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