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Vitani11
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Homework Statement
Why is it that when you integrate to find the moment of inertia of a cone standing on its vertex (like a spinning top) with height h mass M and radius R do you integrate the R limits as 0 to (R/h)z in the triple integral (cylindrical coordinates) below?
Homework Equations
I = moment of inertia
D = density (M/πR2h)
ρ = R distance from rotation axis (limits from 0 to (R\h)z)
φ = 2π the angle swept (limits 0 to 2π)
z = h the height of the cone (limits 0 to h)
The Attempt at a Solution
I = ∫ρ2dm = D∫∫∫ρ3dρdφdz