Calculating Moment of Inertia for Non-Uniform Mass Contribution

AI Thread Summary
Calculating the moment of inertia for a body with non-uniform mass distribution requires a different approach than the standard formula I = (1/2)mr^2, which assumes uniform density. The general definition of moment of inertia, I = ∫_V r^2 ρ dV, can be applied to account for varying density. By knowing the mass distribution function, one can integrate over the volume to find the correct moment of inertia. This method allows for accurate calculations in cases where mass is not uniformly distributed. Understanding the mass distribution is crucial for precise calculations.
myer784
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hi everyone,

ive got problem on calculation of moment of inertia for a body that has non-uniform mass contribution . take for example a disc, i believe we can't apply I = (1/2)mr^2 since if we traced back to the derivation of the inertia formula, it assuming constant rho(density)=mass/volume which is not applicable for a body without uniform mass contribution.

Anyone has any idea how calculate the right moment of inertia:confused: :rolleyes:
 
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Try somehow to apply the general definition of the moment of inertia I = \int_{V} r^2 \rho dV to your problem. If you know the mass distribution function, this shouldn't be hard.
 
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