Moment of Inertia of a Sphere Formula, Solid Sphere |
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| \( I \;=\; \dfrac{2}{5} \cdot m \cdot r^2 \) | ||
| Symbol | English | Metric |
| \(\large{ I }\) = Moment of Inertia | \(lbm\;/\;ft^2-sec\) | \(kg\;/\;m^2\) |
| \(\large{ m }\) = Mass | \( lbm \) | \( kg \) |
| \(\large{ r }\) = Radius | \( in \) | \( mm \) |
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 Formula, Hollow Sphere |
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| \( I \;=\; \dfrac {2}{3} \cdot m \cdot r^2 \) | ||
| 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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| \( I \;=\; \dfrac{2}{5} \cdot m \cdot r^2 \cdot \dfrac{ r_2^5 - r_1^5 }{ r_2^3 - r_1^3 } \) | ||
| 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 | \( in \) | \( mm \) |
