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.
Moment of Inertia of a Sphere Index
- Moment of Inertia of a Sphere, Solid Sphere
- Moment of Inertia of a Sphere, Hollow Sphere
- Moment of Inertia of a Sphere, Hollow Core Sphere
Moment of Inertia of a Sphere Formula, Solid Sphere |
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\( I = \frac {2}{5} \; m \; r^2 \) | ||
Symbol | English | Metric |
\(\large{ I }\) = moment of inertia | \(lbm\;/\;ft^2-sec\) | \(kg\;/\;m^2\) |
\(\large{ m }\) = mass | \( lbm \) | \( kg \) |
\(\large{ r }\) = radius | \( in \) | \( mm \) |
Moment of Inertia of a Sphere Formula, Hollow Sphere |
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\( I = \frac {2}{3} \; m \; r^2 \) | ||
Symbol | English | Metric |
\(\large{ I }\) = moment of inertia | \(lbm\;/\;ft^2-sec\) | \(kg\;/\;m^2\) |
\(\large{ m }\) = mass | \( lbm \) | \( kg \) |
\(\large{ r }\) = radius | \( in \) | \( mm \) |
Moment of Inertia of a Sphere Formula, Hollow Core Sphere |
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\( I = \frac {2}{5} \; m \; \left( \; r_2^5 \;-\; r_1{^5} \;/\; r_2{^3} \;-\; r_1{^3}\; \right) \) | ||
Symbol | English | Metric |
\(\large{ I }\) = moment of inertia | \(lbm\;/\;ft^2-sec\) | \(kg\;/\;m^2\) |
\(\large{ m }\) = mass | \( lbm \) | \( kg \) |
\(\large{ r }\) = radius | \( in \) | \( mm \) |
\(\large{ r_1 }\) = radius | \( in \) | \( mm \) |
\(\large{ r_2 }\) = radius | \( in \) | \( mm \) |
Tags: Moment of Inertia