# 6.1.4: Momentum Equation in Acceleration System

- Page ID
- 714

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} \tag{13}

\]

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} \tag{14}

\]

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

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.