Question

which component of a force does not contribute towards torque?

Answer 1

By definition of the torque, the cross product of the displacement to the point where a force is applied, r, and the force itself, F,
\[ \tau = r \times F \]
it must be that that component of the force F that is parallel to r plays no role. The only part which is non-zero is the part perpendicular to r.