 Moment of inertia of a pointed cubic-profile solid of revolution

ID: moment-of-inertia-of-a-pointed-cubic-profile-solid-of-revolution

Consider the uniform solid of revolution about the

x_{3}

-axis whose boundary is

x_{1}^{2} + x_{2}^{2} = x_{3}^{2} - \frac{x _{3}^{3}}{h}, 0 \leq x_{3} \leq h .

For total mass

M

3 h /5

from the pointed origin, and the principal moments about that origin are

I_{1} = I_{2} = \frac{3}{7} M h^{2}, I_{3} = \frac{2}{35} M h^{2} .

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