I am new to physics and just started with rotational mechanics. I wanted to find the net torque on an object by different forces $\vec F_1, \vec F_2, \dots, \vec F_n$.
My Thinking : $$\vec F_T = \vec F_1 + \vec F_2 \dots$$ $$\vec\Gamma_T = \vec F_T \times \vec r$$
My first thought was to add forces right away vectorially, and then find the torque of the net force. But the textbook says to find torque of each force individually and then add them in vector form.
My question is why the idea of net force doesn't work. Is it just that we relate it with real life where net force is zero but still there is torque, or there is some mathematics behind it?
\times
in math for a $\times$ symbol instead of $x$ or $X$. $\endgroup$