A force can do more than push a body along: applied off-centre, it turns it. That turning effect, the moment, depends not just on how hard you push but on how far from the pivot you push. It is why a long spanner loosens a stubborn bolt and why a child can balance an adult on a seesaw.
The moment of a force about a point is the force multiplied by the perpendicular distance from the point to the line of action of the force: moment = F × d, measured in N m. The centre of gravity is the single point at which the entire weight of a body appears to act. A couple is a pair of equal, antiparallel forces whose only effect is to turn; its torque is one force × the perpendicular separation.
Slide the loads along the beam and change their weights. The beam turns toward the larger moment and sits level only when the clockwise and anticlockwise moments are equal. Notice a small weight far out can balance a large weight close in.
| Quantity | Meaning | Formula |
|---|---|---|
| moment of a force | turning effect about a point | F × d (d perpendicular) |
| couple | two equal, opposite, parallel forces, not in line | no resultant force, pure turning |
| torque of a couple | turning effect of a couple | F × s (s = separation) |
The distance in a moment is always the perpendicular distance from the pivot to the line of action. If a force of magnitude F acts at distance r from the pivot but at angle θ to that line, the moment is F r sinθ, because the perpendicular distance is r sinθ.
Four quick checks on moments, the centre of gravity and couples. Each correct answer earns XP and lights this skill on your star map.
The moment of a force about a pivot is defined as the force multiplied by the:
A force of 12 N acts at a perpendicular distance of 0.25 m from a pivot. The moment is:
The centre of gravity of a body is the point at which:
A couple consists of two forces that are equal in size, opposite in direction and not in line. A couple produces:
Use the perpendicular distance, not the distance along the force or the slanted distance to the pivot. If a force acts at an angle, the moment is F r sinθ, not F r. A second trap: a couple has no resultant force, so do not look for one; its torque is the force times the separation of the two lines of action, and you do not multiply by two even though there are two forces.
Unlocks once the four checks above are done. Worth more XP, written to AS Paper 1 and 2 standard.
A spanner is 0.20 m long. A force of 40 N is applied at its end, perpendicular to the spanner. The moment about the bolt is:
A force of 50 N acts at the end of a 0.40 m rod, at 30° to the rod. The moment of this force about the other end is:
Two forces of 6.0 N form a couple, acting in opposite directions along lines 0.30 m apart. The torque of the couple is:
A uniform metre rule is pivoted at its centre. A 2.0 N weight hangs 40 cm from the pivot on the left. To balance it, a 4.0 N weight must hang on the right at a distance of:
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