APFIVE Rotational Inertia Integral of a Cone
A solid cone with mass M, height h, and base radius R has its rotational inertia about an axis through its vertex and perpendicular to its axis of symmetry given by I = 3MR²/10 + 3Mh²/20. If the cone’s density is uniform, which of the following integrals would directly yield this result?
A
∫(R² + h²)dm integrated over the entire volume
B
∫(x² + z²)dm for a coordinate system with origin at the vertex
C
∫r²dm where r is measured from the cone’s axis of symmetry
D
∫(x² + y²)dm for a coordinate system with origin at the vertex
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