Consider a rigid body, with a force, F, acting at a point 2R from an arbitrary point on the body, and another force 2F, acting in the same direction as the previous force and a distance R from the aforementioned arbitrary point. Notice that there is a net force of 3F in one direction, while the torque is zero. What does Newton's 2nd Law tell you about the motion of the object?
I will help if you review the conditions for translational and rotational equilibrium.