Moment of a Force - PowerPoint PPT Presentation

1 / 17
About This Presentation
Title:

Moment of a Force

Description:

Moment of a Force Objects External Effects a particle translation a 3-D body translation and rotation – PowerPoint PPT presentation

Number of Views:121
Avg rating:3.0/5.0
Slides: 18
Provided by: Wenj152
Category:
Tags: force | line | moment | power

less

Transcript and Presenter's Notes

Title: 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
Write a Comment
User Comments (0)
About PowerShow.com