Centroid & moi table
SUMESHCS1
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Apr 26, 2016
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Figure Length & Centroid Area & Centroid Area Moment of Inertia
Circular arc
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�
??????=
��??????????????????
??????
�
??????=0
Quarter circular arc
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2
�
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2�
??????
�
??????=
2�
??????
Semicircular arc
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�
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�
??????=
2�
??????
Straight line
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2
+�
2
�
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�
??????=�2⁄
Rectangular Area
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�
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�
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??????
�=�ℎ
3
3⁄
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�=ℎ�
3
3⁄
??????
�??????
=�ℎ
3
12⁄
??????
�??????
=ℎ�
3
12⁄
Circular arc
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�
??????=
��??????????????????
??????
�
??????=0
Quarter circular arc
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??????�
2
�
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2�
??????
�
??????=
2�
??????
Semicircular arc
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�
??????=�
�
??????=
2�
??????
Straight line
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2
+�
2
�
??????=�2⁄
�
??????=�2⁄
Rectangular Area
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�
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�
??????=ℎ2⁄
??????
�=�ℎ
3
3⁄
??????
�=ℎ�
3
3⁄
??????
�??????
=�ℎ
3
12⁄
??????
�??????
=ℎ�
3
12⁄
Triangular Area
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�ℎ
2
�
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�
??????=ℎ3⁄
??????
�=�ℎ
3
12⁄
??????
�=ℎ�
3
4⁄
??????
�??????
=�ℎ
3
36⁄
??????
�??????
=ℎ�
3
36⁄
Triangular Area
??????=
�ℎ
2
�
??????=�3⁄
�
??????=ℎ3⁄
??????
�=�ℎ
3
12⁄
??????
�=ℎ�
3
12⁄
??????
�??????
=�ℎ
3
36⁄
??????
�??????
=ℎ�
3
36⁄
Triangular area
??????=
�ℎ
2
�
??????=�2⁄
�
??????=ℎ3⁄
??????
�=�ℎ
3
12⁄
??????
�=7�
3
ℎ48⁄
??????
�??????
=�ℎ
3
36⁄
??????
�??????
=ℎ�
3
48⁄
Quadrant area of a circle
??????=
??????�
2
4
�
??????=4�3??????⁄
�
??????=4�3??????⁄
??????
�=??????�
4
16⁄
??????
�=??????�
4
16⁄
??????
�??????
=(
??????
16
−
4
9??????
)�
4
??????
�??????
=(
??????
16
−
4
9??????
)�
4
Semicircular area
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2
2
�
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�
??????=4�3??????⁄
??????
�=??????�
4
8⁄
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4
8⁄
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=(
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8
−
8
9??????
)�
4
??????
�??????
=??????�
4
8⁄
Circular area
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2
�
??????=�
�
??????=�
??????
�=5??????�
4
4⁄
??????
�=5??????�
4
4⁄
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�??????
=??????�
4
4⁄
??????
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=??????�
4
4⁄
??????=
�ℎ
2
�
??????=2�3⁄
�
??????=ℎ3⁄
??????
�=�ℎ
3
12⁄
??????
�=ℎ�
3
4⁄
??????
�??????
=�ℎ
3
36⁄
??????
�??????
=ℎ�
3
36⁄
Triangular Area
??????=
�ℎ
2
�
??????=�3⁄
�
??????=ℎ3⁄
??????
�=�ℎ
3
12⁄
??????
�=ℎ�
3
12⁄
??????
�??????
=�ℎ
3
36⁄
??????
�??????
=ℎ�
3
36⁄
Triangular area
??????=
�ℎ
2
�
??????=�2⁄
�
??????=ℎ3⁄
??????
�=�ℎ
3
12⁄
??????
�=7�
3
ℎ48⁄
??????
�??????
=�ℎ
3
36⁄
??????
�??????
=ℎ�
3
48⁄
Quadrant area of a circle
??????=
??????�
2
4
�
??????=4�3??????⁄
�
??????=4�3??????⁄
??????
�=??????�
4
16⁄
??????
�=??????�
4
16⁄
??????
�??????
=(
??????
16
−
4
9??????
)�
4
??????
�??????
=(
??????
16
−
4
9??????
)�
4
Semicircular area
??????=
??????�
2
2
�
??????=�
�
??????=4�3??????⁄
??????
�=??????�
4
8⁄
??????
�=5??????�
4
8⁄
??????
�??????
=(
??????
8
−
8
9??????
)�
4
??????
�??????
=??????�
4
8⁄
Circular area
??????=??????�
2
�
??????=�
�
??????=�
??????
�=5??????�
4
4⁄
??????
�=5??????�
4
4⁄
??????
�??????
=??????�
4
4⁄
??????
�??????
=??????�
4
4⁄
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