Center of Mass of Uniform Solid Hemisphere

Theorem

Let $\BB$ be a solid hemisphere of radius $r$ of uniform density.

Then the center of mass of $\BB$ is the point $\dfrac {3 r} 8$ from the center of $\BB$ along the radius of $\BB$ perpendicular to the base of $\BB$.


Proof


This theorem requires a proof.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
To discuss this page in more detail, feel free to use the talk page.
When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.



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
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.