A small child can balance a heavier one on a seesaw, simply by sitting further out. That is the moment of a force at work: what turns an object depends not just on how hard you push, but on how far from the pivot you push.
The moment of a force is force multiplied by the perpendicular distance from the pivot: moment = F × d, in newton metres (N m). For an object in equilibrium, the principle of moments states that the total clockwise moment equals the total anticlockwise moment about any pivot.
Change the forces and their distances from the central pivot. Notice the curved arrows: they represent the *turning effect* (the moment). Sliding a weight further away does not increase the downward force, but it dramatically increases the curved moment arrow. The beam balances only when those curved arrows perfectly match.
An object in equilibrium is neither speeding up nor turning. Both conditions must hold at the same time:
First, a moment uses the perpendicular distance from the pivot to the line of action of the force, not the length of the beam or a slanted distance. Second, balancing moments alone is not full equilibrium. An object is only in equilibrium when there is both no resultant force and no resultant moment. An answer that mentions only one of these is incomplete.
A uniform beam is pivoted at its centre. A 30 N weight hangs 0.40 m to the left of the pivot. How far to the right must a 60 N weight hang to balance the beam?