Second Moment of Area of a Circle Sector formulas |
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\( I_{x} \;=\; \dfrac{ r^4 }{ 4} \cdot \left( \Delta - \dfrac{1}{2} \cdot sin( 2 \cdot \Delta ) \right) \) \( I_{y} \;=\; \dfrac{ r^4 }{ 4} \cdot \left( \Delta + \dfrac{1}{2} \cdot sin( 2 \cdot \Delta ) \right) - \left( \dfrac{ 4 \cdot r^4 }{ 9 \cdot \Delta } \cdot sin^2 ( \Delta ) \right) \) \( I_{x1} \;=\; I_x + r^4 \cdot \Delta \cdot sin^2 (\Delta) \) \( I_{y1} \;=\; \dfrac{ r^4 }{ 4} \cdot \left( \Delta + \dfrac{1}{2} \cdot sin( 2 \cdot \Delta ) \right) \) |
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| Symbol | English | Metric |
| \( I \) = moment of inertia | \( in^4 \) | \( mm^4 \) |
| \( \Delta \) = angle | \( deg \) | \(rad \) |
| \( r \) = radius | \( in \) | \( mm \) |
