H2 Physics in A-Level - The Complete Definitions and Formulae Guide

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13 Aug 2025, 00:00 Z

Measurement and Uncertainty
Kinematics
Forces, Moments and Equilibrium
Fluids
Newton's Laws, Momentum, Work-Energy-Power
Circular Motion
Gravitation and Orbits
Oscillations and SHM
Waves and Superposition
Resolution and Standing Waves
Thermal Physics and Kinetic Theory
Electric Current, Circuits and Materials
Electric Fields and Potential
Magnetism and Electromagnetic Induction
Quantum and Atomic Physics
Nuclear Physics and Radioactivity
References

1 Measurement and Uncertainty

SI base quantities: mass (kg), length (m), time (s), current (A), temperature (K), amount (mol), luminous intensity (cd).
Derived units: formed by products or quotients of base units.

Prefixes: kilo k, mega M, giga G, milli m, micro μ, nano n, pico p.

Accuracy: closeness to true value.
Precision: tight scatter in repeats (small random error).

Random error: causes scatter about the mean, reduced by averaging.
Systematic error: shifts all readings up or down, not reduced by averaging; remove cause.

Uncertainties: absolute \( \Delta x \), fractional \( \Delta x/x \), percentage \( (\Delta x/x)\times 100% \).

Propagation

Sums or differences: \( \Delta y \approx \Delta a + \Delta b \) if \( y = a \pm b \).
Products or quotients: \( \Delta y / y \approx \Delta a / a + \Delta b / b \) if \( y = ab \) or \( y = a/b \).
Powers: \( \Delta y / y \approx |p|\space \Delta a / a \) if \( y = a^p \).

Exam check: Define with quantities, not units. For speed, write "distance per unit time", not "distance per second".

2 Kinematics

Distance: total path length.
Displacement: directed distance from start to end.
Speed: rate of change of distance.
Velocity \( \mathbf{v} \): rate of change of displacement.
Acceleration \( \mathbf{a} \): rate of change of velocity.

Uniform-acceleration relations (straight line): \( v = u + a\space t \), \( s = u\space t + 0.5\space a\space t^2 \), \( v^2 = u^2 + 2 a s \), \( s = 0.5\space (u + v)\space t \).

Graphs:

gradient of \( x-t \) gives \( v \)
gradient of \( v-t \) gives \( a \)
area under \( v-t \) gives displacement
area under \( a-t \) gives \( \Delta v \)

3 Forces, Moments and Equilibrium

Hooke's law (small extension): \( F = k x \).
Elastic potential energy: \( E_{el} = 0.5\space k x^2 \).

Friction: static \( F_s \le \mu_s N \), kinetic \( F_k = \mu_k N \).
Moment about a point: \( \tau = r F \sin\theta \).
Couple: equal, opposite, parallel forces separated by distance \( d \); torque \( \tau = F d \).

Equilibrium (rigid body): \( \sum \mathbf{F} = \mathbf{0} \) and \( \sum \tau = 0 \).
Three-force equilibrium: lines of action intersect at a point.
Centre of gravity: single point through which weight acts.

4 Fluids

Pressure: \( P = F/A \).
Hydrostatic pressure (incompressible, at rest): \( p = \rho g h \).
Upthrust: \( U = \rho g V_{displaced} \).
Flotation: floating body has \( U = W \).

5 Newton's Laws, Momentum, Work-Energy-Power

Newton 1: a body stays at rest or moves uniformly unless a resultant force acts.
Newton 2: \( \sum \mathbf{F} = m \mathbf{a} \).
Newton 3: forces between two bodies are equal, opposite, collinear, and act on different bodies.

Momentum: \( \mathbf{p} = m \mathbf{v} \).
Impulse: \( \mathbf{J} = \int \mathbf{F}\space dt = \Delta \mathbf{p} \) (area under \( F-t \)).

Collisions in isolation: momentum conserved.

Elastic: total KE conserved, relative speed of approach equals separation.
Inelastic: KE not conserved (perfectly inelastic if bodies stick).

Work: \( W = \mathbf{F}\cdot\mathbf{s} = F s \cos\theta \).
Kinetic energy: \( E_k = 0.5\space m v^2 \).
GPE near Earth: \( \Delta E_g = m g\space \Delta h \).
Power: \( P = dW/dt = F v \).
Efficiency: useful output over input.

Weight: \( W = m g \). Apparent weightlessness in free fall: normal reaction is zero.

6 Circular Motion

Angular displacement \( \theta \) (radians), arc length \( s = r\theta \).
Period and frequency: \( T = 1/f \).
Angular speed: \( \omega = 2\pi f = 2\pi/T \).
Tangential speed: \( v = \omega r \).

Centripetal acceleration: \( a_c = v^2/r = \omega^2 r \).
Centripetal force: \( F_c = m v^2/r \).

Why speed can stay constant in a horizontal circle: \( \mathbf{F}_c \perp \mathbf{v} \) so no work, KE constant.

7 Gravitation and Orbits

Newton's law of gravitation: \( F = G m_1 m_2 / r^2 \) (attractive).
Field strength: \( g = GM / r^2 \) directed inward.
Potential: \( \phi = - GM / r \), GPE: \( U = m\space \phi = - GM m / r \).

Circular orbit: \( v^2 = GM / r \), and \( T^2 = (4\pi^2/GM)\space r^3 \).
Geostationary: period 24 h, equatorial plane, west-to-east, fixed \( r \) and \( v \).

Equator vs poles: at equator, part of \( mg \) provides \( m \omega_\oplus^2 R \), so normal reaction is reduced.

8 Oscillations and SHM

Displacement \( x \), amplitude \( A \), period \( T \), frequency \( f \), angular frequency \( \omega = 2\pi f \), phase \( \phi \).

SHM definition: \( a = - \omega^2 x \).
General solution: \( x = A \cos(\omega t + \phi) \).
Energies: \( E_k = 0.5\space m \omega^2 (A^2 - x^2) \), \( E_p = 0.5\space m \omega^2 x^2 \), total \( = 0.5\space m \omega^2 A^2 \).

Special cases:

Mass-spring: \( \omega = \sqrt{k/m} \).
Simple pendulum (small angle): \( \omega = \sqrt{g/L} \).

Damping: light (oscillatory decay), critical (fastest non-oscillatory return), heavy (slow, non-oscillatory).
Forced oscillations and resonance: steady-state at driving frequency; peak amplitude at resonance; damping lowers and broadens the peak, resonant frequency shifts slightly lower.

9 Waves and Superposition

Progressive wave: transports energy via oscillations.
Transverse: oscillations perpendicular to propagation.
Longitudinal: oscillations parallel to propagation.

Harmonic form: \( y(x,t) = A \sin(k x - \omega t + \phi) \) with \( k = 2\pi / \lambda \), \( \omega = 2\pi f \).
Speed: \( v = f \lambda = \omega / k \).
Intensity: power per area; for the same medium \( I \propto A^2 \).

Polarisation: restricts transverse oscillations to one plane. Malus' law: \( I = I_0 \cos^2 \theta \).

Diffraction: spreading when aperture is comparable to \( \lambda \).
Superposition: resultant displacement is the vector sum.
Coherence: constant phase difference.
Interference: constructive if path difference is \( m\lambda \), destructive if \( (m + 0.5)\lambda \).

Young double-slit: fringe spacing \( x = \lambda D / a \) (slit separation \( a \), screen distance \( D \)).
Diffraction grating: maxima satisfy \( d \sin\theta = m \lambda \).

10 Resolution and Standing Waves

Rayleigh criterion: two point images are just resolved when one central maximum coincides with the other's first minimum. Approximate angular resolution \( \theta \approx 1.22\space \lambda / D \) for a circular aperture of diameter \( D \).

Standing wave: two identical counter-propagating waves form fixed nodes and antinodes, with no net energy transport.

Nodes: zero displacement. Antinodes: maximum amplitude.
Strings (fixed-fixed): \( L = n\lambda/2 \).
Air columns: open-open \( L = n\lambda/2 \); closed-open \( L = (2n - 1)\lambda/4 \).
Sound: pressure variation is max at displacement nodes, min at displacement antinodes.

11 Thermal Physics and Kinetic Theory

Internal energy \( U \): microscopic KE plus PE; state function.
Thermal equilibrium: no net heat flow.
Mole: Avogadro number of particles, about 6.02 x 10^23.

Ideal gas: \( pV = nRT = N k T \).
Mean KE per molecule: \( E_{k,avg} = 1.5\space k T \).

First law (this sign convention): \( \Delta U = Q + W_{on} \).
Processes: isochoric (V constant), isobaric (p constant), isothermal (T constant), adiabatic (Q = 0).

Specific heat capacity: energy to raise unit mass by 1 K (no phase change).
Latent heats: fusion (solid to liquid), vaporisation (liquid to gas).
Boiling: temperature constant because heat increases PE.
Evaporation cooling: fastest molecules escape, average KE drops.

Why \( L_v > L_f \): vaporisation involves larger PE increase and expansion work.

12 Electric Current, Circuits and Materials

Charge and current: \( I = dQ/dt \).
Microscopic current: \( I = n A v_d q \).

Emf: energy gained per unit charge from a source around a complete circuit.
Potential difference: energy converted per unit charge between two points.

Resistance: \( R = V/I \). Resistivity: \( R = \rho \ell / A \).
Power: \( P = V I = V^2 / R = I^2 R \).

I-V characteristics:

Metallic conductor: approx linear at constant temperature.
Filament lamp: resistance increases with temperature.
Semiconductor diode: mainly forward conduction, reverse blocking.
NTC thermistor: resistance decreases as temperature rises.
LDR: resistance decreases with light intensity.

Internal resistance \( r \): terminal pd \( V = \varepsilon - I r \); with load \( R \): \( I = \varepsilon / (R + r) \).

Series and parallel: \( R_s = R_1 + R_2 + \dots \); \( 1/R_p = 1/R_1 + 1/R_2 + \dots \).
Potential divider (two resistors): \( V_{out} = V_{in}\space R_2 / (R_1 + R_2) \).

Measuring \( \varepsilon \): potentiometer preferred to voltmeter (zero current draw avoids terminal drop).

13 Electric Fields and Potential

Coulomb's law (point charges): \( F = (1/(4\pi\varepsilon_0))\space Q_1 Q_2 / r^2 \).
Field strength: \( \mathbf{E} = \mathbf{F}/q \); for point charge \( E = (1/(4\pi\varepsilon_0))\space Q / r^2 \) radially.
Potential: \( V = W/q \); for point charge \( V = (1/(4\pi\varepsilon_0))\space Q / r \).
Relation: \( \mathbf{E} = - \nabla V \); uniform field \( E = V/d \).

Conductors in electrostatic equilibrium: \( E = 0 \) inside, charges on surface.
Equipotentials: surfaces of constant \( V \), everywhere perpendicular to \( \mathbf{E} \).
Potential energy: \( U = q V \).
Electron-volt: 1 eV = 1.602 x 10^-19 J.

14 Magnetism and Electromagnetic Induction

Magnetic flux density \( B \) (tesla).
Force on current: \( \mathbf{F} = I \boldsymbol{\ell} \times \mathbf{B} \) so \( F = B I \ell \sin\theta \).
Force on charge: \( \mathbf{F} = q \mathbf{v} \times \mathbf{B} \) so \( F = B q v \sin\theta \).

Uniform \( B \), perpendicular entry: circular motion with \( r = m v / (q B) \), cyclotron frequency \( \omega = q B / m \).

Velocity selector (crossed \( E \) and \( B \)): \( v = E/B \).

Magnetic flux: \( \Phi = B A \cos\theta \); flux linkage: \( N \Phi \).
Faraday-Lenz: \( \varepsilon = - N\space d\Phi/dt \) (minus sign indicates opposition).
Motional emf: \( \varepsilon = B \ell v \) when \( \mathbf{v} \perp \mathbf{B} \).

Eddy currents: circulating currents in bulk conductors cause heating; laminations reduce losses.

AC (sinusoidal): \( I_{rms} = I_0 / \sqrt{2} \), \( V_{rms} = V_0 / \sqrt{2} \); average power \( P = V_{rms} I_{rms} \) for a resistive load.

Transformers (ideal): \( V_p / V_s = N_p / N_s \), \( I_p / I_s = N_s / N_p \), \( P_p = P_s \). Requires AC to sustain changing flux.

15 Quantum and Atomic Physics

Photoelectric effect: emission of electrons when light frequency is sufficiently high.
Observations: threshold frequency \( f_0 \); intensity controls current, not \( E_{k,max} \); emission is prompt; \( E_{k,max} \) increases with \( f \).

Einstein's equation: \( h f = \Phi + E_{k,max} = \Phi + e V_s \); threshold \( f_0 = \Phi / h \).

Wave-particle duality: de Broglie wavelength \( \lambda = h/p = h/(m v) \).
Uncertainty principle: \( \Delta x\space \Delta p \ge \hbar / 2 \), \( \Delta E\space \Delta t \ge \hbar / 2 \).

Atomic energy levels: discrete bound energies; excitation by inelastic collisions or photon absorption; emission/absorption spectra from transitions.
X-rays: characteristic lines from inner-shell transitions, plus continuous bremsstrahlung spectrum; minimum wavelength when one electron loses all KE in a single event.

Semiconductors and lasers (high level): intrinsic vs extrinsic, p-n junctions (diodes, LEDs, photodiodes); lasers need population inversion, gain medium, pumping, optical cavity.

16 Nuclear Physics and Radioactivity

Isotopes: same proton number, different neutron number.
Nucleon: proton or neutron. Nuclide: specified by \( Z \) and \( N \).

Binding energy \( E_b \): energy to separate nucleus into nucleons; mass defect \( \Delta m \): \( E_b = \Delta m\space c^2 \).
Stability: larger \( E_b/A \) usually means more stable.
Energy release in fission and fusion: products lie at higher \( E_b/A \).

Radioactivity: spontaneous and random decay; emissions \( \alpha \), \( \beta \), \( \gamma \).

\( \alpha \): He nucleus, strongly ionising, weakly penetrating.
\( \beta \): electron or positron, moderate.
\( \gamma \): photon, weakly ionising, strongly penetrating.

Decay law: \( N = N_0 \exp(-\lambda t) \); activity \( A = \lambda N \); half-life \( t_{1/2} = (\ln 2)/\lambda \).

Rutherford scattering inference: atom mostly empty space, small dense positive nucleus.

Biological effects: direct DNA damage and indirect radical formation; background radiation is all non-sample sources.