Forces, moments and equilibrium form the control-panel for every mechanics question after WA 1.
Key points
Nail the four compulsory models - field forces, contact forces, Hooke springs and couple torque - then clamp them together with the twin “net-zero” tests (\\( \sum \vec\{F\} = 0 \\) and \\( \sum \tau = 0 \\)).
The pay-off is a one-line checklist that prevents sign slips and missing forces.
Planning a revision session? Use our study places near me map to find libraries, community study rooms, and late-night spots.
Read in layers
1 second
Read the summary above.
10 seconds
Scan the first few sections below.
100 seconds
Jump into the section that matches your decision.
Quick study map
Concrete example: how to use this page
1 Quick syllabus snapshot
2 Field forces every IP student must quote
Q: What does A-Level Physics: 2) Forces & Moments Guide cover? A: From Lorentz force to seesaw balance, this post reverse-engineers Section I Topic 2 of the 2026 H2 Physics syllabus into check-lists.
TL;DR Forces, moments and equilibrium form the control-panel for every mechanics question after WA 1. Nail the four compulsory models - field forces, contact forces, Hooke springs and couple torque - then clamp them together with the twin “net-zero” tests (∑F=0 and ∑τ=0
). The pay-off is a one-line checklist that prevents sign slips and missing forces.
Quick study map
If you only have...
Focus on...
1 second
Identify the force model before calculating
10 seconds
Field forces, contact forces, Hooke's law, and moments
100 seconds
The syllabus snapshot and force-model table
10 minutes
Equilibrium, couples, and free-body diagram traps
Concrete example: how to use this page
When a mechanics question feels messy, first draw the free-body diagram and label every force. Then decide whether the object is translating, rotating, or in equilibrium. That order keeps force and moment equations from mixing too early.
Revisit earlier/later mechanics chapters in our free H2 Physics notes - it chains Topic 1 foundations to this post and onward to kinematics, circular motion, and power drills for Paper 2/3.
1 Quick syllabus snapshot
Section I Topic 2 sets nine learning outcomes, from describing field forces to drawing vector triangles. They are reproduced verbatim in the SEAB 9478 document so you can tick them off one by one.
2 Field forces every IP student must quote
Situation
Model equation
Vector cue
1
Mass in Earth field
F=mg
Down
2
Charge in electric field
F=qE
Along E
3
Charge moving in B
F=qvBsinθ
4
Conductor length L in B
F=ILBsinθ
The last two come straight from the Lorentz force law and its current-carrying variant.
In equation 4, the current-carrying variant for Lorentz force law, the direction of the length L is given by the direction of the current. I is defined to be the magnitude of the current so it's a scalar. Hence we use the length vector to denote the direction of the current.
2.1 Mini-drill
Identify the carrier (mass, charge or current).
Write the matching formula.
Use the right-hand grip rule on your free-body diagram to determine the direction of the force.
3 Contact forces - four names, one diagram
Normal force: surface reaction perpendicular to contact.
Buoyant force (upthrust): weight of displaced fluid.
Friction: parallel to surface, opposes impending motion.
Viscous drag / air resistance: proportional to speed for low v.
Teach your child to label them exactly as the mark scheme: “normal”, “upthrust”, “friction”, “viscous”. Physics Classroom's taxonomy is a handy poster for the study wall.
4 Hooke's law - the spring you will meet ten times
For an ideal spring
F=kx
where k is the force constant and x is the extension or compression. The law holds until the proportional-limit point. Khan Academy's graph tutorial is perfect for WA data-logger questions.
Parent cue: ask your teen to re-plot their practical data as F vs x and fish out k from the gradient.
5 Moment of a force
The turning effect of a single force about point O is
τ=Fd⊥
where d⊥ is the perpendicular distance from O to the line of action. Engineering Statics gives a brilliant interactive showing how d⊥ shrinks as the force slides.
6 Torque of a couple - pure rotation, zero translation
A couple is two equal, opposite, parallel forces whose lines of action are separated by distance s. They cancel translationally but create a pure moment
τcouple=Fs
7 Centre of gravity
For weighted assessment (WA) problems, the weight may be treated as acting at a single point - the centre of gravity (CG). Britannica phrases it as “the imaginary point where the total weight is thought to be concentrated”.
Hack: on uniform beams, centre of gravity (CG) is at the midpoint; on composite beams split into rectangles and take moments about a pivot to find the weighted average.
8 Principle of moments - the seesaw rule
Sum of clockwise moments = sum of anticlockwise moments (about the same point)
Save My Exams calls it the “balanced torque” condition and has an annotated beam diagram you can photocopy.
9 Translational vs rotational equilibrium
Condition
Mathematical test
Typical cue
Translational
∑F=0
Object moves at constant velocity v (constant speed and same direction); No linear acceleration
Rotational
∑τ=0
Object turns at constant angular velocity ω (constant angular speed and angular direction); No angular acceleration
For the system to be in full equilibrium, we need translational and rotational equilibrium - ∑F=0 and ∑τ=0.
10 Free-body diagrams & vector triangles
Isolate the body.
Arrow for every force, labelled.
Check heads and tails form a closed triangle if the body is in equilibrium.
Wired's tutorial plus Physics Classroom's “Equilibrium and Statics” page give clear worked examples.
11 Three WA timing rules (copy to your phone)
Use syllabus pacing as a guide: Paper 2/3 average ~1.6 min/mark; Paper 4 ~3 min/mark.
Write units before numbers in moment questions to avoid cm-m mix-ups.
Keep working lines for method marks, especially in vector components.
12 Bridge to Paper 4 practical
Clamp a metre rule to a pivot, add masses, and verify ∑τ=0.
Use Google Sheets =LINEST() to grab gradient ± standard error when testing Hooke's law.
Need structured practice on Forces and Moments? Our H2 Physics tuition programme covers this topic with weekly problem sets and Paper 4 practical drills.
Comprehensive revision pack
9478 Section I, Topic 2 Syllabus outcomes
Candidates should be able to:
(a) describe the forces on a mass, charge and current-carrying conductor in gravitational, electric and magnetic fields, as appropriate.
(b) show a qualitative understanding of forces including normal force, buoyant force (upthrust), frictional force and viscous force, e.g. air resistance. (Knowledge of the concepts of coefficients of friction and viscosity is not required.)
(c) recall and apply Hooke's law (F=kx, where k is the force constant) to new situations or to solve related problems.
(d) define and apply the moment of a force and the torque of a couple.
(e) show an understanding that a couple is a pair of forces which tends to produce rotation only.
(f) show an understanding that the weight of a body may be taken as acting at a single point known as its centre of gravity.
(g) apply the principle of moments to new situations or to solve related problems.
(h) show an understanding that, when there is no resultant force and no resultant torque, a system is in equilibrium.
(i) use free-body diagrams and vector triangles to represent forces on bodies that are in rotational and translational equilibrium.
Concept map (in words)
Begin with a labelled diagram that separates field forces (weight, electric, magnetic) from contact forces (normal, friction, tension, upthrust). Resolve each vector into perpendicular axes before applying the two equilibrium tests. If a system rotates, check for couples and compute their moments. Link to Hooke's law when springs provide the restoring force, and to friction models when impending motion is mentioned.
Key definitions & relations
Quantity / idea
Expression / reminder
Resultant force
∑F - zero for translational equilibrium
Moment of a force
τ=Fd⊥ about chosen pivot
Principle of moments
∑τcw=∑τacw at equilibrium
Couple
Two equal, opposite, parallel forces → net torque τ=Fs
Hooke's law
F=kx (within elastic limit); energy stored E=21kx2
Lami's theorem (triad)
sinαF1=sinβF2=sinγF3
Centre of gravity
Point where resultant weight acts; for uniform rod = midpoint
Derivations & reasoning to master
Resultant of non-perpendicular forces: resolve forces into components, then reconstruct magnitude via Pythagoras - R=Fx2+Fy2.
Ladder against a wall: write the floor and wall reaction forces (with friction shown qualitatively as a labelled contact force) on a free-body diagram, then apply ∑F=0 and ∑τ=0
Springs in series/parallel: show that keq1=k11+k21
Couple work: prove that work done by a couple is W=τΔθ - independent of pivot choice.
Worked example 1 - non-uniform beam
A 3.0 m beam (mass 18 kg) is supported at the left end and by a cable at the right end making 30° with the horizontal. A 160 N weight hangs 1.2 m from the left. Find the tension in the cable and the reaction at the hinge.
Sketch solution: take moments about the left hinge to solve for tension - Tsin(30∘)×3.0m=160N×1.2m+18kgg×1.5m. Then resolve vertical/horizontal forces to obtain hinge reactions.
Worked example 2 - crate held on rough slope
A 25kg crate rests on a 20∘ rough slope. It is held in place by a light rope parallel to the slope. The slope provides a friction force of magnitude 35N on the crate, acting parallel to the slope. Find the rope tension in the two cases where (i) the friction acts up the slope, and (ii) the friction acts down the slope.
Strategy: draw a free-body diagram showing weight, normal reaction, tension and the given friction force. Resolve along the slope and apply ∑F∥=0 for each direction of friction. Note: 9478 treats friction qualitatively, so its magnitude is given in the question rather than computed from a coefficient.
Practical & data tasks
Use a metre rule with hanging masses to verify the principle of moments (∑τ=0); include quantitative uncertainty analysis.
Build a spring system (series and parallel) and record load vs extension to obtain keq from the gradient.
Film a door closing and plot torque vs angle to appreciate how moment arm changes with geometry.
Common misconceptions & exam traps
Forgetting to convert cm to m before computing moments (units inconsistency).
Missing reaction components at hinges or pins (both horizontal and vertical).
Assuming friction direction incorrectly; always consider impending motion cue.
Using resultant force instead of couple torque when two equal/opposite forces act.
Quick self-check quiz
What two equations must hold for a rigid body in static equilibrium? - ∑F=0 and ∑τ=0.
Define a couple. - Two equal, opposite, parallel forces with different lines of action producing pure rotation.
A 40N force acts 0.25m from a pivot. What is the moment? - 10N⋅m (sense depends on direction).
In Hooke's law, what happens to k when two identical springs are placed in parallel? - It doubles.
What is the common mistake when drawing free-body diagrams of ladders? - Omitting the friction at the contact points or misplacing the weight's line of action.
Revision workflow
Solve two ladder/beam questions from past-year papers; verify each line with both equilibrium equations.
Create a “force library” flashcard set (normal, tension, upthrust, drag, weight) with sketches.
Practise translating word problems into vector component equations within 90 seconds.
Summarise spring combinations and couple properties on a one-page cheat sheet for last-minute review.
Practice Quiz
Test yourself on the key concepts from this guide.
Parents: book a 60-min “Forces & Moments” clinic one week before the first mechanics WA.
Students: stick the moment equation (τ=Fd⊥) on your desk and test it on tonight's textbook questions.
Last updated 14 Jul 2025. Next review when SEAB releases the 2027 draft.
