I will do it in two dimensions, similar in 3
moment = F1 X R1 + (-F1) X R2
= (R1y Fx - R1x Fy)k -(R2y Fx -R2x Fy)k
= Fx(R1y-R2y)k +Fy (R2x-R1y)k
so in k direction and depending only on how far apart the two forces are, not the origin of R1 and R2
Show that when the total external force acting on N particles is zero, the total external torque is independent of the choice of reference point O.
2 answers
typo
= Fx(R1y-R2y)k + Fy (R2x-R1x)k
By the way
the vector product
F X (R2-R1) is a moment called a "couple".
= Fx(R1y-R2y)k + Fy (R2x-R1x)k
By the way
the vector product
F X (R2-R1) is a moment called a "couple".