Calculating Moment of Inertia for Non-Uniform Mass Contribution

[myer784]

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

 

[radou]

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.