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nugget
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Homework Statement
By using spherical coordinates, find the radius of inertia (Is this the same as the radius of gyration?) about the z-axis of the constant density solid which lies above the upper half of the cone x2 + y2 = 3z2 and below the sphere x2 + y2 + (z-2)2 = 4. For a constant density region E of volume V, the radius of inertia about the z-axis is defined as:
VR2 = ∫∫∫(x2 + y2)dV
E
Homework Equations
ρ2 = x2 + y2 + z2
x = ρsin(φ)cos(θ)
y = ρsin(φ)sin(θ)
z = ρcos(φ)
mR2 = I
...where R = radius of gyration and I = moment of inertia about a given axis.
The Attempt at a Solution
At this stage I am beyond confused. Any assistance in beginning this question would be greatly appreciated.