The discussion focuses on calculating the moments of inertia Ixy, Iyz, and Izx for a solid object using triple integrals. Participants clarify that the correct differential mass element is dM = k dV = k dx dy dz, where dV represents the volume element. The integration ranges for dx, dy, and dz are confirmed as valid, with specific limits provided for each variable. Participants emphasize the importance of correctly applying the limits of integration to ensure accurate results.
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Are my Ixx, Iyy and Izz are correct?vela said:You don't. You evaluate the triple integrals.
No, they're not. You can't say ##y^2+z^2=a^2-x^2## because that's true only on the spherical part of the surface. Inside the hemisphere, it doesn't hold.unscientific said:Are my Ixx, Iyy and Izz are correct?
That's dV, not dM. You should write dM = k dV = k dx dy dz.Oh, so it's dM = dx dy dz,
Yes.then the range for dx is from -√(a2-y2-z2) to √(a2-y2-z2)
for dy it's from -√(a2-z2) to √(a2-z2)
for dz it's from 0 to a
Are my ranges of integration right?