H2 Physics Forces & Moments Notes | A-Level 9478

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 ($\sum \vec{F} = 0$ and $\sum \tau = 0$). The pay-off is a one-line checklist that prevents sign slips and missing forces.

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.

Force-and-moment route-selection map

Use this map before substituting numbers. It keeps force equations, moment equations, and spring equations from being mixed in the same first line.

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

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 $\vec{L}$ 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

1. Identify the carrier (mass, charge or current).
2. Write the matching formula.
3. 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

$$\tau = F d_\perp$$

where $d_\perp$ is the perpendicular distance from $O$ to the line of action. Engineering Statics gives a brilliant interactive showing how $d_\perp$ shrinks as the force slides.

Moment-arm checkpoint

Before writing a moments equation, decide what each force is trying to rotate the body about and whether its line of action passes through the pivot. This prevents the common mistake of using the visible length instead of the perpendicular distance.

Misconception check: the pivot does not have to be at the physical support named in the question. You may choose any convenient point, as long as every moment is taken about that same point.

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

$$\tau_\text{couple} = F s$$

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

For the system to be in full equilibrium, we need translational and rotational equilibrium - $\sum \vec{F} = 0$ and $\sum \tau = 0$.

10 Free-body diagrams & vector triangles

1. Isolate the body.
2. Arrow for every force, labelled.
3. Check heads and tails form a closed triangle if the body is in equilibrium.

Free-body diagram audit checkpoint

Before resolving components, audit the diagram by force source. This prevents adding a familiar force that is not actually acting on the isolated body.

Worked check: for a block held at rest on a rough slope by a string, isolate the block only. Draw weight vertically downward, normal perpendicular to the slope, tension along the string, and friction along the slope opposing the possible slipping direction. Then resolve parallel and perpendicular to the slope before writing $\sum F_\parallel = 0$ and $\sum F_\perp = 0$

Misconception check: a free-body diagram is not a picture of everything touching the object. It is a force inventory for one isolated body.

Wired's tutorial plus Physics Classroom's “Equilibrium and Statics” page give clear worked examples.

11 Three WA timing rules (copy to your phone)

1. Use syllabus pacing as a guide: Paper 2/3 average ~1.6 min/mark; Paper 4 ~3 min/mark.
2. Write units before numbers in moment questions to avoid cm-m mix-ups.
3. 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 $\sum \tau = 0$.
• 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

Derivations & reasoning to master

1. Resultant of non-perpendicular forces: resolve forces into components, then reconstruct magnitude via Pythagoras - $R = \sqrt{F_{x}^{2} + F_{y}^{2}}$

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 - $T \sin\left(30^\circ\right) \times \pu{3.0 m} = \pu{160 N} \times \pu{1.2 m} + \pu{18 kg} g \times \pu{1.5 m}$

Worked example 2 - crate held on rough slope

A $\pu{25 kg}$ crate rests on a $\pu{20^\circ}$ rough slope. It is held in place by a light rope parallel to the slope. The slope provides a friction force of magnitude $\pu{35 N}$ 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 $\sum F_\parallel = 0$ 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 $\left(\sum \tau = 0\right)$; include quantitative uncertainty analysis.
• Build a spring system (series and parallel) and record load vs extension to obtain $k_\text{eq}$ 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

1. What two equations must hold for a rigid body in static equilibrium? - $\sum \vec{F} = 0$ and $\sum \tau = 0$.
2. Define a couple. -

Revision workflow

1. Solve two ladder/beam questions from past-year papers; verify each line with both equilibrium equations.
2. Create a “force library” flashcard set (normal, tension, upthrust, drag, weight) with sketches.
3. Practise translating word problems into vector component equations within 90 seconds.
4. 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.

13 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• Khan Academy - Types of forces
• Khan Academy - What is Hooke's law?
• Engineering Statics - Moment of Force
• MIT - What are Couples?
• Britannica - Centre of Gravity
• Save My Exams - Rotational Equilibrium
• Wired - Basics: Free-Body Diagrams

14 Call-to-action

Parents: book a 60-min “Forces & Moments” clinic one week before the first mechanics WA. Students: stick the moment equation ($\tau = F d_\perp$) on your desk and test it on tonight's textbook questions.

Last updated 14 Jul 2025. Next review when SEAB releases the 2027 draft.