11.2 Moments
In the example of the see-saw we looked at the product of each force and its distance from a fixed point. This product is called the moment of the force about the point.
The see-saw balances because the moments of the forces on either side of the fulcrum are the same magnitude and in opposite directions.
One would tend to make the see-saw turn clockwise, the other anticlockwise.
By contrast, the moments about G of the forces on the tray in the last situation do not balance.
They both tend to turn it anticlockwise, so rotation occurs.
Conventions and units:
The moment of a force F about a point O is defined by
moment = Fd
where d is the perpendicular distance from the point O to the line of action of the force (Figure 11.7).
Figure 11.7
In two dimensions, the sense of a moment is described as either positive (anticlockwise) or negative (clockwise) as shown in Figure 11.8.
Figure 11.8
If you imagine putting a pin at O and pushing along the line of F, your page would turn clockwise for (i) and anticlockwise for (ii).
In the S.I. system the unit for moment is the newton meter (Nm), because a moment is the product of a force, the unit of which is the newton, and distance, the unit of which is the meter.
Remember that moments are always taken about a point and you must always specify what that point is. A force acting through the point will have no moment about that point because in that case d = 0.
Figure 11.9 shows two tools for undoing wheel nuts on a car. Discuss the advantages and disadvantages of each.
Figure 11.9
When using the spider wrench (the tool with two ‘arms’), you apply equal and opposite forces either side of the nut. These produce moments in the same direction.
One advantage of this method is that there is no resultant force and hence no tendency for the nut to snap off.