Total angular momentum (torque) of multiple forces If multiple forces act on a single body, we know that if the total angular momentum is null the body does not rotate. How does the principle take into account that I can take any point in space as the one to be used to calculate the different momentum and so the result can be different with different choices of these points?
 A: I suppose you are referring to this:

When the net force on the system is zero, the torque measured from any point in space is the same. For example, the torque on a current-carrying loop in a uniform magnetic field is the same regardless of the point of reference. If the net force $\mathbf {F}$ is not zero, and $\tau_1$ is the torque measured from $\mathbf {r}_{1}$, then the torque measured from $\mathbf {r}_{2}$ is
${\boldsymbol {\tau }}_{2}={\boldsymbol {\tau }}_{1}+(\mathbf {r}_{1}-\mathbf {r}_{2})\times \mathbf {F}$

(emphasis is mine)
The key here is that the statement is true for the case when the total force is zero. Suppose we have several forces, producing zero net torque:
$$
\boldsymbol{\tau}_{total}=\sum_i\mathbf{r}_i\times\mathbf{F}_i=0
$$
if we now calculate the torques in respect to a different point, all the position vectors changes as $\mathbf{r}_i\rightarrow \mathbf{r}_i'=\mathbf{r}_i+\mathbf{R}$, and we have the total torque as
$$ \begin{align}
\boldsymbol{\tau}_{total}' &= \sum_i\mathbf{r}_i'\times\mathbf{F}_i  \\
&= \sum_i\left(\mathbf{r}_i+\mathbf{R}\right)\times\mathbf{F}_i \\
&= \left(\sum_i\mathbf{r}_i\times\mathbf{F}_i \right) + \left( \mathbf{R}\times\sum_i\mathbf{F}_i  \right) \\
&= \boldsymbol{\tau}_{total} + \mathbf{R}\times\mathbf{F}_{total} \\
&=0 \\
 \end{align} $$
since the total force is zero.
