Linux Systems Programming: Inter Process Communication (IPC) using Pipes
centre of gravitry
1. Objectives
To discuss the concept of the center of
gravity, center of mass, and centroids
(centers of area).
To show how to determine the location
of the center of gravity and centroid for
a system of particles and a body of
arbitrary shape.
2. Center of Gravity
The center of gravity G is a point which locates the
resultant weight of a system of particles.
The weights of the particles is considered to be a
parallel force system. The system of weights can be
replaced by a single weight acting at the Center of
Gravity.
3.
4.
5.
n
1
i
i
R W
W Total Weight
n
n
3
3
2
2
1
1
R
R W
x
~
W
x
~
W
x
~
W
x
~
W
x
x location:
n
n
3
3
2
2
1
1
R
R W
y
~
W
y
~
W
y
~
W
y
~
W
y
y location:
n
n
3
3
2
2
1
1
R
R W
z
~
W
z
~
W
z
~
W
z
~
W
z
z location:
13. CENTROID
The centroid C is a point which defines the
geometric center of an object. Its location can
be determined by formulas similar to those
used for center of gravity or center of mass.
25.
dy
1
y
2
dL
y
2
dy
dx
y
x
dy
1
dy
dx
dL
dy
dx
dL
2
2
2
2
2
26.
m
410
.
0
479
.
1
6063
.
0
dy
1
y
4
dy
1
y
4
y
x
y
x
dy
1
y
2
dy
1
y
2
x
dL
dL
x
~
x
1
0
2
1
0
2
2
2
1
0
2
1
0
2
L
L
27.
m
574
.
0
479
.
1
8484
.
0
dy
1
y
4
dy
1
y
4
y
y
dy
1
y
2
dy
1
y
2
y
dL
dL
y
~
y
1
0
2
1
0
2
1
0
2
1
0
2
L
L
40. Composite Bodies
If a body is made up of several simpler
bodies then a special technique can be used.
41. Procedure
Divide body into several subparts.
If the body has a hole or cutout, treat
that as negative area.
Centroid will lie on line of symmetry.
Create Table and calculate centroid.
49. Segment A (ft2) x y xA yA
1 4.5 1 1 4.5 4.5
2 6 -1 1.5 -6 9
3 1 -2.5 0.5 -2.5 0.5
A = 11.5 xA = -4 xA = 14
ft
22
.
1
5
.
11
14
A
A
y
~
y
ft
348
.
0
5
.
11
4
A
A
x
~
x
51. Segement A (ft2) x y xA yA
1 4.5 1 1 4.5 4.5
2 9 -1.5 1.5 -13.5 13.5
3 -2.5 -2.5 2 5 -4
A = 11.5 xA = -4 xA = 14
ft
22
.
1
5
.
11
14
A
A
y
~
y
ft
348
.
0
5
.
11
4
A
A
x
~
x