Radius of Gyration of a Circle Sector formulas |
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\( k_{x} \;=\; \dfrac{1}{4} \cdot \sqrt{ 2 \cdot r^2 \cdot \dfrac{ 2\cdot \Delta - sin(2 \cdot \Delta ) }{ \Delta } } \) \( k_{y} \;=\; \dfrac{1}{12} \cdot \sqrt{ 2 \cdot r^2 \cdot \dfrac{ 180^2 + 9\cdot \Delta \cdot sin(2\cdot \Delta) - 32 + 32 \cdot cos^2(\Delta) }{ \Delta^2 } } \) \( k_{z} \;=\; \dfrac{1}{6} \cdot \sqrt{ 2 \cdot r^2 \cdot \dfrac{ 9 \cdot \Delta^2 - 8 \cdot sin^2(2\cdot \Delta ) }{ \Delta^2 } } \) \( k_{x1} \;=\; \dfrac{1}{4} \cdot \sqrt{ 2 \cdot r^2 \cdot \dfrac{ 2\cdot \Delta - sin(2 \cdot \Delta) }{ \Delta } } \) \( k_{y1} \;=\; \dfrac{1}{4} \cdot \sqrt{ 2 \cdot r^2 \cdot \dfrac{ 2\cdot \Delta + sin(2 \cdot \Delta ) }{ \Delta } } \) \( k_{x1} \;=\; \dfrac{ r }{ \sqrt{2} } \) |
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| Symbol | English | Metric |
| \( k \) = radius of gyration | \( in \) | \( mm \) |
| \( \Delta \) = angle | \( deg \) | \(rad \) |
| \( r \) = radius | \( in \) | \( mm \) |
