Centroids Of Common Shapes Of Areas And Lines Edit
Triangular Area Edit
A
r
e
a
=
b
∗
h
2
{\displaystyle Area={\frac {b*h}{2}}}
Quarter Circular Area Edit
A
r
e
a
=
π
r
2
4
{\displaystyle Area={\frac {\pi \ r^{2}}{4}}}
Semicircular Area Edit
A
r
e
a
=
π
r
2
2
{\displaystyle Area={\frac {\pi \ r^{2}}{2}}}
Semiparabolic Area Edit
A
r
e
a
=
2
a
h
3
{\displaystyle Area={\frac {2ah}{3}}}
Parabolic Area Edit
A
r
e
a
=
4
a
h
3
{\displaystyle Area={\frac {4ah}{3}}}
Parabolic Spandrel Edit
A
r
e
a
=
a
h
3
{\displaystyle Area={\frac {ah}{3}}}
Circular Sector Edit
A
r
e
a
=
α
r
2
{\displaystyle Area=\alpha \ r^{2}}
Quarter Circular Arc Edit
A
r
e
a
=
π
2
{\displaystyle Area={\frac {\pi \ }{2}}}
Semi Circular Arc Edit
A
r
e
a
=
π
r
{\displaystyle Area=\pi \ r}
Arc Of Circle Edit
A
r
e
a
=
2
α
r
{\displaystyle Area=2\alpha \ r}
Area Moments Of Inertia of Common Geometric Shapes Edit
Rectangle Edit
I
x
=
1
3
b
h
3
{\displaystyle I_{x}={\frac {1}{3}}bh^{3}}
I
y
=
1
3
h
b
3
{\displaystyle I_{y}={\frac {1}{3}}hb^{3}}
I
x
′
=
1
12
b
h
3
{\displaystyle I_{x'}={\frac {1}{12}}bh^{3}}
I
y
′
=
1
12
h
b
3
{\displaystyle I_{y'}={\frac {1}{12}}hb^{3}}
Right Triangular Area Edit
I
x
=
1
12
b
h
3
{\displaystyle I_{x}={\frac {1}{12}}bh^{3}}
I
y
=
1
4
h
b
3
{\displaystyle I_{y}={\frac {1}{4}}hb^{3}}
I
x
′
=
1
36
b
h
3
{\displaystyle I_{x'}={\frac {1}{36}}bh^{3}}
I
y
′
=
1
36
h
b
3
{\displaystyle I_{y'}={\frac {1}{36}}hb^{3}}
Triangular Area Edit
I
x
=
1
12
b
h
3
{\displaystyle I_{x}={\frac {1}{12}}bh^{3}}
I
x
′
=
1
36
b
h
3
{\displaystyle I_{x'}={\frac {1}{36}}bh^{3}}
Circular Area Edit
J
C
=
π
r
4
2
{\displaystyle J_{C}={\frac {\pi \ r^{4}}{2}}}
I
x
′
=
I
y
′
=
π
r
4
4
{\displaystyle I_{x'}=I_{y'}={\frac {\pi \ r^{4}}{4}}}
Hollow circle Edit This is used for hollow cylinders where there is solid material between the outer and inner radius, but no material between the inner radius and the center, like a pipe's cross-section.
I
=
π
(
r
o
4
−
r
i
4
)
4
{\displaystyle I={\frac {\pi \ (r_{o}^{4}-r_{i}^{4})}{4}}}
r
o
{\displaystyle r_{o}}
r
i
{\displaystyle r_{i}}
Semicircular Area Edit
I
x
=
I
y
=
1
8
π
r
4
{\displaystyle I_{x}=I_{y}={\frac {1}{8}}\pi \ r^{4}}
I
x
′
=
(
π
8
−
8
9
π
)
r
4
{\displaystyle I_{x'}=({\frac {\pi }{8}}-{\frac {8}{9\pi }})r^{4}}
I
y
′
=
1
8
π
r
4
{\displaystyle I_{y'}={\frac {1}{8}}\pi \ r^{4}}
Quarter Circle Edit
I
x
=
I
y
=
1
16
π
r
4
{\displaystyle I_{x}=I_{y}={\frac {1}{16}}\pi \ r^{4}}
I
x
′
=
I
y
′
=
(
π
16
−
4
9
π
)
r
4
{\displaystyle I_{x'}=I_{y'}=({\frac {\pi }{16}}-{\frac {4}{9\pi }})r^{4}}
further reading Edit 
