What is a couple? What effect does it have on a body? Show that the moment of couple is same irrespective of the point of rotation of a body.

A couple is the equal and opposite forces applied at different points on an object. These forces produce a rotational effect without causing any translational movement. The forces are in opposite directions but act along parallel lines, and thus result in torque, which produces angular acceleration in the body. The defining feature of a couple is that forces are equal in magnitude and opposite in direction separated by a fixed distance known as the arm of the couple.

The main effect of a couple on an object is to make it rotate about an axis. Since the forces cancel each other out, the net force acting on the object is zero, so there can be no linear motion. Instead, the couple creates torque, which causes rotation.

To show that the moment of a couple is independent of the axis of rotation selected, note that the torque of a couple does not depend on the choice of axes of rotation within the body. This is because the distance between the lines of action of the two forces is the same, and the forces are equal and opposite. The couple’s moment is thus uniform all over the body, thereby pointing out the inbuilt stability of its rotational effect.

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