Moment of Inertia of a Rectangle Formulas, Solid Plane, z Axis |
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\( I_z \;=\; \dfrac{1}{12} \cdot m \cdot \left( l^2 + w^2 \right) \) \( I_z \;=\; \dfrac{1}{12} \cdot l\cdot w \cdot \left( l^2 + w^2 \right) \) \( I_{z1} \;=\; \dfrac{1}{12} \cdot m \cdot \left( 4\cdot l^2 + w^2 \right) \) |
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| Symbol | English | Metric |
| \( I \) = Moment of Inertia | \(lbm\;/\;ft^2-sec\) | \(kg\;/\;m^2\) |
| \( l \) = Length | \( in \) | \( mm \) |
| \( m \) = Mass | \( lbm \) | \( kg \) |
| \( w \) = Width | \( in \) | \( mm \) |
Moment of Inertia of a Rectangle Formulas, Solid Plane, x Axis |
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\( I_x \;=\; \dfrac {1}{12} \cdot l\cdot w^3 \) \( I_x \;=\; \dfrac {1}{12} \cdot m \cdot l^2 \) \( I_{x1} \;=\; \dfrac {1}{3} \cdot l\cdot w^3 \) \( I_{x1} \;=\; \dfrac {1}{3} \cdot m \cdot w^2 \) |
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| Symbol | English | Metric |
| \( I \) = Moment of Inertia | \(lbm\;/\;ft^2-sec\) | \(kg\;/\;m^2\) |
| \( l \) = Length | \( in \) | \( mm \) |
| \( m \) = Mass | \(\large{ lbm }\) | \(\large{ kg }\) |
| \( w \) = Width | \( in \) | \( mm \) |
Moment of Inertia of a Rectangle Formulas, Solid Plane, y Axis |
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\( I_y \;=\; \dfrac {1}{12} \cdot l^3\cdot w \) \( I_{y1} \;=\; \dfrac {1}{3} \cdot l^3\cdot w \) |
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| Symbol | English | Metric |
| \( I \) = Moment of Inertia | \(lbm\;/\;ft^2-sec\) | \(kg\;/\;m^2\) |
| \( l \) = Length | \( in \) | \( mm \) |
| \( w \) = Width | \( in \) | \( mm \) |
Moment of Inertia of a Rectangle Formula, Hollow Core Plane, x Axis |
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| \( I_x \;=\; \dfrac{ l\cdot w^3}{12 } - \dfrac{ l_1\cdot w_1{^3} }{ 12 } \) | ||
| Symbol | English | Metric |
| \( I \) = Moment of Inertia | \(lbm\;/\;ft^2-sec\) | \(kg\;/\;m^2\) |
| \( l \) = Length | \( in \) | \( mm \) |
| \( l_1 \) = Length | \( in \) | \( mm \) |
| \( w \) = Width | \( in \) | \( mm \) |
| \( w_1 \) = Width | \( in \) | \( mm \) |
Moment of Inertia of a Rectangle Formula, Hollow Core Plane, Y Axis |
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| \( I_y \;=\; \dfrac{ l^3\cdot w}{12 } - \dfrac{ l_1{^3} \cdot w_1}{12 } \) | ||
| Symbol | English | Metric |
| \( I \) = Moment of Inertia | \(lbm\;/\;ft^2-sec\) | \(kg\;/\;m^2\) |
| \( l \) = Length | \( in \) | \( mm \) |
| \( l_1 \) = Length | \( in \) | \( mm \) |
| \( w \) = Width | \( in \) | \( mm \) |
| \( w_1 \) = Width | \( in \) | \( mm \) |