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Second Moment of Area of a Circle

 

Second Moment of Area of a Circle formulas

\( I_{x} \;=\;   \dfrac{ \pi \cdot r^4}{ 4 }\) 

\( I_{y} \;=\; \dfrac{ \pi \cdot r^4}{ 4 }\)

\( I_{x1} \;=\;   \dfrac{ 5 \cdot \pi \cdot r^4}{ 4 }\) 

\( I_{y1} \;=\;  \dfrac{ 5 \cdot \pi \cdot r^4}{ 4 }\)

Symbol English Metric
\( I \) = Moment of Inertia \( in^4 \) \( mm^4 \)
\( \pi \) = Pi \(3.141 592 653 ...\) \(3.141 592 653 ...\)
\( r \) = Radius \( in \) \(mm \)

Second moment of area of a circle, also called area moment of inertia, represents its resistance to bending or deflection about a given axis.  It's a geometric property that depends on the distribution of the area of the circle relative to that axis.  For a circle, this value is calculated about a specific axis (usually the centroidal axis).

circle xy 1

circle arc 4

 

 

 

 

 

 

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