Center of Mass of Uniform Conical Shell

Theorem

Let $\CC$ be a uniform lamina in the shape of a (right circular) cone of height $h$.

Then the center of mass of $\CC$ is the point $\dfrac {2 h} 3$ from the vertex of $\CC$ along the axis of $\CC$ to the base of $\CC$.


Proof


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Sources

  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $2$: Centres of mass
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Appendix $2$: Centres of mass
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