Calculating an object's moment of inertia

Thread starter Geoffrey F. Miller
Start date Nov 21, 2004
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Inertia Moment Moment of inertia

AI Thread Summary

The moment of inertia of an object is calculated using the volume integral I = ∫∫∫_V ρ(𝑟) r² dV, where ρ(𝑟) represents the density and r is the distance from the axis of rotation. This formula accounts for the distribution of mass relative to the axis, which is crucial for accurate calculations. The discussion highlights the importance of understanding both the density and the geometry of the object when applying this equation. Clarification on the integration limits and specific conditions for different shapes may be necessary for precise calculations. Overall, the moment of inertia is essential for analyzing rotational dynamics in physics.

Nov 21, 2004

Geoffrey F. Miller

What equation(s) is/are used to calculate an object's moment of inertia?

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Nov 21, 2004

cepheid

Staff Emeritus

Science Advisor

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I think it's given by the volume integral:

I = \iiint_V{\rho(\vec{r})r^2}dV

where

\rho(\vec{r}) is the density,

r is the distance from the axis about which the moment of inertia is being calculated.

I'm not totally sure on that though...

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