The moment of a force is the turning effect of a force about some axis or point. It is defined by:
Moment = force x perpendicular distance from the line of action of force from the pivot Moment = Fx
The SI unit for the moment of a force is Nm.
The principle of moments states that, when a body is in equilibrium, the net force acting on it is 0 and its net moment is 0. This means that, for an object in rotational equilibrium, the sum of its anticlockwise moments about any pivot is equal to the sum of its clockwise moments about the same point.
A couple is a pair of equal and opposite forces applied to an object which act parallel to one another and along different lines. They make an object spin without translational motion.
The moment of a couple is called a torque. It is defined by the product of one of the forces and the perpendicular separation between the forces.
Tourque of a couple = Fd
The centre of gravity of an object coincides with its centre of mass. This is the point through which any externally applied force produces straight-line motion but no rotation; it is the point through which the weight of an object appears to act. A freely suspended object will come to rest with its centre of gravity vertically below the point of suspension. A plumb line can hence be used to draw multiple lines upon which the centre of gravity always lies: the plumb line will always pass through the centre of gravity of the object (vertically below the point of suspension), so drawing in the lines delineated by multiple plumb lines when the card is suspended from different points gives a point of intersection demarcating where the centre of gravity is.
Three coplanar forces are in equilibrium when a triangle of forces representing them is closed. If drawing three end-to-end arrows (one for each force) gives a closed triangle, then there is no resultant force so the object is in equilibrium.