Moment -- turning effect, force x distance
A moment is the turning effect a force has about a pivot: moment = force x perpendicular distance, so its unit is the newton metre (Nm). Two things control it -- the force and how far from the pivot it acts -- and doubling either doubles the moment. That is why a long spanner undoes a tight nut more easily and a door handle sits far from the hinge. A moment turns clockwise or anticlockwise, which matters when you balance a structure. Example: 20 N at 0.25 m gives 5 Nm.
Equilibrium -- moments and forces balance
A structure not moving or turning is in equilibrium, and two conditions hold together. Principle of moments: about any pivot the clockwise moment equals the anticlockwise moment. Forces balance: total upward force equals total downward force. On a see-saw this gives F1 x d1 = F2 x d2, so a small force far out balances a large force close in. Example: a 300 N child 1.2 m out (360 Nm) balances a 400 N child where 400 x d = 360, so d = 0.9 m.
Beam reactions -- take moments, then balance
A simply supported beam rests on two supports and carries a downward load, each support pushing up with a reaction (R1, R2) that together hold the load. Step 1: take moments about one support (A) -- the reaction at A has zero distance about A, so it drops out, leaving R2. Step 2: use R1 + R2 = total load for R1. A central load splits equally; a load nearer one support puts more on it. Example: a 3 m span, 90 N load 1 m from A gives R2 x 3 = 90, so R2 = 30 N, R1 = 60 N.
Drawn from real examiner reports.
Mixing millimetres and metres
The most-reported structures slip is a unit error: multiplying a force in newtons by a distance still in millimetres, so the moment is a thousand times too big or small. A moment in newton metres needs the distance in metres, so convert first (400 mm is 0.4 m). Examiners insist the answer carries its unit (Nm) and the working is shown. Convert, substitute, state Nm.
w23 P42 Q9c; s22 Q10d
Wrong reaction equation; missing R1 = R2 = 0
Asked for a beam's reactions, weaker candidates guess the split (often halving) or set the wrong balance. Take moments about one support so its reaction disappears, solve for the other, then subtract from the total load. A special case catches many out: a load directly over a single central support sends the whole load through it, so the two end reactions are zero.
s23 P42 Q10a; w23 P42/P43 Q9c(iii)
Confusing a moment with a force
A force is a push or pull in newtons (N). A moment is the turning effect that force has about a pivot, depending on the force AND its distance from the pivot, with the unit newton metre (Nm), not the newton. Candidates who treat a moment as just the force ignore the distance and cannot explain why a longer lever turns more easily for the same push.
Assuming supports always share load equally
Assuming a beam's two reactions are always half the load each. They are equal ONLY when the load acts midway between the supports. When the load sits nearer one support, that support carries MORE -- the reactions depend on the load position. For a 90 N load 1 m from A on a 3 m span, R2 = 30 N and R1 = 60 N: the nearer support carries twice as much. Locate the load first.
Checking only one equilibrium condition
Equilibrium needs two conditions at once, and candidates often give only one. Forces must balance -- total upward equals total downward -- so it does not move up or down. Moments must ALSO balance -- clockwise equals anticlockwise about any pivot -- so it does not rotate. Both are needed: forces stop it sliding, moments stop it turning.
Dropping a load or using the wrong distance
On a beam with more than one load, take the moment of EVERY load about the chosen support, each with its OWN distance, then add them before dividing by the span. Two slips recur: forgetting one load, and using the wrong distance for a load. Work out force x distance for each load, then combine. Missing a load makes the reaction come out too small.
s23 P42 Q10a
See-saw balances only if forces are equal
A sharp wrong belief: that a see-saw balances only if the two weights are the SAME. Balance depends on the moment each side -- force x distance -- so a small force far out balances a large force close in. A 300 N child 1.2 m out (360 Nm) balances a 400 N child 0.9 m out (360 Nm): unequal forces, equal moments. The test is equal MOMENTS, not equal forces.
Convert to metres first, state the unit
Convert every distance to metres first, so a moment comes out in Nm. Write the rule (moment = force x distance, or clockwise = anticlockwise), substitute, and state the unit (Nm or N). Credit is given at each stage, so working earns method marks even if the arithmetic slips.
Balance problems -- set the two moments equal
For a balance or lever problem, set clockwise = anticlockwise moment (F1 x d1 = F2 x d2) and rearrange for the unknown. Do not just compare forces -- balance depends on force x distance. The larger force sits at the shorter distance: a small effort far out balances a large load close in.
Take moments about a support to isolate a reaction
For a beam reaction, take moments about ONE support: its reaction acts through the pivot, so its distance is zero and drops out, leaving one unknown to solve. Then use R1 + R2 = total load to get the other by subtraction. Either support works; pick the one removing the unknown reaction.
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