Density is mass per unit volume: rho = m / V, measured in kg per cubic metre.
Hooke's Law states that force is proportional to extension: F = k x, as long as the limit of proportionality is not exceeded.
The spring constant k is measured in newtons per metre (N/m).
Beyond the elastic limit the material no longer returns to its original shape when unloaded.
Stress = force / cross-sectional area, units pascals (Pa) or N/m^2.
Strain = extension / original length, and strain has no units (it is a ratio).
The Young modulus E = stress / strain, also measured in pascals.
On a stress-strain graph, the gradient of the straight-line (elastic) region gives the Young modulus.
The elastic limit is the point beyond which the material shows plastic deformation and will not return to its original length.
The UTS (ultimate tensile stress) is the maximum stress a material can withstand before breaking.
Brittle materials (like glass) snap suddenly with little plastic deformation; ductile materials (like copper) stretch a lot before breaking.
Elastic potential energy = area under a force-extension graph.
For a material obeying Hooke's Law: E_el = 0.5 F x = 0.5 k x^2.
If a material is stretched beyond its elastic limit, the loading and unloading curves differ (hysteresis loop) — the area between the curves is the energy dissipated as heat.
Specific heat capacity c: energy to raise 1 kg of a substance by 1 K. Equation: Q = m c (delta)T, units J/(kg K).
Specific latent heat L: energy to change the state of 1 kg of a substance with no temperature change. Equation: Q = m L, units J/kg.
Specific latent heat of fusion applies to melting/freezing; specific latent heat of vaporisation applies to boiling/condensing — vaporisation is always larger than fusion for the same substance because more bonds must be broken.
Internal energy is the sum of the random distribution of kinetic and potential energies of the particles in a system; it increases when temperature rises OR when a substance changes state (even though temperature stays constant during a phase change).
Current I is the rate of flow of charge: I = Q/t, measured in amperes (A). Charge Q is measured in coulombs (C), where 1 C = 1 A flowing for 1 s.
Potential difference (p.d.) is the energy transferred per unit charge: V = W/Q, measured in volts (V), where 1 V = 1 joule per coulomb.
Electromotive force (e.m.f.) is the energy given to each coulomb of charge by a source (like a cell), also in volts. E.m.f. and p.d. are NOT the same thing - e.m.f. includes energy 'lost' inside the source due to internal resistance.
Resistance R = V/I, measured in ohms (Ω). Ohm's law states current through a conductor is directly proportional to p.d. across it, provided temperature stays constant - this only applies to ohmic conductors (like a resistor at constant temperature).
For a filament lamp, resistance increases as it heats up (curve flattens on an I-V graph). For a diode, current only flows one way past the threshold voltage (about 0.6 V for silicon).
Resistivity: R = ρL/A, where ρ (rho) is resistivity in Ω m, L is length, A is cross-sectional area. Resistivity depends on material and temperature, not on the shape of the sample - do not confuse ρ with R.
Electrical power P = VI = I²R = V²/R. Energy transferred W = VIt = Pt, measured in joules.
Kirchhoff's first law: current into a junction equals current out (conservation of charge). Kirchhoff's second law: the sum of e.m.f.s around a closed loop equals the sum of p.d.s (conservation of energy).
Series circuits: current is the same everywhere; total resistance R = R1 + R2 + ...; p.d.s add up to the source e.m.f.
Parallel circuits: p.d. is the same across each branch; total resistance found from 1/R = 1/R1 + 1/R2 + ...; total current is the sum of branch currents.
Every real cell has internal resistance r. E.m.f. ε = I(R + r), so terminal p.d. V = ε - Ir. On short circuit (R = 0), current is at its maximum, limited only by r.
A potential divider splits voltage in proportion to resistance: Vout = V x (R2/(R1+R2)). LDRs (resistance falls as light increases) and thermistors (resistance falls as temperature increases) are common sensor components used in potential dividers.
A wave transfers energy without transferring matter. Transverse waves (light, water, all EM waves) oscillate perpendicular to travel direction; longitudinal waves (sound) oscillate parallel to it.
Path difference in whole wavelengths (nlambda) gives constructive interference (in phase); path difference of (n + 1/2)lambda gives destructive interference (antiphase). Superposition is the addition of displacements when two waves meet.
Formed by two coherent waves of the same frequency travelling in opposite directions, usually a wave and its reflection. Nodes = zero amplitude, always; antinodes = maximum amplitude. Distance between adjacent nodes = lambda/2. Unlike progressive waves, no energy is transferred along a standing wave and all points between nodes are in phase.
n = c / v (c = speed of light in vacuum, 3.00 x 10^8 m/s). Snell's law: n1 sin(theta1) = n2 sin(theta2). Critical angle: sin(thetaC) = n2/n1 (going from dense to less dense). Total internal reflection happens only when going from a denser to a less dense medium AND the angle of incidence exceeds the critical angle — both conditions are needed, a common mistake is forgetting the direction requirement.
nlambda = d sin(theta), where d = 1/(lines per metre). More lines per mm gives wider-spaced maxima. Common error: forgetting to convert 'lines per mm' into d in metres before substituting.
fringe spacing w = lambda D / s (D = slit-to-screen distance, s = slit separation). Requires coherent, monochromatic light. This confirms light's wave nature via interference.
Only transverse waves can be polarised — this is definitive proof light is transverse, since sound (longitudinal) cannot be polarised. Malus's law: I = I0 cos^2(theta).
String fixed both ends: fundamental has a node at each end, one antinode in the middle, length L = lambda/2. Closed pipe (one end closed): only odd harmonics, L = lambda/4 for fundamental. Open pipe: L = lambda/2 for fundamental, same as a string.
A gravitational field is the region around a mass where another mass feels a force. Field strength g is force per unit mass, measured in N/kg.
An electric field is the region around a charge where another charge feels a force. Field strength E is force per unit positive charge, in N/C or V/m.
Magnetic fields exert forces only on moving charges or current-carrying conductors, never on stationary charges.
All three follow similar mathematical patterns but differ in sign, source, and what feels the force. Always check whether a question wants field strength (vector) or potential/potential energy (scalar), and whether the field is radial (point source) or uniform (parallel plates, inside a solenoid).
The nucleus contains protons and neutrons (nucleons), with electrons in shells around it.
Exam tip: always check conservation of charge, baryon number and lepton number when identifying an unknown particle in an equation — it's the fastest way to the answer.