SLIBSciences

Physics

A concept-based Standard Level syllabus connecting forces, energy and particles across motion, matter, waves, fields, and nuclear and quantum physics.

Course units

Estimated study time

110 hours

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Course Overview

IB Physics SL is organized into 5 units and 19 focused topics with 213 Key Concepts sections, 27 questions, and 380 flashcards.

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Begin with Topic A.1: Kinematics.

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Course units

Each unit groups focused topics. Every topic follows the same clear rhythm: review Key Concepts, use the Question Bank, then strengthen recall.

Unit 1
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Space, Time and Motion
Theme A develops the mechanics foundation of Physics SL. It moves from describing motion to explaining it with forces and momentum, then to analysing systems through work, energy and power.
27 hours estimated ·3 topics
Unit 1 progress0%
Topics in this unit
Topic A.1Not started
Kinematics
Kinematics describes motion without initially asking what causes it. Students work in one and two dimensions and move fluently among words, equations, vectors and motion graphs.
540 min estimated
Topic A.1 progress0%
Key Concepts0/10 sections complete Question Bank0/1 questions attempted Flashcards0/20 cards reviewed
Learning objectives
Distinguish distance from displacement and speed from velocity.
Calculate average and instantaneous velocity, speed and acceleration.
Interpret position–time, velocity–time and acceleration–time graphs using gradients and areas.
Apply the constant-acceleration equations with a consistent sign convention.
Resolve projectile motion into independent horizontal and vertical components.
Describe qualitatively how fluid resistance changes projectile trajectories and leads to terminal speed.
Key formulas
Displacement from position
$\Delta x=x_{\mathrm{f}}-x_{\mathrm{i}}$
Average acceleration
$\bar{a}=\frac{\Delta v}{\Delta t}$
Average speed
$\text{average speed}=\frac{\text{total distance}}{\Delta t}$
Average velocity
$\bar{v}=\frac{\Delta x}{\Delta t}$
Instantaneous velocity
$v=\frac{\mathrm{d}x}{\mathrm{d}t}$
Instantaneous acceleration
$a=\frac{\mathrm{d}v}{\mathrm{d}t}$
Speed from one-dimensional velocity
$\text{speed}=|v|$
Velocity from a position–time graph
$v=\text{gradient of the }x\text{-}t\text{ graph}$
Displacement from a velocity–time graph
$\Delta x=\int_{t_1}^{t_2}v\,\mathrm{d}t$
Distance from a velocity–time graph
$\text{distance}=\int_{t_1}^{t_2}|v|\,\mathrm{d}t$
Velocity change from an acceleration–time graph
$\Delta v=\int_{t_1}^{t_2}a\,\mathrm{d}t$
Displacement from mean velocity
$s=\frac{1}{2}(u+v)t$
Velocity after time
$v=u+at$
Displacement after time
$s=ut+\frac{1}{2}at^2$
Time-independent equation
$v^2=u^2+2as$
Vertical acceleration with upward positive
$a_y=-g\approx-9.81\,\mathrm{m\,s^{-2}}$
Initial velocity components
$u_x=u\cos\theta,\qquad u_y=u\sin\theta$
Ideal horizontal motion
$x=x_0+u_xt,\qquad v_x=u_x$
Ideal vertical motion
$y=y_0+u_yt-\frac{1}{2}gt^2,\qquad v_y=u_y-gt$
Speed from perpendicular components
$v=\sqrt{v_x^2+v_y^2}$
Flight time, range and maximum rise: check the conditions
$T=\frac{2u\sin\theta}{g},\quad R=\frac{u^2\sin(2\theta)}{g},\quad H=\frac{u^2\sin^2\theta}{2g}$
Terminal-speed condition
$F_{\mathrm{resultant}}=0\quad\Rightarrow\quad a=0$
Simplified vertical balance
$F_{\mathrm{drag}}=mg\quad\text{at terminal speed (if buoyancy is negligible)}$
Topic A.2Not started
Forces and momentum
This topic links interactions to changes in motion. Students use Newton’s laws, free-body diagrams, contact forces, momentum and circular motion to model real systems.
600 min estimated
Topic A.2 progress0%
Key Concepts0/11 sections complete Question Bank0/3 questions attempted Flashcards0/20 cards reviewed
Learning objectives
Apply Newton’s three laws and identify action–reaction pairs correctly.
Draw and analyse free-body diagrams, resolving forces into useful components.
Model normal force, friction, tension, Hooke’s-law spring forces, viscous drag and buoyancy.
Use momentum and impulse, including conservation of momentum in collisions and explosions.
Relate resultant force to acceleration and to rate of change of momentum.
Analyse uniform circular motion using centripetal acceleration and resultant inward force.
Key formulas
Resultant external force
$\vec F_{\mathrm{net}}=\vec F_1+\vec F_2+\cdots+\vec F_n$
Newton's second law in momentum form
$\vec F_{\mathrm{net}}=\frac{\mathrm{d}\vec p}{\mathrm{d}t}$
Newton's second law for constant mass
$\vec F_{\mathrm{net}}=m\vec a$
Translational equilibrium
$\vec F_{\mathrm{net}}=0\quad\Rightarrow\quad \vec a=0$
Weight near Earth's surface
$W=mg$
Newton's second law by components
$F_{\mathrm{net},x}=ma_x,\qquad F_{\mathrm{net},y}=ma_y$
Newton's third law
$\vec F_{A\to B}=-\vec F_{B\to A}$
Weight components on an incline
$W_{\parallel}=mg\sin\theta,\qquad W_{\perp}=mg\cos\theta$
Normal force on a simple incline
$N=mg\cos\theta\quad\text{if }a_\perp=0\text{ and no other perpendicular force acts}$
Static-friction range
$0\le f_s\le \mu_sN$
Limiting and kinetic friction
$f_{s,\max}=\mu_sN,\qquad f_k=\mu_kN$
Ideal-string tension
$T_1=T_2=T$
Hooke's law
$\vec F_s=-k\vec x\qquad\text{and}\qquad F_s=k|\vec x|\ \text{in magnitude}$
Archimedes' principle
$F_b=\rho_{\mathrm{fluid}}V_{\mathrm{displaced}}g$
Stokes' law
$F_d=6\pi\eta rv$
Terminal-motion balance
$W=F_b+F_d\quad\text{for steady downward motion in still fluid with no other forces}$
Momentum
$\vec p=m\vec v$
Net external impulse
$\vec J_{\mathrm{net}}=\Delta\vec p=\int_{t_1}^{t_2}\vec F_{\mathrm{net}}\,\mathrm{d}t$
Average resultant external force
$\vec F_{\mathrm{net,avg}}=\frac{\Delta\vec p}{\Delta t}$
Momentum conservation
$\vec P_{\mathrm{before}}=\vec P_{\mathrm{after}}\quad\text{when external impulse is negligible}$
Translational kinetic energy
$K=\frac{1}{2}mv^2$
Speed, period and angular speed (uniform circular motion)
$v=\frac{2\pi r}{T}=\omega r$
Angular speed and period (uniform circular motion)
$\omega=\frac{2\pi}{T}$
Centripetal acceleration
$a_c=\frac{v^2}{r}=\omega^2r,\qquad a_c=\frac{4\pi^2r}{T^2}\ \text{for uniform motion}$
Required radial resultant
$F_{\mathrm{radial}}=ma_c=\frac{mv^2}{r}$
Topic A.3Not started
Work, energy and power
Energy methods often provide a shorter route than force-and-acceleration methods. Students learn to track transfers among kinetic, gravitational, elastic and other energy stores and to quantify efficiency and power.
480 min estimated
Topic A.3 progress0%
Key Concepts0/11 sections complete Question Bank0/2 questions attempted Flashcards0/20 cards reviewed
Learning objectives
Apply conservation of energy to mechanical and mixed-energy systems.
Calculate work done by a constant force at an angle to displacement.
Read energy transfers from Sankey diagrams and distinguish useful from dissipated energy.
Use kinetic, gravitational potential and elastic potential energy relationships.
Interpret force–displacement graphs through the area under the graph.
Calculate power as rate of energy transfer and evaluate efficiency.
Key formulas
Conservation of total energy
$E_{\mathrm{initial}}=E_{\mathrm{final}}$
Average power
$P_{\mathrm{avg}}=\frac{\Delta E}{\Delta t}=\frac{W}{\Delta t}$
Efficiency
$\eta=\frac{E_{\mathrm{useful}}}{E_{\mathrm{input}}}=\frac{P_{\mathrm{useful}}}{P_{\mathrm{input}}}$
Work by a constant force
$W=Fs\cos\theta$
Work by the parallel component
$W=F_{\parallel}s$
Work from a variable force
$W=\text{signed area under the }F_{\parallel}\text{ against }s\text{ graph}$
Translational kinetic energy
$E_k=\frac12mv^2=\frac{p^2}{2m}$
Work–energy theorem
$W_{\mathrm{net}}=\Delta E_k=\frac12m(v^2-u^2)$
Change in gravitational potential energy
$\Delta E_g=mg\Delta h$
Gravitational potential energy from a chosen zero
$E_g=mgh$
Work done by gravity
$W_g=-\Delta E_g$
Hooke's law
$F_s=-kx$
Elastic potential energy
$E_s=\frac12kx^2$
Change in elastic potential energy
$\Delta E_s=\frac12k(x_2^2-x_1^2)$
Mechanical energy
$E_{\mathrm{mech}}=E_k+E_g+E_s$
Ideal mechanical-energy conservation
$E_{k,i}+E_{g,i}+E_{s,i}=E_{k,f}+E_{g,f}+E_{s,f}$
System energy change when work is the only boundary energy transfer
$W_{\mathrm{ext}}=\Delta E_{\mathrm{system}}$
Thermal transfer by constant kinetic friction
$\Delta E_{\mathrm{th}}=f_k s$
Non-conservative work
$W_{\mathrm{nc}}=\Delta E_{\mathrm{mech}}$
Idealized braking distance
$d=\frac{mv^2}{2F_b}$
Average power
$P_{\mathrm{avg}}=\frac{W}{\Delta t}=\frac{\Delta E}{\Delta t}$
Instantaneous mechanical power
$P=\vec F\cdot\vec v=Fv\cos\theta$
Parallel force form
$P=F_{\parallel}v$
Energy efficiency
$\eta=\frac{E_{\mathrm{useful}}}{E_{\mathrm{input}}}$
Power efficiency
$\eta=\frac{P_{\mathrm{useful}}}{P_{\mathrm{input}}}$
Percentage efficiency
$\eta_{\%}=100\eta$
Overall efficiency of a simple useful-output cascade
$\eta_{\mathrm{overall}}=\eta_1\eta_2\eta_3\cdots$
Gravitational power of a mass flow
$P_g=\dot m gh$
Mechanical-to-thermal balance with no external energy transfer
$E_{\mathrm{mech},i}=E_{\mathrm{mech},f}+\Delta E_{\mathrm{th}}$
Spring constant from a graph
$k=\frac{\Delta F}{\Delta x}$
Elastic work from graph area
$W=\frac12Fx=\frac12kx^2$
Useful climbing power
$P=\frac{mg\Delta h}{\Delta t}$
Unit 2
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The Particulate Nature of Matter
Theme B connects microscopic particle models with thermal behaviour, radiation, climate, gases and electric circuits. It is one of the most varied parts of Physics SL.
24 hours estimated ·4 topics
Unit 2 progress0%
Topics in this unit
Topic B.1Not started
Thermal energy transfers
Students connect temperature and internal energy to molecular motion, then quantify heating, phase change, conduction and radiation. The topic also introduces the radiation laws used later in stellar physics.
360 min estimated
Topic B.1 progress0%
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Learning objectives
Use the molecular model to distinguish solids, liquids and gases.
Relate Kelvin temperature to average molecular kinetic energy and convert between Kelvin and Celsius.
Calculate density, specific heat energy and latent heat energy.
Explain conduction and convection and calculate steady thermal conduction through a material.
Apply the Stefan–Boltzmann law to black-body radiation.
Use luminosity, apparent brightness and Wien’s displacement law to infer stellar properties.
Key formulas
Energy conservation for an isolated system
$E_{\mathrm{before}}=E_{\mathrm{after}}$
Average rate of energy transfer
$P=\frac{\Delta E}{\Delta t}$
Density
$\rho=\frac{m}{V}$
Mass from density
$m=\rho V$
Celsius to Kelvin
$T=\theta+273.15$
Equal temperature intervals
$\Delta T\,(\mathrm{K})=\Delta\theta\,({}^\circ\mathrm{C})$
Mean translational kinetic energy of an ideal-gas molecule
$\overline{E_k}=\frac32k_BT$
Internal-energy components
$U=E_{\mathrm{microscopic\,kinetic}}+E_{\mathrm{intermolecular\,potential}}$
Simple stationary-sample energy balance
$\Delta U=E_{\mathrm{in}}-E_{\mathrm{out}}$
Energy for a temperature change
$Q=mc\Delta T$
Heat capacity
$C=mc$
Ideal calorimetry balance
$Q_{\mathrm{lost}}=Q_{\mathrm{gained}}$
Magnitude of latent-heat transfer
$Q=mL$
Multi-stage heating
$Q_{\mathrm{total}}=mc_1\Delta T_1+mL+mc_2\Delta T_2$
Latent heat from constant power
$L=\frac{P\Delta t}{m}$
Steady thermal conduction through a slab
$P=\frac{kA\Delta T}{L}$
Thermal resistance of one uniform layer
$R_{\mathrm{th}}=\frac{L}{kA}$
Power from thermal resistance
$P=\frac{\Delta T}{R_{\mathrm{th}}}$
Emissivity
$\varepsilon=\frac{P_{\mathrm{emitted}}}{P_{\mathrm{black\ body}}}$
Absorptivity
$a=\frac{P_{\mathrm{absorbed}}}{P_{\mathrm{incident}}}$
Physical range of emissivity
$0\leq\varepsilon\leq1$
Stefan–Boltzmann law
$P=\varepsilon\sigma AT^4$
Net radiative power to an isothermal black-body enclosure
$P_{\mathrm{net}}=\varepsilon\sigma A(T^4-T_s^4)$
Black-body stellar luminosity
$L=4\pi R^2\sigma T^4$
Wien's displacement law
$\lambda_{\max}T=b_W$
Temperature from peak wavelength
$T=\frac{b_W}{\lambda_{\max}}$
Apparent brightness
$b=\frac{L}{4\pi d^2}$
Luminosity from observations
$L=4\pi d^2b$
Stellar radius from luminosity and temperature
$R=\sqrt{\frac{L}{4\pi\sigma T^4}}$
Electrical energy input
$E=Pt=VIt$
Experimental specific heat capacity
$c=\frac{VIt}{m\Delta T}$
Experimental specific latent heat
$L=\frac{P\Delta t}{m}$
Topic B.2Not started
Greenhouse effect
This topic applies radiation physics and energy balance to the Earth–atmosphere system. Students quantify albedo, emissivity and incoming solar power and explain how greenhouse gases absorb and re-emit infrared radiation.
360 min estimated
Topic B.2 progress0%
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Learning objectives
Apply conservation of energy to planetary energy-balance models.
Use emissivity to compare real surfaces with ideal black-body radiation.
Use albedo to describe the fraction of incident energy reflected or scattered.
Use the solar constant and projected area to estimate mean incoming intensity.
Explain the role of major greenhouse gases and why molecular energy levels allow infrared absorption.
Distinguish the natural greenhouse effect from the enhanced greenhouse effect caused by human activity.
Key formulas
Top-of-atmosphere energy imbalance
$F_{\mathrm{net}}=F_{\mathrm{absorbed}}-F_{\mathrm{outgoing}}$
Radiative equilibrium
$F_{\mathrm{absorbed}}=F_{\mathrm{outgoing}}$
Wien's displacement law
$\lambda_{\max}T=b_W$
Peak wavelength
$\lambda_{\max}=\frac{b_W}{T}$
Projected area of a spherical planet
$A_{\mathrm{projected}}=\pi R^2$
Total incident solar power
$P_{\mathrm{solar}}=S\pi R^2$
Global-mean incident solar flux
$\overline F_{\mathrm{solar}}=\frac{S}{4}$
Albedo
$\alpha=\frac{P_{\mathrm{reflected}}}{P_{\mathrm{incident}}}$
Absorbed shortwave power
$P_{\mathrm{absorbed}}=(1-\alpha)P_{\mathrm{incident}}$
Global-mean absorbed solar flux
$F_{\mathrm{absorbed}}=\frac{(1-\alpha)S}{4}$
Stefan–Boltzmann emission
$P=\varepsilon\sigma AT^4$
Emitted longwave flux
$F_{\mathrm{emitted}}=\varepsilon\sigma T^4$
Emissivity range
$0\leq\varepsilon\leq1$
Uniform-emitter planetary equilibrium balance
$(1-\alpha)S\pi R^2=4\pi R^2\varepsilon\sigma T^4$
Uniform grey-emitter equilibrium temperature
$T=\left[\frac{(1-\alpha)S}{4\varepsilon\sigma}\right]^{\frac{1}{4}}$
Photon energy
$E_\gamma=hf=\frac{hc}{\lambda}$
Atmospheric spectral energy accounting (negligible scattering/reflection)
$P_{\mathrm{incident}}=P_{\mathrm{transmitted}}+P_{\mathrm{absorbed}}$
Surface–effective temperature difference
$\Delta T_{\mathrm{greenhouse}}\approx T_{\mathrm{surface}}-T_e$
Initial enhanced-effect imbalance
$F_{\mathrm{net}}=F_{\mathrm{absorbed}}-F_{\mathrm{outgoing}}>0$
Albedo-change forcing estimate
$\Delta F_{\alpha}=-\frac{S\Delta\alpha}{4}$
Simplified climate response
$\Delta T=\lambda_c\Delta F$
Stored energy per unit area
$\frac{\Delta E}{A}=C_A\Delta T$
Constant-imbalance response time
$\Delta t=\frac{C_A\Delta T}{F_{\mathrm{net}}}$
Absorbed fraction from measured albedo
$f_{\mathrm{absorbed}}=1-\alpha$
Planetary absorbed power
$P_{\mathrm{absorbed}}=(1-\alpha)S\pi R^2$
Equilibrium test
$P_{\mathrm{absorbed}}\stackrel{?}{=}P_{\mathrm{outgoing}}$
Topic B.3Not started
Gas laws
Gas laws connect macroscopic pressure, volume and temperature to a microscopic model of moving particles. Students use both empirical gas relationships and kinetic-theory ideas.
360 min estimated
Topic B.3 progress0%
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Learning objectives
Define pressure and amount of substance and distinguish particle number N from amount n in moles.
Use constant-pressure, constant-volume and constant-temperature gas relationships.
Apply the ideal gas equation in different forms.
Interpret pressure–volume diagrams for changes of state.
Explain gas pressure through molecular collisions and momentum change.
Relate pressure and internal energy to molecular speeds and temperature.
Key formulas
Definition of pressure
$p=\frac{F_{\perp}}{A}$
Absolute and gauge pressure
$p_{\mathrm{absolute}}=p_{\mathrm{gauge}}+p_{\mathrm{atmospheric}}$
Normal momentum change at an elastic rebound from a stationary smooth wall
$|\Delta p_x|=2m|v_x|$
Average force from momentum transfer
$F_{\mathrm{average}}=\frac{\Delta p_{\mathrm{total}}}{\Delta t}$
Microscopic route to pressure
$p=\frac{1}{A}\frac{\Delta p_{\mathrm{total}}}{\Delta t}$
Mean translational kinetic energy
$\langle E_k\rangle=\frac{1}{2}m\langle v^2\rangle=\frac{3}{2}k_{\mathrm B}T$
Root-mean-square molecular speed
$v_{\mathrm{rms}}=\sqrt{\frac{3k_{\mathrm B}T}{m}}=\sqrt{\frac{3RT}{M}}$
Internal energy of a monatomic ideal gas
$U=\frac{3}{2}Nk_{\mathrm B}T=\frac{3}{2}nRT$
Particle number and amount
$N=nN_{\mathrm A}$
Amount from mass
$n=\frac{m_{\mathrm{sample}}}{M}$
Boyle's law proportionality
$p\propto\frac{1}{V}\quad(T,n\text{ constant})$
Boyle's law between two states
$p_1V_1=p_2V_2$
Constant-pressure relationship
$\frac{V}{T}=\text{constant}\quad\Rightarrow\quad\frac{V_1}{T_1}=\frac{V_2}{T_2}$
Constant-volume relationship
$\frac{p}{T}=\text{constant}\quad\Rightarrow\quad\frac{p_1}{T_1}=\frac{p_2}{T_2}$
Molar form of the ideal-gas equation
$pV=nRT$
Particle form and constant bridge
$pV=Nk_{\mathrm B}T,\qquad R=N_{\mathrm A}k_{\mathrm B}$
Combined gas law for fixed amount
$\frac{p_1V_1}{T_1}=\frac{p_2V_2}{T_2}$
Quasistatic boundary work done by a gas
$W_{\mathrm{by}}=\int_{V_1}^{V_2}p\,\mathrm dV$
Work sign convention and constant-pressure quasistatic work
$W_{\mathrm{on}}=-W_{\mathrm{by}},\qquad W_{\mathrm{by}}=p\Delta V\;\text{at constant }p$
Kinetic-theory pressure equation
$pV=\frac{1}{3}Nm\langle v^2\rangle$
Density form of the kinetic equation
$p=\frac{1}{3}\rho v_{\mathrm{rms}}^2$
Mechanical meaning of temperature
$\frac{1}{2}m\langle v^2\rangle=\frac{3}{2}k_{\mathrm B}T$
Compressibility factor
$Z=\frac{pV}{nRT}$
Percentage deviation from ideal behaviour
$\text{percentage deviation}=|Z-1|\times100\%$
First-order maximum-uncertainty estimate for a product
$\frac{\Delta(pV)}{pV}\approx\frac{\Delta p}{p}+\frac{\Delta V}{V}$
Boyle-law linear form
$p=(pV)\left(\frac{1}{V}\right)$
Topic B.5Not started
Current and circuits
Electric circuits are treated through charge flow, energy transfer, resistance and source behaviour. Students analyse both series and parallel combinations and connect macroscopic circuit quantities to a particle model.
360 min estimated
Topic B.5 progress0%
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Learning objectives
Define current as charge flow per unit time and potential difference as energy transferred per unit charge.
Use Ohm’s law for ohmic conductors and interpret current–voltage characteristics.
Relate resistance to resistivity, conductor length and cross-sectional area.
Calculate electrical power and energy transfer.
Analyse current, voltage and equivalent resistance in series and parallel circuits.
Model real cells using emf and internal resistance.
Interpret the behaviour of thermistors, light-dependent resistors and potentiometers.
Key formulas
Average current (or steady current)
$I=\frac{\Delta Q}{\Delta t}$
Quantization of charge
$Q=Ne$
Current in a conductor
$I=nqAv_{\mathrm d}$
Potential difference with specified polarity
$V_{AB}=\frac{W_{\mathrm{transferred}}}{Q}$
Electromotive force
$\varepsilon=\frac{E_{\mathrm{supplied}}}{Q}$
Resistance at an operating point
$R=\frac{V}{I}$
Ohm's law
$V=IR\quad(\text{constant physical conditions})$
Resistance of a uniform conductor
$R=\rho\frac{L}{A}$
Area of a circular wire
$A=\frac{\pi d^2}{4}$
Linear temperature approximation
$\rho=\rho_0[1+\alpha(T-T_0)]$
Electrical power
$P=VI$
Power in a resistor
$P=I^2R=\frac{V^2}{R}$
Energy transferred at constant voltage and current
$E=P\Delta t=VI\Delta t$
Kirchhoff's junction rule
$\sum\limits_{j=1}^{m}I_{j,\mathrm{in}}=\sum\limits_{k=1}^{n}I_{k,\mathrm{out}}$
Kirchhoff's loop rule
$\sum\limits_{k=1}^{n}\Delta V_k=0$
Equivalent series resistance
$R_{\mathrm{eq}}=R_1+R_2+\cdots$
Common voltage across a parallel group
$V_{\mathrm{group}}=V_1=V_2=\cdots$
Total current in parallel
$I_{\mathrm{total}}=I_1+I_2+\cdots$
Equivalent parallel resistance
$\frac{1}{R_{\mathrm{eq}}}=\frac{1}{R_1}+\frac{1}{R_2}+\cdots$
Terminal voltage while delivering current
$V_{\mathrm{terminal}}=\varepsilon-Ir$
Current from a real cell
$I=\frac{\varepsilon}{R+r}$
Internal power transfer
$P_{\mathrm{internal}}=I^2r$
Unloaded potential divider
$V_{\mathrm{out}}=V_{\mathrm{in}}\frac{R_2}{R_1+R_2}$
Uniform potentiometer ratio
$\frac{V_{\mathrm{out}}}{V_{\mathrm{in}}}=\frac{x}{L}$
Unloaded divider output measured across a sensor
$V_{\mathrm{out}}=V_{\mathrm{in}}\frac{R_{\mathrm{sensor}}}{R_{\mathrm{fixed}}+R_{\mathrm{sensor}}}$
Qualitative sensor trends
$T\uparrow\Rightarrow R_{\mathrm{NTC}}\downarrow,\qquad L\uparrow\Rightarrow R_{\mathrm{LDR}}\downarrow$
Parallel loading by a voltmeter
$R_{\mathrm{loaded}}=\frac{R R_{\mathrm V}}{R+R_{\mathrm V}}$
First-order maximum fractional uncertainty in resistance
$\frac{\Delta R}{R}\approx\frac{\Delta V}{V}+\frac{\Delta I}{I}$
Two resistors in parallel
$R_p=\frac{R_1R_2}{R_1+R_2}$
Steady dc operating current from electrical input power
$I=\frac{P}{V}$
Unit 3
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Wave Behaviour
Theme C develops oscillations and waves as models for systems that transfer energy and information. Students study simple harmonic motion, travelling waves, interference, diffraction, standing waves, resonance and the Doppler effect.
17 hours estimated ·5 topics
Unit 3 progress0%
Topics in this unit
Topic C.1Not started
Simple harmonic motion
Simple harmonic motion (SHM) is a model for oscillations in which acceleration is proportional to displacement and directed back toward equilibrium. At SL, the emphasis is on the defining relation, period and qualitative energy changes.
180 min estimated
Topic C.1 progress0%
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Learning objectives
Identify the conditions that produce simple harmonic motion.
Use the defining acceleration–displacement relation and interpret its negative sign.
Describe an oscillator using amplitude, equilibrium position, displacement, frequency, period and angular frequency.
Calculate periods for ideal mass–spring systems and simple pendulums.
Describe qualitatively how kinetic and potential energy vary during one cycle.
Key formulas
Displacement from equilibrium
$x=s-s_{\mathrm{eq}}$
Direction test for a restoring force
$F_{\mathrm{restoring}}x<0\quad(x\ne0)$
Defining SHM relation
$a=-\omega^2x$
Gradient of an acceleration-displacement graph
$\frac{\Delta a}{\Delta x}=-\omega^2$
Maximum acceleration magnitude
$a_{\max}=\omega^2A$
Period-frequency relationship
$f=\frac{1}{T}$
Angular frequency
$\omega=2\pi f=\frac{2\pi}{T}$
Phase-offset magnitude from time-offset magnitude
$|\Delta\phi|=\omega|\Delta t|=2\pi\frac{|\Delta t|}{T}$
SHM displacement
$x=A\cos(\omega t+\phi)$
SHM velocity
$v=-\omega A\sin(\omega t+\phi)$
SHM acceleration
$a=-\omega^2A\cos(\omega t+\phi)=-\omega^2x$
Speed-displacement relation
$v^2=\omega^2(A^2-x^2)$
Normalized SHM phase ellipse
$\frac{x^2}{A^2}+\frac{v^2}{\omega^2A^2}=1$
Phase-plane intercepts
$(x,v)=(\pm A,0)\quad\text{or}\quad(0,\pm\omega A)$
SHM phase separations
$|\Delta\phi_{xv}|=\frac{\pi}{2},\qquad|\Delta\phi_{xa}|=\pi$
Net restoring force about spring equilibrium
$F_{\mathrm{rest}}=-kx$
Spring angular frequency
$\omega=\sqrt{\frac{k}{m}}$
Mass-spring period
$T=2\pi\sqrt{\frac{m}{k}}$
Small-angle approximation
$\sin\theta\approx\theta\quad(|\theta|\ll1\text{ rad})$
Pendulum angular frequency
$\omega=\sqrt{\frac{g}{L}}$
Simple-pendulum period
$T=2\pi\sqrt{\frac{L}{g}}$
Total energy of spring SHM
$E_{\mathrm{total}}=\frac{1}{2}kA^2$
Oscillator potential energy relative to equilibrium
$E_{\mathrm p}=\frac{1}{2}kx^2$
Kinetic energy in spring SHM
$E_{\mathrm k}=\frac{1}{2}k(A^2-x^2)$
Experimental SHM proportionality test
$\frac{a}{x}=-\omega^2=\text{constant}$
Percentage deviation from a model
$\text{percentage deviation}=\frac{|y_{\mathrm{measured}}-y_{\mathrm{model}}|}{|y_{\mathrm{model}}|}\times100\%$
Period from multiple-cycle timing
$T=\frac{t_N}{N}$
Linearized mass-spring relationship
$T^2=\frac{4\pi^2}{k}m$
Linearized pendulum relationship
$T^2=\frac{4\pi^2}{g}L$
Topic C.2Not started
Wave model
Students use the wave model to describe how local disturbances transfer energy. Both mechanical and electromagnetic waves are considered.
180 min estimated
Topic C.2 progress0%
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Learning objectives
Distinguish transverse and longitudinal travelling waves.
Define wavelength, frequency, period, amplitude and wave speed.
Describe particle motion in a medium as a wave passes through it.
Explain the nature of sound waves.
Describe the electromagnetic spectrum and distinguish electromagnetic waves from mechanical waves.
Key formulas
Average wave propagation speed
$v=\frac{\Delta x}{\Delta t}$
Energy transferred by a wave
$E=P\Delta t$
Transverse-direction condition
$\vec{s}\cdot\vec{v}=0$
Longitudinal-direction condition
$\vec{s}\parallel\vec{v}$
Frequency-period relationship
$f=\frac{1}{T}$
Frequency from counting cycles
$f=\frac{N}{\Delta t}$
Optional phase model: angular frequency
$\omega=2\pi f=\frac{2\pi}{T}$
Wave equation
$v=f\lambda=\frac{\lambda}{T}$
Optional model: Wave number
$k=\frac{2\pi}{\lambda}$
Optional model: Positive-direction sinusoidal wave
$y=A\sin(kx-\omega t+\phi)$
Optional model: Phase speed
$v=\frac{\omega}{k}$
Optional: spatial phase-offset magnitude
$\lvert\Delta\phi\rvert=\frac{2\pi\lvert\Delta x\rvert}{\lambda}$
Optional: temporal phase-offset magnitude
$\lvert\Delta\phi\rvert=\frac{2\pi\lvert\Delta t\rvert}{T}$
Optional: particle velocity for a fixed-shape right-moving transverse wave
$u_y=-v\frac{\partial y}{\partial x}$
Optional: wave speed on an ideal uniform string
$v=\sqrt{\frac{F_T}{\mu}}$
Linear mass density
$\mu=\frac{m}{L}$
Echo-ranging distance
$d=\frac{v\Delta t}{2}$
Sound intensity
$I=\frac{P}{A}$
Optional: sinusoidal travelling pressure variation
$\Delta p=\Delta p_{\max}\cos(kx-\omega t)$
Electromagnetic wave relation in vacuum
$c=f\lambda$
Quantum-physics link: photon energy
$E=hf$
Optional: plane-wave field-amplitude ratio in vacuum
$\frac{E_0}{B_0}=c$
Intensity definition
$I=\frac{P}{A}$
Uniform spherical spreading
$I=\frac{P}{4\pi r^2}$
Intensity ratio: same medium, frequency and amplitude definition
$\frac{I_2}{I_1}=\left(\frac{A_2}{A_1}\right)^2$
Mean wavelength over several intervals
$\lambda=\frac{L}{n}$
Percentage uncertainty
$\%\,u=\frac{\Delta q}{\lvert q\rvert}\times100\%$
Speed from repeated distance-time measurements
$v=\frac{\Delta d}{\Delta t}$
Topic C.3Not started
Wave phenomena
This topic explains what waves do at boundaries, apertures and when they overlap. It is a major source of diagrams and multi-step reasoning questions.
300 min estimated
Topic C.3 progress0%
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Learning objectives
Use rays and wavefronts to represent two- and three-dimensional wave propagation.
Explain reflection, refraction, transmission and diffraction.
Apply Snell’s law, critical angle and total internal reflection.
Apply superposition to wave pulses and continuous waves.
Use path difference to identify constructive and destructive interference.
Analyse double-source interference and the geometry of double-slit fringes.
Describe single-slit diffraction and multiple-slit/diffraction-grating patterns qualitatively at SL.
Key formulas
Ray-wavefront geometry
$\vec{v}\perp\text{wavefront}$
Wave speed from wavefront spacing
$v=f\lambda$
Law of reflection
$\theta_i=\theta_r$
Frequency continuity at a stationary boundary
$f_i=f_r=f_t$
Power balance at a passive boundary in steady state
$P_i=P_r+P_t+P_{\mathrm{abs}}$
Refractive index
$n=\frac{c}{v}$
Snell’s law
$n_1\sin\theta_1=n_2\sin\theta_2$
Speed–angle–wavelength ratio: nonzero ray angles; use undivided Snell at normal incidence
$\frac{\sin\theta_1}{\sin\theta_2}=\frac{v_1}{v_2}=\frac{\lambda_1}{\lambda_2}=\frac{n_2}{n_1}$
Wavelength in a refractive medium
$\lambda=\frac{\lambda_0}{n}$
Critical-angle form of Snell’s law
$n_1\sin c=n_2\sin90^\circ$
Critical-angle equation
$\sin c=\frac{n_2}{n_1}$
Total-internal-reflection conditions
$n_1>n_2\quad\text{and}\quad\theta_i>c$
Diffraction-control ratio
$\mathcal{D}=\frac{\lambda}{a}$
Strong-spreading condition
$a\lesssim\lambda$
Same-medium wave relation
$v=f\lambda=\text{constant}$
Principle of superposition
$y_{\mathrm{resultant}}=\sum\limits_{i=1}^{N}y_i$
In-phase amplitude addition
$A_{\max}=A_1+A_2$
Opposite-phase resultant amplitude
$A_{\min}=\left|A_1-A_2\right|$
Path difference
$\Delta r=\left|r_2-r_1\right|$
Constructive and destructive conditions
$\Delta r=m\lambda\quad\text{or}\quad\Delta r=\left(m+\frac12\right)\lambda$
Path-induced unwrapped phase-lag magnitude
$\Delta\phi=\frac{2\pi\Delta r}{\lambda}$
Double-slit path difference
$\Delta r\approx s\lvert\sin\theta\rvert\approx\frac{s\lvert y\rvert}{D}$
Bright-fringe position: far field, small angles
$y_m=\frac{m\lambda D}{s}$
Fringe spacing: far field, small angles
$w=\frac{\lambda D}{s}$
Wavelength from a near-axis fringe pattern
$\lambda=\frac{ws}{D}$
Optional HL link: small-angle single-slit angular scale
$\theta_{\mathrm{spread}}\propto\frac{\lambda}{a}$
Optional HL link: grating principal maxima at normal incidence
$d\sin\theta=m\lambda$
Mean fringe spacing
$w=\frac{L}{N}$
Double-slit graph gradient
$\frac{\Delta w}{\Delta D}=\frac{\lambda}{s}$
Percentage uncertainty
$\%\,u=\frac{\Delta q}{\lvert q\rvert}\times100\%$
Topic C.4Not started
Standing waves and resonance
Standing waves arise from the superposition of identical waves travelling in opposite directions. Boundary conditions determine the allowed modes in strings and pipes, while resonance describes large responses near a system’s natural frequency.
240 min estimated
Topic C.4 progress0%
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Learning objectives
Explain standing-wave formation through superposition.
Identify nodes and antinodes and compare amplitude and phase at different positions.
Determine allowed wavelengths and frequencies for strings and open/closed pipes from boundary conditions.
Use the term first harmonic for the lowest-frequency mode.
Explain resonance, natural frequency and the effect of driving frequency.
Describe qualitatively how light, critical and heavy damping affect oscillations and resonance.
Key formulas
Right-moving component
$y_1=A\sin(kx-\omega t)$
Left-moving component
$y_2=A\sin(kx+\omega t)$
Resultant standing wave
$y=2A\sin(kx)\cos(\omega t)$
Adjacent-node or adjacent-antinode spacing
$\Delta x=\frac{\lambda}{2}$
Node-to-nearest-antinode spacing
$\Delta x=\frac{\lambda}{4}$
Neighbouring-loop phase difference
$\Delta\phi=\pi\,\mathrm{rad}$
Fixed–fixed string: allowed wavelengths
$\lambda_n=\frac{2L}{n}$
Fixed–fixed string: harmonic frequencies
$f_n=\frac{nv}{2L}=nf_1$
Optional supporting model: wave speed on a uniform ideal string
$v=\sqrt{\frac{F_T}{\mu}}$
Optional uniform fixed–fixed string: first-harmonic frequency
$f_1=\frac{1}{2L}\sqrt{\frac{F_T}{\mu}}$
Open–open pipe allowed wavelengths
$\lambda_n=\frac{2L}{n}$
Open–open pipe frequencies
$f_n=\frac{nv}{2L}$
Open–open pipe first-harmonic length
$L=\frac{\lambda_1}{2}$
Closed-open allowed wavelengths
$\lambda_m=\frac{4L}{2m-1}$
Closed-open resonance frequencies
$f_m=\frac{(2m-1)v}{4L}$
Closed-open first harmonic
$f_1=\frac{v}{4L}$
Light-damping resonance: approximate frequency condition
$f_d\approx f_0$
Natural period
$T_0=\frac{1}{f_0}$
Energy supplied by the driver over an interval, not net stored-energy gain
$\Delta E=P_{\mathrm{in}}\Delta t$
Optional supporting model: linear viscous damping
$F_d=-bv$
Optional supporting model: free underdamped amplitude envelope
$A(t)=A_0e^{-\gamma t}$
Optional narrow-resonance bandwidth estimate
$Q\approx\frac{f_0}{\Delta f}$
Travelling-wave intensity at fixed medium and frequency
$I\propto A^2$
Energy transferred by a driver
$E=P\Delta t$
Wavelength from string loops
$\lambda=\frac{2L}{n}$
Closed–open pipe first-harmonic sound speed
$v=4Lf_1$
Optional combined model: uniform fixed–fixed string
$f_n=\frac{n}{2L}\sqrt{\frac{F_T}{\mu}}$
Equal ideal length and sound speed: pipe first-harmonic ratio
$\frac{f_{\mathrm{open-open}}}{f_{\mathrm{closed-open}}}=2$
Percentage difference from a model
$\%\,\mathrm{difference}=\frac{\left|q_{\mathrm{measured}}-q_{\mathrm{model}}\right|}{\left|q_{\mathrm{model}}\right|}\times100\%$
Topic C.5Not started
Doppler effect
The Doppler effect describes the observed change in frequency or wavelength caused by relative motion between a source and an observer. At SL, students study qualitative sound-wave cases and the small-speed approximation for light.
120 min estimated
Topic C.5 progress0%
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Learning objectives
Explain the Doppler effect for sound and electromagnetic waves.
Draw wavefront diagrams for a moving source or observer.
Use the small-speed approximation for the fractional change in light frequency or wavelength.
Interpret redshift and blueshift of spectral lines as evidence of motion of stars and galaxies.
Recognize practical uses of Doppler measurements.
Key formulas
Wave equation using quantities in the same frame
$v_w=f\lambda$
Frequency and period
$f=\frac{1}{T}$
Fractional frequency shift
$\text{fractional shift}=\frac{\Delta f}{f_s}=\frac{f_o-f_s}{f_s}$
Optional HL link: Wavelength ahead of a moving source
$\lambda_{ahead}=(v_w-v_s)T_s=\frac{v_w-v_s}{f_s}$
Optional HL link: Wavelength behind a moving source
$\lambda_{behind}=(v_w+v_s)T_s=\frac{v_w+v_s}{f_s}$
Frequency received by a stationary observer
$f_o=\frac{v_w}{\lambda}$
Optional HL link: Observer approaching a stationary source
$f_o=f_s\left(\frac{v_w+v_o}{v_w}\right)$
Optional HL link: Observer receding from a stationary source
$f_o=f_s\left(\frac{v_w-v_o}{v_w}\right)$
Radial component
$v_r=v\cos\theta$
Optional extension: Direct approach in a stationary medium
$f_o=f_s\left(\frac{v_w+v_o}{v_w-v_s}\right)$
Optional extension: Direct recession in a stationary medium
$f_o=f_s\left(\frac{v_w-v_o}{v_w+v_s}\right)$
Optional extension: Mach number
$M=\frac{v_s}{v_w}$
Light wave relationship
$c=f\lambda$
Small-speed wavelength shift
$\frac{\Delta\lambda}{\lambda_0}\approx\frac{v_r}{c}$
Small-speed frequency shift
$\frac{\Delta f}{f_0}\approx-\frac{v_r}{c}$
Opposite fractional changes
$\frac{\Delta f}{f_0}\approx-\frac{\Delta\lambda}{\lambda_0}$
Redshift parameter
$z=\frac{\lambda_{obs}-\lambda_0}{\lambda_0}=\frac{\Delta\lambda}{\lambda_0}$
Low-speed Doppler radial-velocity estimate
$v_r\approx zc$
Observed wavelength from redshift
$\lambda_{obs}=(1+z)\lambda_0$
Optional quantitative application: Low-speed reflected electromagnetic shift
$\frac{|\Delta f|}{f_0}\approx\frac{2|u_r|}{c}$
Optional quantitative application: Doppler ultrasound echo shift
$|\Delta f|\approx\frac{2f_0u|\cos\theta|}{v_w}$
Optional quantitative application: Blood speed inferred from shift
$u\approx\frac{|\Delta f|v_w}{2f_0|\cos\theta|},\quad |\cos\theta|>0$
Wavelength change from radial velocity
$\Delta\lambda\approx\frac{\lambda_0}{c}v_r$
Signed radial velocity component
$u_r=u\cos\theta$
Percentage wavelength shift
$\text{percentage shift}=100\frac{\lambda_{obs}-\lambda_0}{\lambda_0}$
Optional HL link: Approaching-source frequency
$f_o=f_s\frac{v_w}{v_w-v_s}$
Optional HL link: Source speed from observed frequency
$v_s=v_w\left(1-\frac{f_s}{f_o}\right)$
First-order light shift: total relative speed much smaller than c
$\left|\frac{\Delta f}{f_0}\right|\approx\left|\frac{v_r}{c}\right|\ll1$
Unit 4
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Fields
Theme D develops gravitational, electric and magnetic fields as models of interactions at a distance. Students then study the motion and forces of charged particles and current-carrying conductors in electromagnetic fields.
19 hours estimated ·3 topics
Unit 4 progress0%
Topics in this unit
Topic D.1Not started
Gravitational fields
Students model gravitational interactions using Newton’s law and field strength, and connect these ideas to orbital motion through Kepler’s laws.
300 min estimated
Topic D.1 progress0%
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Learning objectives
State and apply Kepler’s three laws of orbital motion qualitatively and quantitatively where appropriate.
Apply Newton’s universal law of gravitation to point masses and suitable spherical bodies.
Define gravitational field strength as force per unit mass.
Calculate gravitational field strength around a spherical mass.
Sketch and interpret gravitational field lines.
Recognize when the near-Earth approximation g ≈ constant is appropriate and when an inverse-square model is required.
Key formulas
Definition of gravitational field strength
$g=\frac{F}{m}$
Weight
$W=mg$
Equivalent field-strength units
$1\ \mathrm{N\,kg^{-1}}=1\ \mathrm{m\,s^{-2}}$
Newton's law of gravitation
$F=G\frac{m_1m_2}{r^2}$
Gravitational constant
$G\approx6.67\times10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$
Inverse-square force ratio
$\frac{F_2}{F_1}=\frac{m_{1,2}m_{2,2}}{m_{1,1}m_{2,1}}\left(\frac{r_1}{r_2}\right)^2$
Radial gravitational field strength
$g=G\frac{M}{r^2}$
Force on a mass in a field
$\vec F=m\vec g$
Source mass from field data
$M=\frac{gr^2}{G}$
Inverse-square field ratio
$\frac{g_2}{g_1}=\left(\frac{r_1}{r_2}\right)^2$
Radial vector direction
$\vec g=-\frac{GM}{r^2}\hat r$
Area of a sphere
$A=4\pi r^2$
Field strength at altitude
$g(h)=\frac{GM}{(R+h)^2}$
Altitude-to-surface field ratio
$\frac{g(h)}{g_0}=\left(\frac{R}{R+h}\right)^2$
Optional first-order estimate of small-height fractional change
$\frac{\Delta g}{g_0}\approx-\frac{2h}{R}\quad(h\ll R)$
Superposition of gravitational fields
$\vec g_{net}=\sum\limits_{i=1}^{N}\vec g_i$
Two-mass cancellation condition
$\frac{GM_1}{x^2}=\frac{GM_2}{(d-x)^2}$
Zero-field position between two masses
$x=\frac{d\sqrt{M_1}}{\sqrt{M_1}+\sqrt{M_2}}$
Optional ellipse geometry: periapsis and apoapsis distances
$r_p=a(1-e),\qquad r_a=a(1+e)$
Kepler's equal-area statement
$\frac{\Delta A}{\Delta t}=\text{constant}$
Optional small-sector area approximation
$\Delta A\approx\frac{1}{2}r^2\Delta\theta$
Kepler's third-law ratio
$\frac{T_1^2}{a_1^3}=\frac{T_2^2}{a_2^3}$
Newton–Kepler orbital relationship
$T^2=\frac{4\pi^2a^3}{GM}$
Central mass from an orbit
$M=\frac{4\pi^2a^3}{GT^2}$
Orbital period from central mass
$T=2\pi\sqrt{\frac{a^3}{GM}}$
Gradient of T squared against a cubed
$S=\frac{4\pi^2}{GM}$
Small-angle simple-pendulum estimate of g (SHM link)
$g=\frac{4\pi^2L}{T_p^2}$
Inverse-square scaling check
$g\propto\frac{M}{r^2}$
Orbital-period scaling
$\frac{T_2}{T_1}=\left(\frac{a_2}{a_1}\right)^{\frac{3}{2}}$
Percentage difference from surface g
$\text{percentage change}=100\frac{g(h)-g_0}{g_0}$
Topic D.2Not started
Electric and magnetic fields
This topic introduces electric charge, electrostatic forces, electric field strength and magnetic-field patterns. SL students focus on forces and field representations rather than electric potential energy and potential, which are HL extensions.
480 min estimated
Topic D.2 progress0%
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Learning objectives
Use the direction of force between positive and negative charges.
Apply Coulomb’s law and the conservation of electric charge.
Explain Millikan’s experiment as evidence that electric charge is quantized.
Describe charge transfer by friction, contact and electrostatic induction, including grounding.
Define electric field strength and sketch electric field lines.
Relate field-line density to field strength.
Use the uniform electric-field relationship between parallel plates.
Sketch and interpret magnetic fields for bar magnets, straight wires, circular coils and solenoids.
Key formulas
Net charge from particle counts
$Q=(N_p-N_e)e$
Elementary charge
$e\approx1.60\times10^{-19}\ \mathrm{C}$
Third-law force pair
$\vec F_{1\to2}=-\vec F_{2\to1}$
Charge conservation
$Q_{\text{total,before}}=Q_{\text{total,after}}$
Equal charge sharing under equivalent electrical conditions
$Q_{\text{each}}=\frac{Q_1+Q_2+\cdots}{N}$
Transferred-electron count
$N_e=\frac{|\Delta Q|}{e}$
Neutral polarized conductor
$Q_{\text{near}}+Q_{\text{far}}=0$
Charge gained through grounding
$Q_{\text{final}}=Q_{\text{initial}}+\Delta Q_{\text{Earth}}$
Optional two-point polarization model: equal opposite induced charges
$\frac{F_{\text{near}}}{F_{\text{far}}}=\left(\frac{r_{\text{far}}}{r_{\text{near}}}\right)^2$
Coulomb's law
$F=k\frac{|q_1q_2|}{r^2}$
Coulomb constant
$k=\frac1{4\pi\epsilon_0}\approx8.99\times10^9\ \mathrm{N\,m^2\,C^{-2}}$
Force superposition
$\vec F_{\text{net}}=\sum\limits_{i=1}^{N}\vec F_i$
Charge quantization
$Q=ne,\qquad n=0,\pm1,\pm2,\ldots$
Stationary oil drop: upward electric force, negligible buoyancy
$|q|E=mg$
Elementary-charge count
$N=\frac{|Q|}{e}$
Electric field definition
$\vec E=\frac{\vec F}{q_{\text{test}}}\quad(q_{\text{test}}>0)$
Force in an electric field
$\vec F=q\vec E$
Electric-field unit equivalence
$1\ \mathrm{N\,C^{-1}}=1\ \mathrm{V\,m^{-1}}$
Point-charge field strength
$E=k\frac{|Q|}{r^2}$
Electric-field superposition
$\vec E_{\text{net}}=\sum\limits_{i=1}^{N}\vec E_i$
Inverse-square field ratio
$\frac{E_2}{E_1}=\left(\frac{r_1}{r_2}\right)^2$
Uniform parallel-plate field
$E=\frac{V}{d}$
Electric force between plates
$\vec F=q\vec E$
D.3 link: non-relativistic acceleration when electric force dominates
$\vec a=\frac{q\vec E}{m}$
Magnetic-field superposition
$\vec B_{\text{net}}=\sum\limits_{i=1}^{N}\vec B_i$
External bar-magnet direction
$N\longrightarrow S\quad(\text{outside})$
Internal return direction
$S\longrightarrow N\quad(\text{inside})$
Optional long-wire exterior model: Current scaling
$B\propto I\quad(r\text{ fixed})$
Optional long-wire exterior model: Distance scaling
$B\propto\frac{1}{r}\quad(I\text{ fixed})$
Optional long-wire exterior model: Two-condition field ratio
$\frac{B_2}{B_1}=\frac{I_2r_1}{I_1r_2}$
Turn density
$n=\frac{N}{L}$
Optional long air-core model: Solenoid field scaling
$B\propto nI$
Optional long air-core model: Solenoid comparison
$\frac{B_2}{B_1}\approx\frac{n_2I_2}{n_1I_1}$
Electrostatic-force scaling
$F\propto\frac{|q_1q_2|}{r^2}$
Field-force connection
$\vec F=q\vec E$
Combined-source rule
$\vec X_{\text{net}}=\sum\limits_{i=1}^{N}\vec X_i\quad(\vec X=\vec F,\vec E,\vec B)$
Topic D.3Not started
Motion in electromagnetic fields
Students combine field ideas with mechanics to analyse charged particles and currents in electric and magnetic fields. Magnetic forces often produce circular motion because they act perpendicular to velocity.
360 min estimated
Topic D.3 progress0%
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Learning objectives
Describe charged-particle motion in uniform electric fields.
Describe charged-particle motion in uniform magnetic fields.
Analyse motion in crossed perpendicular electric and magnetic fields.
Calculate the magnetic force on a moving charge.
Calculate the force on a current-carrying conductor in a magnetic field.
Use the force per unit length between parallel current-carrying wires.
Determine magnetic-field direction from current and force directions.
Use circular-motion ideas to determine or compare charge-to-mass ratios.
Key formulas
Electric force
$\vec F_E=q\vec E$
Magnetic force
$\vec F_B=q\vec v\times\vec B$
Combined Lorentz force
$\vec F=q(\vec E+\vec v\times\vec B)$
Electric acceleration
$\vec a=\frac{q\vec E}{m}$
Velocity under constant electric acceleration
$\vec v=\vec u+\frac{q\vec E}{m}t$
Displacement under constant electric acceleration
$\vec s=\vec u t+\frac{1}{2}\frac{q\vec E}{m}t^2$
Transit time through plates
$t=\frac{L}{v_x}$
Transverse deflection
$y=\frac{1}{2}\frac{qE}{m}t^2$
Electric-field trajectory
$y=\frac{qE}{2mv_x^2}x^2$
Magnetic-force magnitude
$F_B=|q|vB\sin\theta$
Perpendicular speed
$v_\perp=v\sin\theta$
Magnetic power
$P_B=\vec F_B\cdot\vec v=0$
Magnetic centripetal balance
$|q|vB=\frac{mv^2}{r}$
Magnetic orbit radius
$r=\frac{mv}{|q|B}$
Magnetic orbit period
$T=\frac{2\pi m}{|q|B}$
Velocity components
$v_\parallel=v\cos\theta,\qquad v_\perp=v\sin\theta$
Helix radius
$r=\frac{mv_\perp}{|q|B}$
Helix pitch
$p=|v_{\parallel}|T=\frac{2\pi m|v_{\parallel}|}{|q|B}$
Selector force balance
$|q|E=|q|vB$
Selected speed
$v=\frac{E}{B}$
Initial transverse force magnitude in the standard selector geometry
$F_{\text{net}}=|q|\,|E-vB|$
Charge-to-mass ratio from a magnetic orbit
$\frac{|q|}{m}=\frac{v}{Br}$
Selector plus analyser
$\frac{|q|}{m}=\frac{E}{B_sB_ar}$
Mass-to-radius comparison
$\frac{r_2}{r_1}=\frac{m_2|q_1|}{m_1|q_2|}$
Conductor-force magnitude
$F=BIL\sin\theta$
Vector conductor force
$\vec F=I\vec L\times\vec B$
Force per unit active length
$\frac{F}{L}=BI\sin\theta$
Field of wire 1 at wire 2
$B_1=\frac{\mu_0I_1}{2\pi d}$
Parallel-wire force per length
$\frac{F}{L}=\frac{\mu_0I_1I_2}{2\pi d}$
Permeability of free space
$\mu_0\approx4\pi\times10^{-7}\ \mathrm{T\,m\,A^{-1}}$
Field from current balance: nonzero current, length and sine of angle
$B=\frac{F}{IL\sin\theta}$
Current-balance gradient
$\frac{\Delta F}{\Delta I}=BL\quad(\theta=90^\circ)$
Force reversal checks
$I\to-I\Rightarrow\vec F\to-\vec F,\qquad \vec B\to-\vec B\Rightarrow\vec F\to-\vec F$
Electromagnetic decision equation
$\vec F=q(\vec E+\vec v\times\vec B)$
Magnetic-radius scaling
$r\propto\frac{mv_\perp}{|q|B}$
Parallel-wire scaling
$\frac{F}{L}\propto\frac{I_1I_2}{d}$
Unit 5
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Nuclear and Quantum Physics
Theme E moves from atomic evidence and spectra to nuclear stability, radioactive decay, fission, fusion and stellar evolution. It links microscopic physics with some of the largest scales in the universe.
23 hours estimated ·4 topics
Unit 5 progress0%
Topics in this unit
Topic E.1Not started
Structure of the atom
Students use experimental evidence to develop the nuclear model of the atom and connect discrete atomic energy levels to line spectra and photons.
360 min estimated
Topic E.1 progress0%
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Learning objectives
Explain how the Geiger–Marsden–Rutherford scattering experiment supports a small, dense, positively charged nucleus.
Use nuclear notation with nucleon number A and proton number Z.
Interpret emission and absorption spectra as evidence for discrete atomic energy levels.
Explain photon emission and absorption during transitions between energy levels.
Relate photon frequency to the energy difference of an atomic transition.
Use spectra to identify chemical composition.
Key formulas
Neutral-atom charge balance
$Q_{\text{atom}}=Ze-Ze=0$
Alpha-particle charge
$q_\alpha=+2e$
Nuclear-to-atomic radius scale
$\frac{r_{\text{nucleus}}}{r_{\text{atom}}}\sim10^{-5}$
Detected fraction
$f=\frac{N_{\text{detected}}}{N_{\text{incident}}}$
Percentage of events
$p=100\frac{N_{\text{selected}}}{N_{\text{total}}}\%$
Alpha-particle composition
${}^{4}_{2}\mathrm{He}^{2+}=2p+2n$
Optional support: alpha–nucleus Coulomb force magnitude
$F=k\frac{(2e)(Ze)}{r^2}$
Optional support: force ratio for the same two charges
$\frac{F_2}{F_1}=\left(\frac{r_1}{r_2}\right)^2$
Average count rate
$R=\frac{N}{\Delta t}$
Atomic-to-nuclear radius ratio
$\frac{r_{\text{atom}}}{r_{\text{nucleus}}}\sim\frac{10^{-10}}{10^{-15}}=10^5$
Atomic mass unit
$1\,\mathrm u\approx1.66\times10^{-27}\,\mathrm{kg}$
Approximate nuclear mass
$m_{\text{nucleus}}\approx A\mathrm{u}$
Nuclear notation
${}^{A}_{Z}X$
Neutron number
$N=A-Z$
Nucleon count
$A=Z+N$
Ion charge
$Q_{\text{ion}}=(Z-N_e)e$
Electron count from ion charge
$N_e=Z-\frac{Q_{\text{ion}}}{e}$
Isotope condition
$Z_1=Z_2,\qquad A_1\ne A_2$
Excitation energy
$\Delta E=E_{\text{higher}}-E_{\text{lower}}>0$
Upper–lower level-pair count: an upper bound on transition lines
$N_{\text{transitions}}=\frac{n(n-1)}{2}$
Ionization energy from a bound level
$E_{\text{ion}}=E_{\text{limit}}-E_{\text{bound}}$
Photon energy
$E_\gamma=hf$
Emission condition
$hf=E_i-E_f\quad(E_i>E_f)$
Absorption condition
$E_f=E_i+hf$
Photon energy from wavelength
$E_\gamma=hf=\frac{hc}{\lambda}$
Energy-gap wavelength
$\lambda=\frac{hc}{|\Delta E|}$
Electronvolt conversion
$1\,\mathrm{eV}\approx1.60\times10^{-19}\,\mathrm J$
Spectral frequency
$f=\frac{c}{\lambda}$
Line energy difference
$|\Delta E|=\frac{hc}{\lambda}$
Wavelength match condition
$\lambda_{\text{abs}}=\lambda_{\text{em}}\quad(\text{same level pair})$
Optional C.3 AHL link: normal-incidence grating equation
$d\sin\theta=m\lambda$
Optional grating support: spacing from line density
$d=\frac{1}{n_g}$
Percentage deviation from a positive reference wavelength
$\text{percentage difference}=100\frac{|\lambda_{\text{meas}}-\lambda_{\text{ref}}|}{\lambda_{\text{ref}}}\%$
Particle-count checklist
$p=Z,\qquad n=A-Z,\qquad Q=(Z-N_e)e$
One-photon bound-bound energy checklist: consistent units, vacuum wavelength
$E_\gamma=|E_i-E_f|=hf=\frac{hc}{\lambda}$
Energy-wavelength scaling
$E_\gamma\propto f\propto\frac{1}{\lambda}$
Topic E.3Not started
Radioactive decay
This topic combines nuclear structure, mass–energy, stability and the statistical nature of radioactive decay. At SL, students use half-life through discrete repeated-halving reasoning rather than the full exponential decay equations used at HL.
420 min estimated
Topic E.3 progress0%
Key ConceptsSubscription required Question BankSubscription required FlashcardsSubscription required
Learning objectives
Define isotopes and interpret nuclear notation.
Explain mass defect and binding energy and interpret the binding-energy-per-nucleon curve.
Apply mass–energy equivalence to nuclear reactions.
Describe the strong nuclear force as a short-range attractive interaction between nucleons.
Describe alpha, beta-minus, beta-plus and gamma decay and balance nuclear equations.
Explain the role of neutrinos and antineutrinos in beta processes.
Compare penetration and ionizing ability of alpha, beta and gamma radiation.
Use activity, count rate and half-life for integer numbers of half-lives.
Correct measured count rates for background radiation.
Key formulas
Neutron number
$N=A-Z$
Nucleon count
$A=Z+N$
Ion charge
$Q=(Z-N_e)e$
Mass–energy equivalence
$\Delta E=\Delta m c^2$
Atomic mass unit
$1\,u\approx1.66054\times10^{-27}\,\mathrm{kg}$
Energy equivalent of u
$1\,u\,c^2\approx931.5\,\mathrm{MeV}$
Nuclear-mass defect
$\Delta m=Zm_p+(A-Z)m_n-m_{\text{nucleus}}$
Atomic-mass defect
$\Delta m\approx Zm_{\mathrm H}+(A-Z)m_n-m_{\text{atom}}$
Binding energy
$E_b=\Delta m c^2$
Binding energy per nucleon
$\overline{E}_b=\frac{E_b}{A}$
Total binding from average
$E_b=A\overline{E}_b$
Binding-energy change: unchanged total proton and neutron counts
$Q=E_{b,\text{final}}-E_{b,\text{initial}}$
Nuclear length scale
$1\,\mathrm{fm}=10^{-15}\,\mathrm{m}$
Neutron-to-proton ratio
$R_{np}=\frac{N}{Z}$
Proton-pair count
$N_{pp}=\frac{Z(Z-1)}{2}$
Nucleon-number conservation
$A_{\text{parent}}=A_{\text{daughters}}+A_{\text{emitted}}$
Charge-number conservation
$Z_{\text{parent}}=Z_{\text{daughters}}+Z_{\text{emitted}}$
Nuclear reaction energy
$Q=(m_{\text{initial}}-m_{\text{final}})c^2$
General alpha decay
${}^{A}_{Z}X\rightarrow{}^{A-4}_{Z-2}Y+{}^{4}_{2}\mathrm{He}$
Momentum conservation from rest
$\vec p_{\alpha}+\vec p_{\text d}=0$
Released kinetic energy
$Q=K_{\alpha}+K_{\text d}$
Beta-minus decay
${}^{A}_{Z}X\rightarrow{}^{A}_{Z+1}Y+{}^{0}_{-1}e+\bar\nu_e$
Beta-plus decay
${}^{A}_{Z}X\rightarrow{}^{A}_{Z-1}Y+{}^{0}_{+1}e+\nu_e$
Nucleon changes in energetically allowed beta decays
$n\rightarrow p+e^-+\bar\nu_e,\qquad p\rightarrow n+e^++\nu_e$
Gamma transition
${}^{A}_{Z}X^*\rightarrow{}^{A}_{Z}X+\gamma$
Gamma photon energy
$E_\gamma=hf=\frac{hc}{\lambda}$
Photon momentum
$p_\gamma=\frac{E_\gamma}{c}$
Electric force
$\vec F=q\vec E$
Magnetic-path radius
$r=\frac{p}{|q|B}$
Steady isotropic point source: negligible attenuation and background
$I\propto\frac{1}{r^2}$
Average activity
$A=\frac{\Delta N_{\text{decays}}}{\Delta t}$
Measured count rate
$C=\frac{N_{\text{counts}}}{\Delta t}$
Idealized net detection: one relevant emission per decay
$C_{\text{source}}=\varepsilon g A$
Parents after integer half-lives
$N=N_0\left(\frac{1}{2}\right)^n$
Activity after integer half-lives
$A=A_0\left(\frac{1}{2}\right)^n$
Elapsed complete half-lives
$n=\frac{t}{T_{\frac{1}{2}}}$
Background correction
$C_{\text{net}}=C_{\text{measured}}-C_{\text{background}}$
Supporting counting statistics: independent raw Poisson counts
$\sigma_N\approx\sqrt{N}$
Supporting fractional uncertainty: sufficiently many raw counts
$\frac{\sigma_N}{N}\approx\frac{1}{\sqrt{N}}$
Steady isotropic point source, negligible attenuation: distance trend
$\frac{I_2}{I_1}=\left(\frac{r_1}{r_2}\right)^2$
Time after complete half-lives
$t=nT_{\frac{1}{2}}$
Single parent, fixed response: integer-half-life net count model
$C_{\text{net}}=(C_{\text{measured}}-C_{\text{background}})=C_0\left(\frac{1}{2}\right)^n$
Topic E.4Not started
Fission
Nuclear fission releases energy when a heavy nucleus splits. Students connect binding energy, chain reactions and reactor design to the production of electrical energy and the management of radioactive products.
240 min estimated
Topic E.4 progress0%
Key ConceptsSubscription required Question BankSubscription required FlashcardsSubscription required
Learning objectives
Explain spontaneous and neutron-induced fission.
Calculate energy released using mass differences and E = $mc^{2}$ .
Explain how a chain reaction develops and how criticality relates to neutron production.
Describe the functions of control rods, moderators, heat exchangers and shielding in a nuclear power plant.
Discuss the properties, hazards and long-term management of fission products and nuclear waste.
Key formulas
Fission bookkeeping: spontaneous parent or already formed compound nucleus
${}^{A}_{Z}X\rightarrow{}^{A_1}_{Z_1}Y+{}^{A_2}_{Z_2}W+x{}^{1}_{0}n+\text{energy}$
Nucleon-number conservation
$A=A_1+A_2+x$
Charge-number conservation
$Z=Z_1+Z_2$
Compound-nucleus formation
${}^{235}_{92}\mathrm U+{}^{1}_{0}n\rightarrow{}^{236}_{92}\mathrm U^*$
Representative fission channel
${}^{236}_{92}\mathrm U^*\rightarrow{}^{141}_{56}\mathrm{Ba}+{}^{92}_{36}\mathrm{Kr}+3{}^{1}_{0}n+Q$
Missing-neutron count
$x=A_{\text{initial}}-A_1-A_2$
Fission mass difference
$\Delta m=m_{\text{initial}}-m_{\text{final}}$
Energy from SI mass
$Q=\Delta mc^2$
Energy from mass in u
$\frac{Q}{\mathrm{MeV}}\approx931.5\frac{\Delta m}{\mathrm u}$
Binding energy per nucleon
$\overline{E}_b=\frac{E_b}{A}$
Binding increase: unchanged separate total proton and neutron counts
$Q=E_{b,\text{products}}-E_{b,\text{initial}}$
Converted mass fraction
$f_m=\frac{\Delta m}{m_{\text{initial}}}$
Energy from many fissions
$E_{\text{total}}=N_fE_f$
Steady thermal-power model: mean recoverable energy per fission
$R_f=\frac{P_{\text{th}}}{E_f}$
Mass represented by consumed isotope nuclei, not loaded fuel
$m=\frac{N_fM}{N_A}$
Supporting model: expected next-generation population
$N_{g+1}=kN_g$
Supporting model: constant factor, no independent source
$N_g=N_0k^g$
Supporting illustration: exactly two next-generation fissions
$N_g=N_0\,2^g$
Supporting model: expected-population multiplication factor
$k=\frac{N_{g+1}}{N_g}$
Supporting model: expected generation change
$N_{g+1}-N_g=(k-1)N_g$
Supporting model: percentage generation change
$\%\Delta N=100(k-1)$
Nonrelativistic neutron kinetic energy
$K=\frac{1}{2}m_nv^2$
Nonrelativistic speed from kinetic energy
$v=\sqrt{\frac{2K}{m_n}}$
Same nonrelativistic neutron: positive initial energy
$\frac{K_f}{K_i}=\left(\frac{v_f}{v_i}\right)^2$
Supporting toy model: extra fractional loss, all other effects fixed
$k_{\text{after}}=k_0(1-f_{\text{abs}})$
Control change
$\Delta k=k_{\text{after}}-k_{\text{before}}$
Mean absorption rate over a positive interval
$R_{\text{abs}}=\frac{N_{\text{absorbed}}}{\Delta t}$
Mean thermal-energy transfer over a positive interval
$P=\frac{Q}{\Delta t}$
Steady single-phase coolant: constant heat capacity, negligible other changes
$P=\dot m c\Delta T$
Power-station efficiency
$\eta=\frac{P_{\text{electrical}}}{P_{\text{thermal}}}$
Supporting model: steady isotropic point source, negligible attenuation/background
$\frac{I_2}{I_1}=\left(\frac{r_1}{r_2}\right)^2$
Supporting concept: mean absorbed dose in the stated mass
$D=\frac{E_{\text{absorbed}}}{m}$
Supporting concept: equivalent dose to one tissue, one radiation type
$H=w_RD$
Single isolated parent, no replenishment: integer-half-life activity
$A=A_0\left(\frac{1}{2}\right)^n$
Elapsed whole half-lives, not a universal safe-storage duration
$t=nT_{\frac{1}{2}}$
Electrical-energy audit: Q is mean recoverable heat per fission here
$E_{\text{electrical}}=\eta N_fQ$
Topic E.5Not started
Fusion and stars
Fusion powers stars and provides the link between nuclear physics and stellar evolution. Students use equilibrium, HR diagrams, parallax and radiation relationships to interpret stars.
360 min estimated
Topic E.5 progress0%
Key ConceptsSubscription required Question BankSubscription required FlashcardsSubscription required
Learning objectives
Explain stellar stability as a balance between inward gravitational effects and outward pressure.
Describe the temperature and density conditions needed for fusion and why fusion releases energy for light nuclei.
Explain how stellar mass affects a star’s life cycle and final state.
Interpret the main regions of a Hertzsprung–Russell diagram.
Use stellar parallax to determine distance.
Convert among astronomical units, light years and parsecs.
Combine luminosity and temperature relationships to determine stellar radius.
Key formulas
Mean density
$\rho = \frac{M}{V}$
Volume of a spherical star
$V = \frac{4}{3}\pi R^3$
Newtonian spherical-star surface field: supporting relation
$g = \frac{GM}{R^2}$
Supporting spherical hydrostatic model: total pressure
$\frac{\mathrm{d}P}{\mathrm{d}r} = -\rho g$
Supporting thin-layer estimate: nearly constant density and field
$|\Delta P| \approx \rho g\Delta r$
Radial force on a local layer element: outward positive
$F_{\text{net}} = F_{\text{pressure}} - F_{\text{gravity}}$
Supporting nonrelativistic classical-particle mean translational energy
$\overline{E_k} = \frac{3}{2}k_{\text{B}}T$
Supporting point-charge Coulomb energy: zero at infinite separation
$E_{\text{electric}} = \frac{kQ_1Q_2}{r}$
Supporting identical-species rate scaling: same temperature and reaction
$R \propto n^2$
Supporting net proton–proton nuclear equation, before positron annihilation
$4\,{}^{1}_{1}\mathrm{H} \rightarrow {}^{4}_{2}\mathrm{He} + 2e^{+} + 2\nu_e + \mathrm{energy}$
Completed-chain count
$N_{\text{chain}} = \frac{N_p}{4}$
Average completed-chain rate over the stated interval
$r = \frac{N_{\text{chain}}}{\Delta t}$
Reaction mass defect
$\Delta m = m_{\text{initial}} - m_{\text{final}}$
Mass–energy equivalence
$E = \Delta m c^2$
Energy conversion
$\frac{E}{\mathrm J}\approx1.602\times10^{-13}\frac{E}{\mathrm{MeV}}$
Average emitted luminosity over the stated interval
$L = \frac{E}{\Delta t}$
Isotropic inverse-square flux without intervening extinction
$F = \frac{L}{4\pi d^2}$
Flux ratio: same luminosity and no extinction
$\frac{F_2}{F_1} = \left(\frac{d_1}{d_2}\right)^2$
Wien law: black-body spectrum per unit wavelength
$\lambda_{\max}T = b$
Total black-body emission, or stellar effective-temperature definition
$\frac{P}{A} = \sigma T^4$
Black-body temperature estimate from wavelength-spectrum peak
$T = \frac{b}{\lambda_{\max}}$
Luminosity in solar units
$L = \left(\frac{L}{L_{\odot}}\right)L_{\odot}$
Logarithmic coordinate when this luminosity axis is specified
$y = \log_{10}\left(\frac{L}{L_{\odot}}\right)$
Inverse of the specified logarithmic luminosity coordinate
$\frac{L}{L_{\odot}} = 10^y$
Approximate mass–luminosity relation
$\frac{L}{L_{\odot}} \approx \left(\frac{M}{M_{\odot}}\right)^{3.5}$
Supporting lifetime scaling: comparable usable-fuel fraction and energy per mass
$t \propto \frac{M}{L}$
Approximate lifetime–mass relation
$\frac{t}{t_{\odot}} \approx \left(\frac{M}{M_{\odot}}\right)^{-2.5}$
Supporting Newtonian gravitational binding-energy scale, not an exact value
$E_{\text{g}} \sim -\frac{GM^2}{R}$
Surface area
$A = 4\pi R^2$
Black-body luminosity
$L = A\sigma T^4$
Supporting Schwarzschild horizon: non-rotating, uncharged black hole
$r_{\text{s}} = \frac{2GM}{c^2}$
Supporting Euclidean spherical mean density, not a black-hole interior model
$\rho = \frac{3M}{4\pi R^3}$
Supporting Newtonian escape speed: weak field and no further propulsion
$v_{\text{esc}} = \sqrt{\frac{2GM}{R}}$
Parallax distance
$\frac{d}{\mathrm{pc}}=\frac{1}{\frac{p}{\mathrm{arcsec}}}$
Parallax from maximum annual full diameter, other motions removed
$p = \frac{\theta_{\text{full}}}{2}$
Small-angle geometry
$\frac{p}{\mathrm{rad}}\approx\frac{1\,\mathrm{AU}}{d}$
Astronomical unit
$1\,\mathrm{AU}\approx1.496\times10^{11}\,\mathrm m$
Light-year
$1\,\mathrm{ly} \approx 9.46\times10^{15}\,\mathrm{m}$
Parsec conversions
$1\,\mathrm{pc}\approx3.086\times10^{16}\,\mathrm m\approx3.26\,\mathrm{ly}\approx206265\,\mathrm{AU}$
Stellar luminosity
$L = 4\pi R^2\sigma T^4$
Solar ratio form
$\frac{L}{L_{\odot}} = \left(\frac{R}{R_{\odot}}\right)^2\left(\frac{T}{T_{\odot}}\right)^4$
Radius ratio
$\frac{R}{R_{\odot}} = \sqrt{\frac{L}{L_{\odot}}}\left(\frac{T_{\odot}}{T}\right)^2$

Physics

Course Overview

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Space, Time and Motion

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Kinematics

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Forces and momentum

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Work, energy and power

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The Particulate Nature of Matter

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Thermal energy transfers

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Greenhouse effect

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Gas laws

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Current and circuits

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Wave Behaviour

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Simple harmonic motion

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Wave model

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Wave phenomena

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Standing waves and resonance

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Doppler effect

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Fields

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Gravitational fields

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Electric and magnetic fields

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Motion in electromagnetic fields

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Nuclear and Quantum Physics

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Structure of the atom

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Radioactive decay

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Fission

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Fusion and stars

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