Moments
Introduction
For stability or equilibrium we have already
seen that:
F 0
For rotational forces this means that the
effect of the forces rotating the object
clockwise must equal the forces rotating
the object in an anticlockwise direction. A
MOMENT is the measure of the turning
effect of a force.
What is a Moment?
A moment is defined as:
MOMENT (M) =
force (f) x perpendicular distance from a pivot (d)
So the units of a moment are:
Newton metres or Nm
M
f d
There are two ways of increasing
the size of a moment……..
• Increase the size of the force
• Increase the distance from the pivot
This can be seen in several everyday situations:
•A long spanner undoes a nut easier then a short one
•Its hard to open a door by pushing near the hinge
•a large weight can be lifted using a large lever
•A crane has a limited working radius
Increasing the moment….
For equilibrium (balance):
The sum of the clockwise moments must be
equal to the sum of the anticlockwise
moments
(moments may be taken about any point on a structure)
This is known as ‘The principle of Moments’
For Example…..
Example 2
Unknown weight y=?
Clockwise moments about fulcrum= yx0.1 +5x0.4=0.1y+2
•Anticlockwise moments about fulcrum= 20x0.3=6
•For Balance clockwise moments = Anticlockwise moments
•0.1y+2.0=6
0.1y=4
y=40N
Example 3
•What are the sizes of the reactions X and Y at the trestles?
Hints:
•Take moments about any point
•Total Upwards forces must equal total downwards forces
•Moments through the point chosen as fulcrum=0
•Answers: Y=240N X=360N