Moment of a Force

1
Moment of a Force
Objects External Effects a particle
translation a 3-D body
translation and rotation
The moment of a force about a point or an axis a
measure of the tendency of the force to rotate a
body about that point or the axis.
2
Definition Moment
Common-sense definition
Magnitude
F
o
d
Direction
is perpendicular to the plane defined by the
force and the rotation center and can be
determined by the right-hand rule.
Vector representation
r is a position vector from the rotation center
to any point on the line of action of the force.
3
Example 1 Find the moments of F , F and F
about point o.
1
2
3
o
4
Example 2 Determine (a) the
moment of force F about point A
(b) the perpendicular distance from point
A to the line of action of
the force.
30o
5
Moment of a Force about a Line
Definition
l
F
Example
What is the moment about x axis?
z
M
y
x
6
Couples

• Definition
• two equal, noncollinear, parallel forces of
  opposite senses are called a couple.
• Effects
• rotation only, no translation

7
Moment of a Couple

• Common sense definition
• Vector representation

F
Magnitude
d
Direction right-hand rule
-F
F
r
-F
8
Couples

• Characteristics
• The magnitude of the moment of the couple
• The direction of the moment of a couple
• Equivalent couples - same and

F
d
F
F
d
F
F
d
F
9
Equivalent Force/Couple Systems

• External effects
• translation
• rotation
• Conditions for two force/couple systems to be
  equivalent

10
The Force-and-Couple Resultant of a Force System
F2
F1
R
F3
o
o
C
F5
F4
11
Equivalent Force / Couple Systems
Example 1 (a) Replace F by an equivalent
force/couple system
applied at A. (b) Replace F by
an equivalent force/couple system
applied at B.
5m
F100N
B
5m
A
30m
12
Equivalent Force / Couple Systems
Example 2 Reduce the force/couple system by an
equivalent single force
y
1000N
500N
500N
45o
x
2m
1m
3m
13
Equivalent Force / Couple Systems

• Questions
• Can any general force/couple system be reduced to
  a single force/couple system?
• Can any general force/couple system be reduced to
  a single force?
• If two force/couple systems have the same moments
  about point P and
• have the same net force, is
  valid? Q is an arbitrary point
• other than P.

14
Distributed Force Systems

• Force distributed over a line
• Force distributed over a surface
• Force distributed over a volume

F(x,y,z)
15
Force Distributed Over a Line
F
d
L
Examples
16
Centroid of an Area
Definition
Example 1 Find the centroid of a rectangle.
h
w
17
Centroid of an Area
Composite body
Example 2 Find the centroid of the following
area.
h
w
w
4h
w