8. Wafulah
Oduor
Moments of forces
The moment of a force is a measure of the turning effect
of the force about a point
The moment depends on the following:
•The magnitude of the force
•The length of the lever upon which the force acts
(the lever being the perpendicular distance between
the line of action of the force and the point about
which the moment is being taken)
9. Wafulah
Oduor
Moment
-Is the measure of the capacity or ability of the force to produce
twisting or turning effect about an axis. This axis is perpendicular
to the plane containing the line of action of the force.
-The magnitude of moment is equal to the product of the force
and the perpendicular distance from the axis to the line of
action of the force.
-The intersection of the plane and the axis is commonly called
the moment center, and the perpendicular distance from the
moment center to the line of action of the force is called
moment arm.
11. Wafulah
Oduor
Resultant moment:
When two or more forces are acting about a point
their combined effect can be represented by one
imaginary moment called the ‘Resultant
Moment’.
The process of finding the resultant moment is referred
to as the ‘Resolution of the Component Moments’.
The magnitude of the moment:
is the product of the force and the length of the lever.
Thus, if the force is measured in Newtons and the length
of the lever in metres, the moment found will be
expressed in Newton- metres (Nm).
12. Wafulah
Oduor
Resolution of moments:
To calculate the resultant moment about a point find:
• The sum of the moments to produce rotation in a
clockwise direction about the point.
•The sum of the moments to produce rotation
in an anticlockwise direction.
•Take the lesser of these two moments from the greater
and the difference will be the magnitude of the
resultant.
•The direction in which it acts will be that of the greater of
the two component moments.
13. Wafulah
Oduor
Weight & Mass
Mass is the fundamental measure of the quantity of
matter in a body and is expressed in KG and TON
Weight is the force exerted on a body by the Earth’s
gravitational force and is measured in Newton (N) and
kilo – Newton (KN)
Weight = Mass x Acceleration
14. Wafulah
Oduor
MOMENTS OF MASS
Since:
•The Force Of Earth’s Gravity is Constant = 9.81 m/s2
Therefore:
•The Weight Of Bodies Is Proportional To Their Mass
•The Resultant Moment Of two Or More Weights About A Point
Could Be Expressed In Terms Of Their Mass Moments
15. Wafulah
Oduor
Moment of force about different points
Assuming clockwise moments as positive, compute the
moment of force F = 200 kg and force P = 165 kg about
points A, B, C, and D.
16. Wafulah
Oduor
Moment of resultant force about a
point
Two forces P and Q pass through a point A
which is 4 m to the right of and 3 m above a
moment center O. Force P is 890 N directed up
to the right at 30° with the horizontal and force
Q is 445 N directed up to the left at 60° with the
horizontal. Determine the moment of the
resultant of these two forces with respect to O.
17. Wafulah
Oduor
0.5 1 m 0.5 1 m
10 kg 30 kg
Moments are taken about O, the middle of the
plank.
Clockwise moment = 30 X 0.5 = 15 kg m
Anti-clockwise moment = 10 X 1.0 = 10 kg m
Resultant moment 5 kg m clockwise
3 m
18. For a body in equilibrium:
A uniform beam has length 8 m and mass 60
kg. It is suspended by two ropes, as shown in
the diagram below.
19. Wafulah
Oduor
2. A beam, of mass 50 kg and length 5 m, rests on two
supports as shown in the diagram. Find the magnitude
of the reaction force exerted by each support. Find the
maximum mass that could be placed at either end of
the beam if it is to remain in equilibrium.
20. Wafulah
Oduor
Moments Calculations
In the image below, the mass provides
a force some distance away from the pivot:
We define the turning effect with the equation:
Moment = Force × Perpendicular distance from the pivot
Since force is measured in newtons (N)
and distances in metres (m) the unit for a moment is the
newton- metre (Nm).
Moments can act in two ways: clockwise or anticlockwise.
21. Wafulah
Oduor
Here are the answers to the questions. We have used the formula:
moment = force × distance:
Moments Questions
For each situation below, determine the moment of the force, and
state the direction in which it acts.
MomentsAnswers
22. Wafulah
Oduor
Moment = 4 N × 0·4 m Moment = 1·6 Nm
anticlockwise
Moment = 4 N × 0·25 m Moment = 1·0 Nm
anticlockwise
Moment = 5 N × 0·50 m Moment = 2·5 Nm
clockwise
One force on its own isn't much use to us. We normally look at
situations where turning effects are balanced (or not!).
Let's look at the example below and find the missing force F:
If the system is balanced, the anticlockwise turning effect of
Balancing Moments
23. Wafulah
Oduor
Sometimes moments can easily become unbalanced - even when we
don't want them to!
copyright for image unknown Click here to read the writing!
In these unfortuante examples, it would seem that in loading the
cart, some of the boxes must have slipped to the back - further
away from the pivot - greatly increasing their turning effect.
In the case of the lorry, its weight wasn't enough to balance the
force F must equal the clockwise turning effect:
clockwise moment = anticlockwise moment
Clockwise moment = 5 N × 0·50 m = 2·50 Nm.
Anticlockwise moment = F × 0·25 m = 2·50 Nm
Force F = 2·50 Nm ÷ 0·25 m = 10 N
In order to balance the 5 N force acting at 0·5 m from the pivot, we require 10
N acting in the opposite direction but at 0·25 m.
Unbalanced Moments
24. Wafulah
Oduor
Many Moments
Sometimes more than one force acts on the same side of
the pivot. Their overall turning effect is easy to work out.
The 2 N force has a moment of 2 × 0·2 m = 0·4 Nm
clockwise. The 5 N force has a moment of 5 × 0·5 m = 2·5
Nm clockwise.
Their combined moment = 0·4 Nm + 2·5 Nm = 2·9 Nm
clockwise.
Moments can just be added, but they must act in the same
direction.
25. Wafulah
Oduor
Balancing Many Moments
We have seen that more than one moment can act in one direction.
We may sometimes wish to work out how these could be balanced.
At what distance must the 6 N force act to balance the other forces?
When balanced: sum of clockwise moments = sum of
anticlockwise moments
It is easily shown that the clockwise moment = 3.0 Nm. To balance
this, the anticlockwise moment must also be 3·0 Nm. So:
6 × d = 3·0
d = 3·0 ÷ 6 = 0·5 m
29. Wafulah
Oduor
Couples
This refers to the two Forces having the
same magnitude, parallel lines of action, and
opposite sense separated by a perpendicular
distance.
In this situation, the sum of the forces in
each direction is zero, so a couple does not
affect the sum of forces equations
A force couple will however tend to rotate
the body it is acting on
39. Wafulah
Oduor
When analyzing forces in a structure or machine, it is conventional to
classify forces as external forces, constraint forces or internal forces.
I. External forces arise from interaction between the system of interest and
its surroundings.
Examples; gravitational forces; lift or drag forces arising from wind loading;
electrostatic and electromagnetic forces; and buoyancy forces; among others.
I. Constraint forces are exerted by one part of a structure on another,
through joints, connections or contacts between components.
II. Internal forces are forces that act inside a solid part of a structure or
component.
Example; a stretched rope has a tension force acting inside it, holding the
rope together. Most solid objects contain very complex distributions of
internal force.
These internal forces ultimately lead to structural failure, and also cause the
structure to deform.
Classification of forces:
