CHAPTER V 
MOMENTS AND CENTROIDS 
59. Moment of a Force.—The moment of a force about a point or 
axis, perpendicular to its line of action, is the measure of its turning 
power round that point or axis. The magnitude of the moment 
(generally called the moment) is the product of the magnitude of the 
force and the perpendicular distance of its line of action from the point 
or axis. For example, the moment of the foree AB (Fig. 40) about the 
point M is equal to the magnitude of the force AB multiplied by MN, 
the perpendicular distance of M from the line AB. If the unit of force 
is the pound, and the unit of distance is the inch, then the unit of ~ 
moment is the inch-pound or pound-inch. Other units of moment in 
common use are the foot-pound or pouwnd-foot, the foot-ton or ton-foot, 
and the inch-ton or ton-inch. 
The construction shown in Fig. 40 is a very convenient one for 
determining graphically the moment 
of a force about a point. AB is 
the line of action of the force, and 
M is the point. The construction 
is as follows. Draw abd parallel to 
AB, and make the length of ab to 
represent the magnitude of the force. 
Through M draw a’MO’ parallel to 
AB. Choose a pole 0. Join oa and 
ob, Take any point o’in AB. Draw 
o’a’ parallel to oa to meet a’Md’ at 
a’, and draw o’b’ parallel to ob to 
meet a’Mh’ at 6’.. Then a’b’ measured with a suitable scale will be the 
magnitude of the moment of the force AB about the point M. 
Draw oh perpendicular to ab, and o’h’ perpendicular to a’b’. The 
triangles oad and o’a’b’ are obviously similar, and ab:a’b’:: oh:o'h’. 
Hence ab xo’h’=a’b’ x oh. But ad is the magnitude of the force AB, 
and o’h’, which is equal to MN, is the perpendicular distance of M from 
AB. Therefore abxo’h’ is equal to the moment of AB about M, and 
therefore a’b’ x oh is equal to the moment of AB about M. 
If oh is made equal to the linear unit, then a’b’ measured with the 
force scale will give the moment required. For example, if of is 1 inch 
and a@’b’ measures 20 lbs. on the force scale, then the required moment is 
20 inch-pownds. It is not always convenient to make of equal to the 
unit of distance, but it should be made a simple multiple or sub- 
multiple of it. 
The following is the simple rule for determining the moment scale. 
Let oh be m times the linear unit, and let the force scale be ~ units of 
42 
Fie. 40. 
