Effect of a pure couple in planar mechanics A free couple acting on a rigid body produces which type of motion (neglecting constraints and other forces)?

Introduction / Context:
A couple is a system of two equal, opposite, and parallel forces separated by a perpendicular distance. Its net force is zero, but it produces a pure moment. Recognizing the motion caused by a couple is fundamental in statics and dynamics.

Given Data / Assumptions:

• Rigid body, unconstrained (free) unless otherwise stated.
• Only a couple (net moment M) acts; net resultant force is zero.
• Planar motion considered for simplicity.

Concept / Approach:
Because the vector sum of forces in a couple is zero, there is no net translational effect on the center of mass. However, the net moment is non-zero, which produces angular acceleration about the mass centre according to M = I_c * α, where I_c is the mass moment of inertia about the centre.

Step-by-Step Solution:

Verification / Alternative check:
Real-world examples: turning a steering wheel with both hands in opposite directions, or applying a torque with a wrench while the nut is free to rotate. In both cases, the object spins without translating.

Why Other Options Are Wrong:

• Translatory / Combined: Require a non-zero resultant force.
• None of the above / SHM: A free couple does not cause zero motion nor oscillation; it produces rotation with angular acceleration proportional to the couple.

Common Pitfalls:
Confusing a couple with two non-parallel forces (which would create both a net force and a moment). A true couple is a free vector producing only rotational effect.

Final Answer:
rotational motion