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