Suppose the coordinates ##(\bar{x}, \bar{y})## of the centroid (or the centre of mass) of an arc is defined as follows(adsbygoogle = window.adsbygoogle || []).push({});

##\bar{x}=\frac{1}{L}\int x\,ds## and ##\bar{y}=\frac{1}{L}\int y\,ds##, where ##L## is the arc length.

Could you prove that the centroid is invariant under a rotation of the coordinate axes?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Prove centre of mass of an arc is rotationally invariant

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Prove centre mass | Date |
---|---|

I A problematic limit to prove | Jan 26, 2018 |

I Proving equivalence between statements about a sequence | Feb 12, 2017 |

I Prove that ∫f(x)δ(x)dx=f(0) | Jan 22, 2017 |

I Prove ln(x) <= x-1 for positive x | Jan 15, 2017 |

Double Integrals - application to centre of mass. | Sep 3, 2012 |

**Physics Forums - The Fusion of Science and Community**