Moment of Inertia of a Sphere
This calculation is for the moment of inertia of a sphere. There are three separate calculations: a solid sphere, a hollow sphere and a hollow core sphere. The difference between a hollow sphere and a hollow core sphere is a hollow sphere has a thin shell, or a thickness that is neglible. Because a sphere is the same dimensions in every dimension, the moment of inertia is the same about every axis.
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Moment of Inertia of a Sphere Formula, Solid Sphere |
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\(\large{ I = \frac {2}{5} \; m \; r^2 }\) | ||
Symbol | English | Metric |
\(\large{ I }\) = moment of inertia | \(\large{\frac{lbm}{ft^2-sec}}\) | \(\large{\frac{kg}{m^2}}\) |
\(\large{ m }\) = mass | \(\large{ lbm }\) | \(\large{ kg }\) |
\(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Moment of Inertia of a Sphere Formula, Hollow Sphere |
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\(\large{ I = \frac {2}{3} \; m \; r^2 }\) | ||
Symbol | English | Metric |
\(\large{ I }\) = moment of inertia | \(\large{\frac{lbm}{ft^2-sec}}\) | \(\large{\frac{kg}{m^2}}\) |
\(\large{ m }\) = mass | \(\large{ lbm }\) | \(\large{ kg }\) |
\(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Moment of Inertia of a Sphere Formula, Hollow Core Sphere |
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\(\large{ I = \frac {2}{5} \; m \; \left( \frac { r_2^5 \;-\; r_1{^5} } { r_2{^3} \;-\; r_1{^3} } \right) }\) | ||
Symbol | English | Metric |
\(\large{ I }\) = moment of inertia | \(\large{\frac{lbm}{ft^2-sec}}\) | \(\large{\frac{kg}{m^2}}\) |
\(\large{ m }\) = mass | \(\large{ lbm }\) | \(\large{ kg }\) |
\(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ r_1 }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
\(\large{ r_2 }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Moment of Inertia of a Sphere Calculator
Tags: Moment of Inertia