So... torque is measured in Newton meters ....

We have an arm fixed at one end ,but free to rotate about that anchor point.

We can apply a torque of 1Nm , which will want to make the arm rotate about the anchor point ... this could be a force of 1N , 1 m from the pivot ...or 2 N half a meter from pivot , of 4N a quarter meter from pivot ...etc .. all exert a torque of 1Nm

torque = f x (distance of force from anchor pt.)

Whether this arm has angular velocity or not is irrelevant .

It's very similar to linear force acting on a mass , it doesn't matter if the mass already has a velocity , the aplied force will want to change this already present velocity.