To implement angular momentum injection in our outflows, following ​Federrath 2014, we first define the following quantities:

m_{acc}=\sum \Delta m_i
com_{acc}=\sum \Delta m_i r_i
p_{acc}=\sum \Delta m_i v_i
L_{acc}=\sum \Delta m_i r_i \times v_i

these represent the total *accreted* mass (m_acc), center of mass (COM_acc), momentum (p_acc) and angular momentum (L_acc) from all the cells within the accretion volume surrounding the sink particle.

We use these quantities to update the particle's mass, COM, and so on, following:

m'=m + m_{acc}
com'=com + com_{acc}
p'=p + p_{acc}

where primes (') denote post-accretion quantities (i.e. m'-m represents the change in particle mass after an accretion event).

Now, angular momentum does not have the same form as above, namely:

q'=q+q_{acc}