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Question 11.4: Calculate the moment of inertia of a homogeneous massive cub...

Calculate the moment of inertia of a homogeneous massive cube about one of its edges.

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Let \varrho be the density and s the edge length of the cube. A mass element is then given by

dm =\varrho dV =\varrho  dx  dy  dz.

The moment of inertia about AB (see Fig. 11.8) is evaluated as

\Theta_{AB} =\varrho \int\limits_{0}^{s}{\int\limits_{0}^{s}{\int\limits_{0}^{s}{(x^{2} +y^{2})dx  dy  dz}}} = \frac{2}{3} \varrho s^{5} = \frac{2}{3} Ms^{2}.
11.8

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