Recall the important and general relation (basically Newtons second
law for rotation)
to graduate this equation to a vector equation we obviously need to specify
the vector version of force. This is in fact very easy. We simply take the cross product of Newtons second law for translation
with 
the displacement
vector from a point of reference to the particle:
We can now identify the expression on the left hand side as the
torque with respect to the reference point:
As we have tried to make clear previously the torque associated with
a given force depends crucially on the chosen point of reference.
An important formula is derived in the book for the relationship
between torque with respect to different points of reference:
It may remind you about the parallel axis theorem because it relates
torque associated with an arbitrary point with the torque
associated with the torque around the center of mass of the system.
As a special case note that if no net force acts (
)
then the torque on the
system is independent of the choice of reference axis. This will be important when we consider static equilibrium.