Question

Twisting couple on the wire

Answer 1

When the two equal or opposite forces are exerted at the two ends of an object, it constitutes a couple. The net force of couple is zero.
The twisting of a structural member about its longitudinal axis by two equal and opposite torques is expressed through a certain angle.  When the disc is rotated on a horizontal plane in order to twist the wire, the different elements of the wire undergo shearing strains. 

The twisting couple per unit twist of the wire is called the torsional rigidity or modulus of torsion of the cylinder of wire. 
Twisting couple per unit twist = C ∅ = - I d² ∅/dt²,

where the Angle of twist at the lower end of the wire is ∅, restoring couple is C∅, where C is the torsional rigidity of the wire, and I is the moment of inertia of the disc about the axis of the wire. the '-' sign indicates that the couple C∅ decreases the twist.

Answer 2

when two equal and opposite forces are exerted to two ends of a thing it forms a couple
In a couple the net force is 0
But the net momentum at that is not
There is no transition motion but there is rotational motion present in it
The twisting of a structural member at its longitudinal axis by two torque equal and opposite to each other is expressed through a angle that is specific