15
PART II
CONTENTS:
•
VECTOR REPRESENTATION OF A MOMENT
•
MOMENT OF A FORCE ABOUT A LINE (AXIS)
•
COUPLES
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16
VECTOR REPRESENTATION OF A MOMENT
In Fig. 41, the moment of the force
F
about point
O
can be represented by the expression
O
=
×
M
r
F
(9)
where
r
is a
position vector
from point
O
to a point
A
on the line of action of the force
F
.
The
sign
×
means the cross product of two vectors, and is defined as
sin
sin
O
α
α
=
×
=
⋅
⋅
⋅
=
⋅
⋅
⋅
M
r
F
r
F
e
F
r
e
Disp
where
α
is the angle (0
180 )
α
°
°
≤
≤
between the two vectors
r
and
F
,
e
is a unit vector
perpendicular to the plane determined by vectors
r
and
F
as shown in Fig. 43
a
.
It can be seen that the term

 sin
α
⋅
r
denotes the perpendicular distance
d
from the
moment center
O
to the line of action.
The distance
d
is independent of the position
A
along the
line of action of the force since
A
3
A
2
A
1