Moments

Introduction For stability or equilibrium we have already seen that: 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

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 For Balance clockwise moments = Anticlockwise moments 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