6.1.4: Momentum Equation in Acceleration System

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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.