# 6.1.4: Momentum Equation in Acceleration System


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.