The moment of inertia of the tetrahedron will be 435.75,Moment of inertia is found by the application of integration.
The sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation expresses a body's tendency to resist angular acceleration.
The moment of inertia of a tetrahedron of constant density is found as;
[tex]\rm I_Z = \int\limits^a_b {dz} \, dv \\\\ dv=dxdy\\\\ I_Z = \int_0^9 \int_0^{8-\frac{8x}{9}} \int_0^{5-\frac{5x}{9} -\frac{5x}{8} }(x^2+y^2)dzdy[/tex]
After applying the limit, we get the answer is;
[tex]\rm I_Z= \frac{1743}{4} \\\\ I_Z= 435.75[/tex]
Hence, the moment of inertia of tetrahedron will be 435.75
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