Forces and Momentum: Study Guide

This guide covers sub-topic A.2, Forces and Momentum, from Topic A, Space, Time and Motion, of IB Diploma Programme Physics, first assessment 2025. Unlike several other sub-topics in the DP Physics syllabus, A.2 has no additional higher level (AHL) extension – the guide allocates it 10 teaching hours and specifies identical content for both Standard Level and Higher Level students.

Where this fits in DP Physics

A.2 builds directly on A.1 Kinematics: where A.1 describes motion without reference to its causes, A.2 introduces the forces responsible for that motion and extends the description to momentum, impulse and circular motion. It sits alongside A.3 (Work, energy and power) as the syllabus’s core treatment of mechanics. This content is examinable across the external written papers, and can equally underpin an appropriate student-designed internal assessment investigation, such as one exploring momentum conservation or a variable-force scenario. For the full five-topic picture of the syllabus, see the IB DP Physics syllabus guide; for the SUVAT and motion content that precedes this sub-topic, see the Kinematics revision notes.

Syllabus coverage

IB DIPLOMA PROGRAMME PHYSICS — A.2 FORCES AND MOMENTUM (SL AND HL, 10 HOURS)

• Newton’s three laws of motion, and forces understood as interactions between bodies
• Representing forces acting on a body in a free-body diagram, and analysing such diagrams to find the resultant force on a system (one- and two-dimensional situations)
• Named contact forces: the normal force; surface friction (static, where Ff ≤ μsFN, and dynamic, where Ff = μdFN); tension; the elastic restoring force given by Hooke’s law, FH = −kx; viscous drag on a small sphere moving through a fluid; and buoyancy, Fb = ρVg
• Named field forces: gravitational force (weight, Fg = mg), electric force, and magnetic force
• Linear momentum, p = mv, which remains constant unless a resultant external force acts on the system
• Impulse, J = FΔt, and the principle that an applied impulse equals the resulting change in momentum
• Newton’s second law in its momentum form, F = Δp/Δt, which – unlike the more familiar F = ma – applies even where mass is changing
• Elastic and inelastic collisions between two bodies, explosions, and the energy considerations that distinguish each case
• Circular motion at constant speed: centripetal acceleration, a = v²/r = ω²r = 4π²r/T², caused by a centripetal force acting perpendicular to the velocity
• The relationship between angular velocity ω and linear speed v, v = 2πr/T = ωr

The guide notes explicitly that there is no additional higher level content in A.2 – HL students study exactly the same material as SL students for this sub-topic, which is unusual across the DP Physics syllabus and worth knowing so revision time is not spent hunting for HL-only extension material that does not exist here.

How to approach it

Because A.2 spans several distinct but related ideas – forces, momentum, collisions and circular motion – the most efficient revision path is to treat it as three linked mini-topics rather than one block: first master free-body diagrams and Newton’s laws, then move to momentum and impulse (including the momentum form of Newton’s second law, which many students under-revise because F = ma feels more familiar), and finally circular motion, which uses a different mathematical toolkit (angular quantities) but describes forces acting in exactly the same Newtonian framework. For collisions, get in the habit of checking both momentum conservation and the energy condition (elastic collisions conserve kinetic energy; inelastic ones do not) – exam questions frequently test whether a collision is elastic by asking students to compare kinetic energy before and after rather than stating it directly. For circular motion, remember that the centripetal force is not a new, separate force – it is whichever named force (tension, gravity, friction, the normal force) happens to be providing the centre-directed resultant in a given scenario, and misidentifying it as an independent force is one of the most common errors at this level.

Common mistakes

Applying F = Δp/Δt to the rocket alone as if that fixes the problem of its changing mass, without accounting for the momentum carried away by the ejected fuel. The rocket by itself is not a closed system, so its own F = ma still holds once the thrust force from the escaping exhaust is included as an external force; alternatively, take Δp/Δt for the total momentum of the closed rocket-plus-exhaust system, which requires no external force to stay constant. Treating “centripetal force” as an additional force acting on a body, rather than correctly naming the real force (gravity, tension, friction, or the normal force) that is producing the centripetal effect. Assuming kinetic energy is conserved in every collision – it is only conserved in elastic collisions. Forgetting that dynamic friction uses μd while an object still at rest is governed by the inequality Ff ≤ μsFN, not an equality, until the point of slipping.

Quick revision checklist

• Draw and correctly label free-body diagrams for one- and two-dimensional force scenarios.
• Know all six named contact forces and both named field-force formulae given in the syllabus.
• Be able to switch fluently between F = ma and F = Δp/Δt, and explain when each form is appropriate.
• Distinguish elastic from inelastic collisions using kinetic energy, not just momentum.
• Convert confidently between linear (v) and angular (ω) descriptions of circular motion.

Worked example: elastic vs inelastic

A 2 kg trolley moving at 3 m/s collides with a stationary 1 kg trolley. After the collision they move off together at 2 m/s. Momentum before: (2)(3) + (1)(0) = 6 kg m/s. Momentum after: (2+1)(2) = 6 kg m/s – momentum is conserved, as it must be in any collision with no external resultant force. Kinetic energy before: ½(2)(3²) = 9 J. Kinetic energy after: ½(3)(2²) = 6 J. Since kinetic energy has fallen from 9 J to 6 J, this collision is inelastic (the trolleys coupling together and moving as one is itself a strong clue – a perfectly elastic collision between two different masses never leaves them moving at the same final velocity). The “missing” 3 J has not vanished; it has been transferred to other forms, typically heat and deformation at the point of impact. This two-step method – check momentum conservation first, then compare kinetic energy before and after – is the reliable way to classify any collision the exam presents, rather than trying to judge from the scenario’s description alone.

Official syllabus

International Baccalaureate Organization, Physics guide (Diploma Programme), first assessment 2025, sub-topic A.2. Overview at ibo.org.