter 4 Moment of a force
This chapter is about the turning effect of a force, which is called a moment.
unit 4.1 Moment: The turning effect of a force
Quick activity: Feel a turning effect
•	 You need a stick about half the length of a broom handle 
and the same diameter.
•	 You will hold the stick very fi rmly and a classmate will 
try to turn you around using the stick. 
•	 Hold the stick horizontally, with two hands, near your 
stomach. A classmate holds the stick with one hand 
very close to your hands. You are the centre and your 
classmate’s challenge is to try to turn you around – 
gently. Can he/she do it?
•	 Then allow your classmate to hold the stick further away 
and try again. What happens now?
•	 Even if you are the biggest learner in the class, the 
smallest learner will fi nd it easy to turn you if he/she 
holds the stick far away from the centre.
Figure 4.1 What makes it easier to turn 
you around? 
the turning effect of a force
If a force is applied to an object which is connected to a 
fulcrum* (say FOOL-kruhm), the force will try to turn the 
object around the fulcrum. When this happens we say that 
the force has a turning effect about the fulcrum.
In Figure 4.2, the hand applies a force to the spanner. 
The spanner and nut experience a turning effect about 
the bolt.
defi nition:  The turning effect of a force about a 
fulcrum is called the moment of the 
force, or just the moment.
Your weight, for example, can have a turning effect. Your 
weight (measured in newtons) is a force towards the centre 
of the Earth. 
? ? Fulcrum – the support or point 
of rest about which a lever turns
Figure 4.2 The force of the hand has 
a turning effect about the bolt.
Force
being
applied
Turning
effect
TechSci_G10-LB-Eng-DBE3_9781431522842.indb   103 2015/12/17   10:01 AM
Page 2


 technical science GRADE 10 103
chapter 4 Moment of a force
This chapter is about the turning effect of a force, which is called a moment.
unit 4.1 Moment: The turning effect of a force
Quick activity: Feel a turning effect
•	 You need a stick about half the length of a broom handle 
and the same diameter.
•	 You will hold the stick very fi rmly and a classmate will 
try to turn you around using the stick. 
•	 Hold the stick horizontally, with two hands, near your 
stomach. A classmate holds the stick with one hand 
very close to your hands. You are the centre and your 
classmate’s challenge is to try to turn you around – 
gently. Can he/she do it?
•	 Then allow your classmate to hold the stick further away 
and try again. What happens now?
•	 Even if you are the biggest learner in the class, the 
smallest learner will fi nd it easy to turn you if he/she 
holds the stick far away from the centre.
Figure 4.1 What makes it easier to turn 
you around? 
the turning effect of a force
If a force is applied to an object which is connected to a 
fulcrum* (say FOOL-kruhm), the force will try to turn the 
object around the fulcrum. When this happens we say that 
the force has a turning effect about the fulcrum.
In Figure 4.2, the hand applies a force to the spanner. 
The spanner and nut experience a turning effect about 
the bolt.
defi nition:  The turning effect of a force about a 
fulcrum is called the moment of the 
force, or just the moment.
Your weight, for example, can have a turning effect. Your 
weight (measured in newtons) is a force towards the centre 
of the Earth. 
? ? Fulcrum – the support or point 
of rest about which a lever turns
Figure 4.2 The force of the hand has 
a turning effect about the bolt.
Force
being
applied
Turning
effect
TechSci_G10-LB-Eng-DBE3_9781431522842.indb   103 2015/12/17   10:01 AM
104 c hapter 4 MOMENT OF A FORCE
Think about a see-saw like the one you can see  
in Figure 4.3. There the object that turns is a 
long pole. The fulcrum is a structure in 
the middle.
When nobody is on the see-saw, the pole is 
(or should be) balanced. If a person gets on at 
one end, their weight (a force) will make that 
end go down, and the pole will turn around 
the fulcrum. The force makes the see-saw 
unbalanced and it turns around the fulcrum.
Figure 4.4 A see-saw in balance and an unbalanced see-saw with a person sitting on one side
Balanced Unbalanced
a turning effect can be clockwise or  
anti-clockwise
The hands of a clock are described as turning in a 
clockwise direction.
We use the words “clockwise” and “anti-clockwise” to 
describe the direction of the turning effect of a force.
In Figure 4.6a, the force causes a clockwise turning effect. 
In Figure 4.6b, the turning effect is anti-clockwise.
Figure 4.6a The see-saw turns clockwise. Figure 4.6b The see-saw turns anti-clockwise.
Figure 4.3 A seesaw with a heavy duty fulcrum
Figure 4.5 Clockwise direction
1
2
3
4
5
6
7
8
9
10
11
12
TechSci_G10-LB-Eng-DBE3_9781431522842.indb   104 2015/12/17   10:01 AM
Page 3


 technical science GRADE 10 103
chapter 4 Moment of a force
This chapter is about the turning effect of a force, which is called a moment.
unit 4.1 Moment: The turning effect of a force
Quick activity: Feel a turning effect
•	 You need a stick about half the length of a broom handle 
and the same diameter.
•	 You will hold the stick very fi rmly and a classmate will 
try to turn you around using the stick. 
•	 Hold the stick horizontally, with two hands, near your 
stomach. A classmate holds the stick with one hand 
very close to your hands. You are the centre and your 
classmate’s challenge is to try to turn you around – 
gently. Can he/she do it?
•	 Then allow your classmate to hold the stick further away 
and try again. What happens now?
•	 Even if you are the biggest learner in the class, the 
smallest learner will fi nd it easy to turn you if he/she 
holds the stick far away from the centre.
Figure 4.1 What makes it easier to turn 
you around? 
the turning effect of a force
If a force is applied to an object which is connected to a 
fulcrum* (say FOOL-kruhm), the force will try to turn the 
object around the fulcrum. When this happens we say that 
the force has a turning effect about the fulcrum.
In Figure 4.2, the hand applies a force to the spanner. 
The spanner and nut experience a turning effect about 
the bolt.
defi nition:  The turning effect of a force about a 
fulcrum is called the moment of the 
force, or just the moment.
Your weight, for example, can have a turning effect. Your 
weight (measured in newtons) is a force towards the centre 
of the Earth. 
? ? Fulcrum – the support or point 
of rest about which a lever turns
Figure 4.2 The force of the hand has 
a turning effect about the bolt.
Force
being
applied
Turning
effect
TechSci_G10-LB-Eng-DBE3_9781431522842.indb   103 2015/12/17   10:01 AM
104 c hapter 4 MOMENT OF A FORCE
Think about a see-saw like the one you can see  
in Figure 4.3. There the object that turns is a 
long pole. The fulcrum is a structure in 
the middle.
When nobody is on the see-saw, the pole is 
(or should be) balanced. If a person gets on at 
one end, their weight (a force) will make that 
end go down, and the pole will turn around 
the fulcrum. The force makes the see-saw 
unbalanced and it turns around the fulcrum.
Figure 4.4 A see-saw in balance and an unbalanced see-saw with a person sitting on one side
Balanced Unbalanced
a turning effect can be clockwise or  
anti-clockwise
The hands of a clock are described as turning in a 
clockwise direction.
We use the words “clockwise” and “anti-clockwise” to 
describe the direction of the turning effect of a force.
In Figure 4.6a, the force causes a clockwise turning effect. 
In Figure 4.6b, the turning effect is anti-clockwise.
Figure 4.6a The see-saw turns clockwise. Figure 4.6b The see-saw turns anti-clockwise.
Figure 4.3 A seesaw with a heavy duty fulcrum
Figure 4.5 Clockwise direction
1
2
3
4
5
6
7
8
9
10
11
12
TechSci_G10-LB-Eng-DBE3_9781431522842.indb   104 2015/12/17   10:01 AM
 technical science GRADE 10 105
calculate a moment
Moments are calculated in all branches of engineering, but most especially in structural 
engineering.
Figure 4.7 The size of the moment depends on the size of the force F and the distance d.
d
F
definition:  The size of a moment (M) depends on the size of the force (F) and the 
perpendicular distance from the fulcrum to line of the force (d).
We can describe this in a word formula: 
moment = the force × perpendicular distance from the fulcrum to the line of the force
Using symbols and abbreviations the formula is: 
M = F × d
where:
•	 M is the symbol for moment measured in newton metres (N m)
•	 F is the symbol for force measured in newtons (N)
•	 d is the symbol for distance measured in metres (m)
NOTE: The SI unit for a moment is derived directly from the units for the two physical 
quantities that are multiplied together to give a moment: a newton multiplied by a metre 
gives a newton metre.
a moment is a vector quantity
When you calculate a moment you must remember that force is a vector quantity: it has a 
magnitude and a direction. So a moment also has a direction – it will usually be described as 
either clockwise or anti-clockwise.
To calculate a moment we need to know three things:
•	 the distance of the force from the fulcrum
•	 the magnitude (size) of the force
•	 the direction of the force
TechSci_G10-LB-Eng-DBE3_9781431522842.indb   105 2015/12/17   10:01 AM
Page 4


 technical science GRADE 10 103
chapter 4 Moment of a force
This chapter is about the turning effect of a force, which is called a moment.
unit 4.1 Moment: The turning effect of a force
Quick activity: Feel a turning effect
•	 You need a stick about half the length of a broom handle 
and the same diameter.
•	 You will hold the stick very fi rmly and a classmate will 
try to turn you around using the stick. 
•	 Hold the stick horizontally, with two hands, near your 
stomach. A classmate holds the stick with one hand 
very close to your hands. You are the centre and your 
classmate’s challenge is to try to turn you around – 
gently. Can he/she do it?
•	 Then allow your classmate to hold the stick further away 
and try again. What happens now?
•	 Even if you are the biggest learner in the class, the 
smallest learner will fi nd it easy to turn you if he/she 
holds the stick far away from the centre.
Figure 4.1 What makes it easier to turn 
you around? 
the turning effect of a force
If a force is applied to an object which is connected to a 
fulcrum* (say FOOL-kruhm), the force will try to turn the 
object around the fulcrum. When this happens we say that 
the force has a turning effect about the fulcrum.
In Figure 4.2, the hand applies a force to the spanner. 
The spanner and nut experience a turning effect about 
the bolt.
defi nition:  The turning effect of a force about a 
fulcrum is called the moment of the 
force, or just the moment.
Your weight, for example, can have a turning effect. Your 
weight (measured in newtons) is a force towards the centre 
of the Earth. 
? ? Fulcrum – the support or point 
of rest about which a lever turns
Figure 4.2 The force of the hand has 
a turning effect about the bolt.
Force
being
applied
Turning
effect
TechSci_G10-LB-Eng-DBE3_9781431522842.indb   103 2015/12/17   10:01 AM
104 c hapter 4 MOMENT OF A FORCE
Think about a see-saw like the one you can see  
in Figure 4.3. There the object that turns is a 
long pole. The fulcrum is a structure in 
the middle.
When nobody is on the see-saw, the pole is 
(or should be) balanced. If a person gets on at 
one end, their weight (a force) will make that 
end go down, and the pole will turn around 
the fulcrum. The force makes the see-saw 
unbalanced and it turns around the fulcrum.
Figure 4.4 A see-saw in balance and an unbalanced see-saw with a person sitting on one side
Balanced Unbalanced
a turning effect can be clockwise or  
anti-clockwise
The hands of a clock are described as turning in a 
clockwise direction.
We use the words “clockwise” and “anti-clockwise” to 
describe the direction of the turning effect of a force.
In Figure 4.6a, the force causes a clockwise turning effect. 
In Figure 4.6b, the turning effect is anti-clockwise.
Figure 4.6a The see-saw turns clockwise. Figure 4.6b The see-saw turns anti-clockwise.
Figure 4.3 A seesaw with a heavy duty fulcrum
Figure 4.5 Clockwise direction
1
2
3
4
5
6
7
8
9
10
11
12
TechSci_G10-LB-Eng-DBE3_9781431522842.indb   104 2015/12/17   10:01 AM
 technical science GRADE 10 105
calculate a moment
Moments are calculated in all branches of engineering, but most especially in structural 
engineering.
Figure 4.7 The size of the moment depends on the size of the force F and the distance d.
d
F
definition:  The size of a moment (M) depends on the size of the force (F) and the 
perpendicular distance from the fulcrum to line of the force (d).
We can describe this in a word formula: 
moment = the force × perpendicular distance from the fulcrum to the line of the force
Using symbols and abbreviations the formula is: 
M = F × d
where:
•	 M is the symbol for moment measured in newton metres (N m)
•	 F is the symbol for force measured in newtons (N)
•	 d is the symbol for distance measured in metres (m)
NOTE: The SI unit for a moment is derived directly from the units for the two physical 
quantities that are multiplied together to give a moment: a newton multiplied by a metre 
gives a newton metre.
a moment is a vector quantity
When you calculate a moment you must remember that force is a vector quantity: it has a 
magnitude and a direction. So a moment also has a direction – it will usually be described as 
either clockwise or anti-clockwise.
To calculate a moment we need to know three things:
•	 the distance of the force from the fulcrum
•	 the magnitude (size) of the force
•	 the direction of the force
TechSci_G10-LB-Eng-DBE3_9781431522842.indb   105 2015/12/17   10:01 AM
106 chapter 4 MOMENT OF A FORCE
Worked examples: calculate moments
1. Calculate the moment in each diagram in Figure 4.8 below.
 Figure 4.8 
a)
0,4 m
4 N
b)
0,25 m
400 N
c)
0,5 m
7,5 N
 Solutions
a) Given 4 N acts downwards 0,4 m to the left of the fulcrum
  Unknown moment
  Formula M = F × d
   = 4 × 0,4 (substitute)
   = 1,6 N m anti-clockwise
TechSci_G10-LB-Eng-DBE3_9781431522842.indb   106 2015/12/17   10:01 AM
Page 5


 technical science GRADE 10 103
chapter 4 Moment of a force
This chapter is about the turning effect of a force, which is called a moment.
unit 4.1 Moment: The turning effect of a force
Quick activity: Feel a turning effect
•	 You need a stick about half the length of a broom handle 
and the same diameter.
•	 You will hold the stick very fi rmly and a classmate will 
try to turn you around using the stick. 
•	 Hold the stick horizontally, with two hands, near your 
stomach. A classmate holds the stick with one hand 
very close to your hands. You are the centre and your 
classmate’s challenge is to try to turn you around – 
gently. Can he/she do it?
•	 Then allow your classmate to hold the stick further away 
and try again. What happens now?
•	 Even if you are the biggest learner in the class, the 
smallest learner will fi nd it easy to turn you if he/she 
holds the stick far away from the centre.
Figure 4.1 What makes it easier to turn 
you around? 
the turning effect of a force
If a force is applied to an object which is connected to a 
fulcrum* (say FOOL-kruhm), the force will try to turn the 
object around the fulcrum. When this happens we say that 
the force has a turning effect about the fulcrum.
In Figure 4.2, the hand applies a force to the spanner. 
The spanner and nut experience a turning effect about 
the bolt.
defi nition:  The turning effect of a force about a 
fulcrum is called the moment of the 
force, or just the moment.
Your weight, for example, can have a turning effect. Your 
weight (measured in newtons) is a force towards the centre 
of the Earth. 
? ? Fulcrum – the support or point 
of rest about which a lever turns
Figure 4.2 The force of the hand has 
a turning effect about the bolt.
Force
being
applied
Turning
effect
TechSci_G10-LB-Eng-DBE3_9781431522842.indb   103 2015/12/17   10:01 AM
104 c hapter 4 MOMENT OF A FORCE
Think about a see-saw like the one you can see  
in Figure 4.3. There the object that turns is a 
long pole. The fulcrum is a structure in 
the middle.
When nobody is on the see-saw, the pole is 
(or should be) balanced. If a person gets on at 
one end, their weight (a force) will make that 
end go down, and the pole will turn around 
the fulcrum. The force makes the see-saw 
unbalanced and it turns around the fulcrum.
Figure 4.4 A see-saw in balance and an unbalanced see-saw with a person sitting on one side
Balanced Unbalanced
a turning effect can be clockwise or  
anti-clockwise
The hands of a clock are described as turning in a 
clockwise direction.
We use the words “clockwise” and “anti-clockwise” to 
describe the direction of the turning effect of a force.
In Figure 4.6a, the force causes a clockwise turning effect. 
In Figure 4.6b, the turning effect is anti-clockwise.
Figure 4.6a The see-saw turns clockwise. Figure 4.6b The see-saw turns anti-clockwise.
Figure 4.3 A seesaw with a heavy duty fulcrum
Figure 4.5 Clockwise direction
1
2
3
4
5
6
7
8
9
10
11
12
TechSci_G10-LB-Eng-DBE3_9781431522842.indb   104 2015/12/17   10:01 AM
 technical science GRADE 10 105
calculate a moment
Moments are calculated in all branches of engineering, but most especially in structural 
engineering.
Figure 4.7 The size of the moment depends on the size of the force F and the distance d.
d
F
definition:  The size of a moment (M) depends on the size of the force (F) and the 
perpendicular distance from the fulcrum to line of the force (d).
We can describe this in a word formula: 
moment = the force × perpendicular distance from the fulcrum to the line of the force
Using symbols and abbreviations the formula is: 
M = F × d
where:
•	 M is the symbol for moment measured in newton metres (N m)
•	 F is the symbol for force measured in newtons (N)
•	 d is the symbol for distance measured in metres (m)
NOTE: The SI unit for a moment is derived directly from the units for the two physical 
quantities that are multiplied together to give a moment: a newton multiplied by a metre 
gives a newton metre.
a moment is a vector quantity
When you calculate a moment you must remember that force is a vector quantity: it has a 
magnitude and a direction. So a moment also has a direction – it will usually be described as 
either clockwise or anti-clockwise.
To calculate a moment we need to know three things:
•	 the distance of the force from the fulcrum
•	 the magnitude (size) of the force
•	 the direction of the force
TechSci_G10-LB-Eng-DBE3_9781431522842.indb   105 2015/12/17   10:01 AM
106 chapter 4 MOMENT OF A FORCE
Worked examples: calculate moments
1. Calculate the moment in each diagram in Figure 4.8 below.
 Figure 4.8 
a)
0,4 m
4 N
b)
0,25 m
400 N
c)
0,5 m
7,5 N
 Solutions
a) Given 4 N acts downwards 0,4 m to the left of the fulcrum
  Unknown moment
  Formula M = F × d
   = 4 × 0,4 (substitute)
   = 1,6 N m anti-clockwise
TechSci_G10-LB-Eng-DBE3_9781431522842.indb   106 2015/12/17   10:01 AM
 technical science GRADE 10 107
b) Given 400 N acts downwards 0,25 m to the left of the fulcrum
  Unknown moment
  Formula M = F × d
   = 400 × 0,25 (substitute)
   = 100 N m anti-clockwise
c) Given 7,5 N acts downwards 0,5 m to the right of the fulcrum
  Unknown moment
  Formula M = F × d
   = 7,5 × 0,5 (substitute)
   = 3,75 N m clockwise
2. A 2 N force acts downwards 1 m to the right of a fulcrum. Calculate its moment.
 Solution
a) Given 2 N acts downwards 1 m to the right of the fulcrum
  Unknown moment
  Formula M = F × d
   = 2 × 1 (substitute)
   = 2 N m clockwise
3. A 30 N force acts downwards 3 m to the left of a fulcrum. Calculate its moment.
 Solution
a) Given 30 N acts downwards 3 m to the left of the fulcrum
  Unknown moment
  Formula M = F × d
   = 30 × 3 (substitute)
   = 90 N m anti-clockwise
4. A 45 N force acts upwards 2,5 m to the left of a fulcrum. Calculate its moment.
 Solution
a) Given 45 N upwards and 2,5 m to the left of the fulcrum
  Unknown moment
  Formula M = F × d
   = 45 × 2,5 (substitute)
   = 1 12,5 N m clockwise
TechSci_G10-LB-Eng-DBE3_9781431522842.indb   107 2015/12/17   10:01 AM