Chapter 14.6, Problem 67E

EXPLORING CONCEPTS

Moment of Inertia Determine whether the moment of inertia about the v-axis of the cylinder in Exercise 57will increase or decrease for the nonconstantdensity $\rho (x,y,z)=\sqrt{x^2+z^2}.$.

Moments of Inertia In Exercises 57 and 58, verify the moments of inertia for the solid of uniform density. Use a computer algebra system to evaluate the triple integrals.

$\begin{array}{l}{I}_x=\frac{1}{12}m(3a^2+L^2)\\ I_y=\frac{1}{2}m{a}^2\\ I_z=\frac{1}{12}m(3a^2+L^2)\end{array}$