Theme A — Space, Time and Motion

A.2 Forces and Momentum — IB Physics SL Revision Notes & Topical Questions

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Lesson summary

A.2 Forces and Momentum — IB SL Notes — IB PHYSICS SL notes: Apply Newton's laws of motion, identify contact and field forces, and use momentum, impulse and circular-motion ideas to analyse how bodies interact.Free-body diagram — it shows one body only, with every force on it dra…

Translational equilibrium
Resultant force
Second law
What the symbols mean
Normal force FN
Surface friction

Part 1 of 9Forces and free-body diagrams

Forces and free-body diagrams

Free-body diagram

Free-body diagram it shows one body only, with every force on it drawn as a labelled arrow from the point of action.
Arrow lengths show relative size.

Translational equilibrium

Translational equilibrium the vector sum of the forces is zero.

Resultant force

Resultant force the single force with the same effect as all the forces on a body combined.

Part 2 of 9Newton's laws

First law

First law a body stays at rest or moves with constant velocity unless a resultant force acts.
A resultant force is needed to change the velocity, not to keep an object moving.

Second law

Second law the resultant force equals the rate of change of momentum, F = Δp/Δt.
What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s⁻¹); FΔt is the impulse (N s)
For constant mass this becomes F = ma.

Third law

Third law when A exerts a force on B, B exerts an equal and opposite force of the same type on A.
The pair acts on different bodies, so the forces do not cancel.

Part 3 of 9Contact forces

Normal force FN

Normal force FN it acts perpendicular to a surface.

Surface friction

Surface friction static F_f ≤ μ_sF_N and dynamic F_f = μ_dF_N.

Elastic restoring force

Elastic restoring force it follows Hooke's law, F_H = −kx.

Viscous drag

Viscous drag on a small sphere it follows Stokes' law, F_d = 6πηrv.

Buoyancy

F_b = ρVg, where ρ is the fluid density and V the volume of fluid displaced.

Part 4 of 9Field forces

Gravitational force

Gravitational force the weight F_g = mg acts on mass.

Electric force

Electric force it acts on charge.

Magnetic force

Magnetic force it acts on moving charge or current.

No contact

No contact field forces act at a distance.

Part 5 of 9Momentum and impulse

Linear momentum

Linear momentum p = mv is a vector with unit kg m s⁻¹ or N s.

Impulse

J = FΔt equals the change in momentum and the area under a force–time graph.

Longer collision time

Longer collision time it gives a smaller average force for the same change of momentum, as in crumple zones and airbags.

Part 6 of 9Collisions and explosions

Conservation of momentum

Conservation of momentum the total momentum of an isolated system is conserved in every collision and explosion.

Explosion from rest

Explosion from rest the total momentum stays zero.

Feature	Elastic collision	Inelastic collision
Momentum	Conserved	Conserved
Total energy	Conserved	Conserved
Kinetic energy	Conserved	Not conserved
Typical example	Collisions between gas molecules	Vehicles that crumple or stick together

1Perfectly inelastic

Perfectly inelastic if the bodies stick together the loss of kinetic energy is the greatest possible.

2Kinetic energy and momentum

E_k = p²/2m, useful for bodies with the same momentum.

Part 7 of 9Circular motion

Angular velocity

ω = 2π/T = v/r.
What the symbols mean: ω = angular frequency (rad s⁻¹) · f = frequency (Hz) · T = period (s)

Centripetal acceleration

Centripetal acceleration a = v²/r = ω²r = 4π²r/T², directed to the centre.
What the symbols mean: a = centripetal acceleration towards the centre (m s⁻²) · v = speed (m s⁻¹) · ω = angular speed (rad s⁻¹) · r = radius (m)

Centripetal force

F = mv²/r = mω²r, the resultant of real forces such as tension, friction, gravity and the normal force.
What the symbols mean: F = centripetal force towards the centre (N) · m = mass (kg) · v = speed (m s⁻¹) · ω = angular speed (rad s⁻¹) · r = radius (m)
It is not an extra force, and it does no work because it is perpendicular to the velocity.

Part 8 of 9Solving force problems

Isolate the body and draw its free-body diagram.

Choose axes, usually along and perpendicular to the motion.

Resolve forces into components along the axes.

Apply ΣF = ma along each axis (a = 0 for equilibrium and a = v²/r towards the centre for circular motion).

For collisions, equate the total momentum before and after, using signs for direction.

Part 9 of 9More from the specification

1Free-body diagram

Free-body diagram shows all forces acting on a single object, drawn as arrows from a point with length showing magnitude

2Normal reaction

Normal reaction the contact force perpendicular to a surface, balancing the weight component into the surface

3Circular motion

Circular motion an object moving in a circle at constant speed has changing velocity, so it accelerates towards the centre

4Centripetal force

Centripetal force the resultant of forces acting towards the centre, F = mv²/r, not a separate force

5Angular and linear speed

Angular and linear speed angular speed omega = 2 pi/T, and linear speed v = omega r where r is the radius of the circle

6Normal reaction

The contact force perpendicular to a surface.

7Reaction force

Force from a support pushing up on an object.

8Fluid resistance

Drag force from a fluid opposing motion.

Key terms

Term	Meaning
Resultant force	The single force with the same effect as all the forces acting on a body combined
Linear momentum	The product of mass and velocity; a vector
Impulse	The product of force and the time for which it acts; equal to the change in momentum
Elastic collision	A collision in which total kinetic energy is conserved
Inelastic collision	A collision in which total kinetic energy is not conserved
Centripetal force	The resultant force directed towards the centre of a circular path
Angular velocity	The angle swept out per unit time, ω = Δθ/Δt
Coefficient of friction	The ratio of the frictional force to the normal force between two surfaces

Avoid these mistakes

Thinking a resultant force is needed to keep a body moving — it is needed only to change the velocity.

Treating third-law pairs as acting on one body — they act on different bodies.

Calling centripetal force an extra force — it is the resultant of the real forces towards the centre.

Saying kinetic energy is always conserved in collisions — only in elastic collisions.

Saying resultant force causes velocity — it causes acceleration.

Last updated: 15 October 2026