Center of Mass of Uniform Triangular Lamina

Theorem

Let $\LL$ be a uniform lamina in the shape of a triangle.

Then the center of mass of $\LL$ is at the centroid of $\LL$.

That is, it lies $\dfrac 2 3$ of the way along an arbitrary median of $\LL$ from its vertex.


Proof


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Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Appendix: Table $4$ Centres of mass The position of the centre of mass of certain uniform bodies.
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Appendix: Table $4$ Centres of mass The position of the centre of mass of certain uniform bodies.
  • 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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