Verify that the moment of inertia of a spherical shell of uniform density about its
Chapter 15, Problem 34(choose chapter or problem)
In Exercises 33 and 34, use the following formulas for the moments of inertia about the coordinate axes of a surface lamina of density \(\rho\).
\(I_{x}=\int_{S} \int\left(y^{2}+z^{2}\right) \rho(x, y, z) d S\)
\(I_{y}=\int_{S} \int\left(x^{2}+z^{2}\right) \rho(x, y, z) d S\)
\(I_{z}=\int_{S} \int\left(x^{2}+y^{2}\right) \rho(x, y, z) d S\)
Verify that the moment of inertia of a spherical shell of uniform density about its diameter is \(\frac{2}{3} m a^{2}\), where m is the mass and a is the radius.
Text Transcription:
rho
I_x = int_S int(y^2 + z^2) rho(x, y, z) dS
I_y = int_S int(x^2 + z^2) rho(x, y, z) dS
I_z = int_S int(x^{2} + y^2) rho(x, y, z) dS
2 / 3 ma^2
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