Skip to main content
Engineering LibreTexts

6.1.4: Momentum Equation in Acceleration System

  • Page ID
    714
    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    For accelerate system, the right hand side has to include the following acceleration
    \[
    \pmb{a}_{acc} =
    \boldsymbol{\omega} \times \left( \pmb{r}\times \boldsymbol{\omega} \right) +
    2\,\boldsymbol{U} \times \boldsymbol{\omega} +
    \pmb{r} \times \dot{\boldsymbol{\omega}} -
    \pmb{a}_0
    \label{mom:eq:accelartion}
    \]
    Where \(\pmb{r}\) is the distance from the center of the frame of reference and the add force is
    \[
    \pmb{F}_{add} = \int_{V_{c.v.}} \pmb{a}_{acc} \,\rho\,dV
    \label{mom:eq:addF}
    \]

    Integral of Uniform Pressure on Body

    In this kind of calculations, it common to obtain a situation where one of the term will be an integral of the pressure over the body surface. This situation is a similar idea that was shown in Section . In this case the resulting force due to the pressure is zero to all directions.

    Contributors and Attributions

    • Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.


    This page titled 6.1.4: Momentum Equation in Acceleration System is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.


    This page titled 6.1.4: Momentum Equation in Acceleration System is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Genick Bar-Meir via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.