Us eful Ta bl e s
TABLE D/3
PROPERTIES OF PLANE FIGURES
FIGURE
Arc Segm en t
AREA MOMENTS
OF INERTlA
CE NTROID
r=
a
C
4
_,a r~.
r§
»-
<,
r sina
-
2r
K
-
a
,
Qu a rter a nd Se micircu la r Arcs
~~
)' = -
I
V
r
L ___ ' ___ _ ~ _ _
,
)'
Ci rcula r Area
I :c = I.v = -If4,. "'
0'
If ,.4
/z = -
2
l[
.
I
Semicircular
Area
,.4
Ix = I,. = -
)'
GtJ
r if
4r
3K
- (K
8)
8 - 91l'
t, =
)' = -
--x
8
,.4
Kr'
1,. = - 4
lOA
Ix = I y = .
16
)'
I
I
Qu ar t er -Cir cul ar
Area
{Sh
-
-
4r
x =Y = -
3K
~
I
aXe
"-
Marwan and Waseem AI-Iraqi
[
= ]
Iz = -
Ix =
--x
=
_
_ _
,.4
x
n ,.4
- - x
)'
Area of Circ ula r
Sector
- -.v (K
4)
16 9rr
2 r sina
a
x = ----
3
8
r'
-(a
4
r'
ly = 7((1 + '21 sin 2a )
/z = ~ r4a
www.gigapedia.com
- '12 sin 2u )
483
484
Appendi x D
TABLE
n/a
Useful Tables
PROPERTIES OF PLANE FIGURES Con t in ued
FIGURE
CENTROID
AREA ~IOMENTS
OF INE RTlA
bh'
Recta ngul ar Area
1 =•
3
Yo
rf- ;c -1
•
--x
!--b--.j
~Xl
x C h
Y
I
T ri angu lar Area
Y
I
I--b-J
L
-
bh'
I: =
bh Cb' +h' )
1 = •
12
-
x
12
bh'
1 = •
12
a wb
x = -3
-
-
bh'
1= •
36
h
Y =3
I
bh'
=
"
Area of Ellipt ical
Qu adr ant
-
4a
x = -
Y
I
I
3
1 = -Jrab Ix =
x
16 '
(-,,- i..-)ab'
16 9 ~
:I<
Jra 3 b
- 4b
)' = -
.
bE 5 D __ .,
I.v = 16' ly =
I = !rob (0 2 + b2)
z
16
Subpa rabolic Area
y =
Y
I
kx 2
t,
b
= _x 2
=
-
3a
x =4
ly =
Area A = ab I
3 I
- 3b
x>tb
/"
I
a
jy
Y =10
- x
I
b
y=kx 2 = _ x 2
·'P (
MarNan and Waseem AI-Iraqi
x- = 3a
-
8
- 3b
y =-
5
ab'
21
a'b
5
(a'
+ -b' )
5 21
I =ab z
Pa ra bolic Area
Y
(-,,- i..-)a'b
16 9Jr
:I<
a
AreaA = 2ab
3
4
2ab'
t, = -73b
1 = -2a
'
15
(a'15 +b')
7
I = 2ab z
www. gigapedia.com