Skip to main content
Physics LibreTexts

1.S: Centers of Mass (Summary)

  • Page ID
    8349
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    SUMMARY

    Triangular lamina: 2/3 of way from vertex to midpoint of opposite side

    Solid Tetrahedron, Pyramid, Cone: 3/4 of way from vertex to centroid of opposite face.

    Hollow cone: 2/3 of way from vertex to midpoint of base.

    Semicircular lamina: \(\frac{4a}{3\pi}\)

    Lamina in form of a sector of a circle, angle \(2\alpha\) : \( \frac{(2a \sin\alpha)}{(3\alpha)}\)

    Semicircular wire: \( \frac{2a}{\pi}\)

    Wire in form of an arc of a circle, angle \( 2\alpha\) : \( \frac{(a \sin \alpha)}{\alpha}\)

    Solid hemisphere: \( \frac{3a}{8}\)

    Hollow hemisphere: \( \frac{a}{2}\)


    This page titled 1.S: Centers of Mass (Summary) is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

    • Was this article helpful?