A-Level Physics — 2) Forces & Moments (IP-Friendly Guide)

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14 Jul 2025, 00:00 Z

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

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 \(\vec E\)
3	Charge moving in \(\vec B\)	\(F = qvB\sin\theta\) (Lorentz)	\(\vec v \times \vec B\)
4	Conductor length \(L\) in \(\vec B\)	\(F = ILB \sin\theta\)	\(\vec L \times \vec B\)

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 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 right 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.

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

Condition	Mathematical test	Typical cue
Translational	\(\Sigma \vec F = 0\)	Object moves at constant velocity \(v\) (constant speed and same direction); No linear acceleration
Rotational	\(\Sigma \tau = 0\)	Object turns at constant angular velocity \(\omega\) (constant angular speed and angular direction); No angular acceleration

For the system to be in full equilibrium, we need translational and rotational equilibrium - \(\Sigma \vec F = 0\) and \(\Sigma \tau = 0\).

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)

1 mark ≈ 1.5 min — identical to Paper 4 design.
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 \(\Sigma \tau = 0\).
Use Google Sheets =LINEST() to grab gradient ± standard error when testing Hooke 's law.

13 Further reading

14 Call-to-action

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

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