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: Vector representation:
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.2 3 o

4. (a) the moment of force F about point A
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 F Magnitude: d
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

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
F=100N 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 3m 2m 1m

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 x
f (x) x y
f (x,y)
F(x,y,z)

15. Force Distributed Over a Linex
f (x) d L
Examples: L O x f0 x
f (x)=f0 L O

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