A.2 Forces and momentum

UNIT SYLLABUS

SL/HL 10 hours

This is the heart of mechanics: Newton's three laws tell you how forces change motion, and momentum gives you the bookkeeping tool that survives even violent collisions. You will learn to draw free-body diagrams — the single most valuable habit in physics — and to recognise the standard cast of forces: weight, normal force, friction, tension, spring force, drag and buoyancy. Conservation of momentum then lets you analyse collisions and explosions without knowing anything about the complicated forces inside them, and circular motion shows that a force perpendicular to velocity changes direction, not speed.

Guiding Questions

? How can the forces acting on a system be represented both visually and algebraically?
? How can Newton's laws be modelled mathematically?
? How can knowledge of forces and momentum predict the behaviour of interacting bodies?

Free-body diagram of a block on a rough incline: weight resolved into components, with the normal force and friction balancing them at constant velocity.

✓ What the IB expects you to master

State and apply Newton's three laws, treating forces as interactions between bodies (third-law pairs act on different bodies).
Draw and analyse free-body diagrams to find resultant forces in one and two dimensions.
Use the contact forces: normal force, friction ( $F_f \le \mu_s F_N$ static, $F_f = \mu_d F_N$ dynamic), tension, Hooke's law ( $F_H = -kx$ ), viscous drag ( $F_d = 6\pi\eta r v$ ) and buoyancy ( $F_b = \rho V g$ ).
Use the field forces: gravitational ( $F_g = mg$ ), electric and magnetic.
Apply conservation of linear momentum ( $p = mv$ ) to elastic and inelastic collisions and to explosions, including their energy accounting.
Relate impulse to change of momentum ( $J = F\Delta t = \Delta p$ ) and use $F = \Delta p / \Delta t$ when mass changes.
Analyse uniform circular motion: centripetal acceleration $a = v^2/r = \omega^2 r$ , the centripetal force that causes it, and angular velocity $\omega$ with $v = \omega r$ .

1 Key Formulas

Newton's second law

F = ma = \frac{\Delta p}{\Delta t}

Static friction

F_{f} \le \mu_{s} F_{N}

Dynamic friction

F_{f} = \mu_{d} F_{N}

Hooke's law

F_{H} = -kx

Viscous drag (Stokes)

F_{d} = 6\pi\eta r v

Buoyancy

F_{b} = \rho V g

Linear momentum

p = mv

Impulse

J = F\Delta t = \Delta p

Angular velocity

\omega = \frac{2\pi}{T} = 2\pi f

Linear speed (circular)

v = \omega r

Centripetal acceleration

a = \frac{v^{2}}{r} = \omega^{2} r = \frac{4\pi^{2}r}{T^{2}}

Centripetal force

F = \frac{mv^{2}}{r} = m\omega^{2} r

2 Exam Preparation & Topic Explanations

Free-body diagrams that earn marks

Examiners award marks for correctly drawn and labelled free-body diagrams before any algebra begins. Draw the body as a point or simple box, include only forces acting ON the body, give each arrow a conventional label ( $W$ or $mg$ , $F_N$ , $F_f$ , $T$ ), and make lengths roughly reflect magnitudes.

Then translate the diagram into equations along sensible axes — parallel and perpendicular to a slope, or radial and tangential for circular motion.

Pro Exam Strategy

Never draw "centripetal force" as an extra arrow — it is the resultant of the real forces (tension, gravity, friction, normal force).
In collision questions, always define a positive direction first and keep signs consistent.
Elastic collision = kinetic energy conserved; momentum is conserved in every collision.
For vertical circles, analyse the top and bottom points — those are the exam favourites.

3 MCQ Practice

Q1. A book rests on a table. According to Newton's third law, the reaction to the weight of the book is:

The normal force from the table on the book
The gravitational pull of the book on the Earth
The normal force from the book on the table
The friction between book and table

Q2. A $0.16\ \text{kg}$ cricket ball arrives at $30\ \text{m s}^{-1}$ and is hit straight back at $40\ \text{m s}^{-1}$ . The bat and ball are in contact for $0.02\ \text{s}$ . What is the average force on the ball?

$80\ \text{N}$
$240\ \text{N}$
$560\ \text{N}$
$1120\ \text{N}$

Q3. A car travels at constant speed around a horizontal circular bend. Which statement is correct?

There is no resultant force since the speed is constant
The resultant force acts towards the centre of the circle
The resultant force acts outwards, away from the centre
The resultant force acts in the direction of motion

4 Short Answer Questions

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