Quick Formula Index¶
Every formula on the Physics 11–12 (2025) HSC Data Sheet, reorganised by topic with each entry expandable for what the symbols mean and when to reach for it. This isn't a replacement for the topic pages — it's a fast lookup for revision, once you already understand the concept. For the full explanation and worked examples, follow the "See:" link on each entry where one exists.
Notation matches the data sheet exactly (checked against the actual document, not textbook convention) — see Resources for the source PDF.
Covers both years
This data sheet is shared across Year 11 and Year 12 — some formulas below (circular motion, gravitation/orbits, electromagnetic induction, quantum/relativity/nuclear) are Year 12 content and don't have a full topic page on this site yet. They're included here anyway since the data sheet doesn't separate them, and it's useful to see the whole picture early.
Constants¶
| Constant | Symbol | Value |
|---|---|---|
| Charge on electron | \(q_e\) | \(-1.602\times10^{-19}\ \text{C}\) |
| Mass of electron | \(m_e\) | \(9.109\times10^{-31}\ \text{kg}\) |
| Mass of neutron | \(m_n\) | \(1.675\times10^{-27}\ \text{kg}\) |
| Mass of proton | \(m_p\) | \(1.673\times10^{-27}\ \text{kg}\) |
| Speed of sound in air | — | \(340\ \text{m s}^{-1}\) |
| Earth's gravitational acceleration | \(g\) | \(9.8\ \text{m s}^{-2}\) |
| Speed of light | \(c\) | \(3.00\times10^8\ \text{m s}^{-1}\) |
| Electric permittivity constant | \(\varepsilon_0\) | \(8.854\times10^{-12}\ \text{A}^2\text{s}^4\text{kg}^{-1}\text{m}^{-3}\) |
| Magnetic permeability constant | \(\mu_0\) | \(4\pi\times10^{-7}\ \text{N A}^{-2}\) |
| Universal gravitational constant | \(G\) | \(6.67\times10^{-11}\ \text{N m}^2\text{kg}^{-2}\) |
| Mass of Earth | \(M_E\) | \(5.97\times10^{24}\ \text{kg}\) |
| Radius of Earth | \(r_E\) | \(6.371\times10^6\ \text{m}\) |
| Planck constant | \(h\) | \(6.626\times10^{-34}\ \text{J s}\) |
| Rydberg constant (hydrogen) | \(R\) | \(1.097\times10^7\ \text{m}^{-1}\) |
| Atomic mass unit | \(u\) | \(1.661\times10^{-27}\ \text{kg} = 931.5\ \text{MeV}/c^2\) |
| Electron volt | \(1\ \text{eV}\) | \(1.602\times10^{-19}\ \text{J}\) |
| Wien's displacement constant | \(b\) | \(2.898\times10^{-3}\ \text{m K}\) |
Motion, Forces and Gravity¶
Kinematics¶
Final velocity (vector form)
Symbols: \(\vec{v}\) — final velocity; \(\vec{u}\) — initial velocity; \(\vec{a}\) — acceleration; \(t\) — time.
When to use it: Constant acceleration only. Use when you know initial velocity, acceleration and time, and need final velocity (or rearrange for any other variable).
See: Motion Relationships
Displacement (vector form)
Symbols: \(\vec{s}\) — displacement; \(\vec{u}\) — initial velocity; \(\vec{a}\) — acceleration; \(t\) — time.
When to use it: Constant acceleration only. Use when final velocity isn't given (or needed) — this equation skips it entirely.
See: Motion Relationships
Velocity–displacement relation
Symbols: \(v\) — final velocity; \(u\) — initial velocity; \(a\) — acceleration; \(s\) — displacement.
When to use it: Constant acceleration only. Use when time isn't given (or needed) — the only SUVAT equation without \(t\) in it.
See: Motion Relationships
Average velocity
Symbols: \(\vec{v}_{av}\) — average velocity; \(\Delta \vec{s}\) — change in displacement; \(\Delta t\) — time interval.
When to use it: Works for any motion, not just constant acceleration — this is the general definition, not a SUVAT shortcut.
See: Quantities of Motion
Acceleration (general definition)
Symbols: \(\vec{a}\) — acceleration; \(\Delta \vec{v}\) — change in velocity; \(\Delta t\) — time interval.
When to use it: Works for any motion, including non-uniform acceleration — this is the definition, not a constant-acceleration-only shortcut.
Relative velocity
Symbols: \(\vec{v}_{AB}\) — velocity of A relative to B; \(\vec{v}_A\), \(\vec{v}_B\) — velocities of A and B (relative to the same fixed reference, e.g. the ground).
When to use it: Whenever a question asks how one moving object appears to move from the point of view of another moving object, not a stationary observer.
See: Motion Relationships
Dynamics¶
Newton's second law
Symbols: \(\vec{F}_{net}\) — net (unbalanced) force; \(m\) — mass; \(\vec{a}\) — acceleration.
When to use it: Whenever you need to connect force and acceleration. Remember it's the net force — add up every force acting on the object first.
See: Forces and Motion
Weight force
Symbols: \(\vec{F}_w\) — weight force; \(m\) — mass; \(\vec{g}\) — gravitational acceleration (\(9.8\ \text{m s}^{-2}\) near Earth's surface).
When to use it: To find the force of gravity on an object. Weight is a force (N); mass is not.
See: Forces and Motion
Resolving a force into components
Symbols: \(F\) — force magnitude; \(\theta\) — angle from the reference axis; \(F_x\), \(F_y\) — components along each axis.
When to use it: Any time a force acts at an angle and you need to analyse motion along a specific direction (horizontal/vertical, or along/perpendicular to an incline).
See: Forces and Motion
Weight components on an incline
Symbols: \(F_\perp\) — component of weight perpendicular to the incline; \(F_{||}\) — component parallel to the incline; \(\theta\) — incline angle.
When to use it: Specifically for inclined-plane problems — \(F_\perp\) balances the normal force, \(F_{||}\) drives motion down the slope.
Friction
Symbols: \(f_{friction}\) — friction force; \(\mu\) — coefficient of friction (static or kinetic); \(F_N\) — normal force.
When to use it: Whenever surfaces are in contact and you need the maximum static friction, or the kinetic friction of a sliding object.
See: Forces and Motion
Work, Energy and Power¶
Work done by a force
Symbols: \(W\) — work done; \(F_{||}\) — component of force along the displacement; \(F\) — force magnitude; \(s\) — displacement; \(\theta\) — angle between force and displacement.
When to use it: Only the force component along the direction of motion does work — a force perpendicular to displacement does zero work.
See: Momentum and Energy
Power
Symbols: \(P\) — power; \(W\) — work done; \(\Delta E\) — energy transferred; \(\Delta t\) — time taken.
When to use it: Whenever you need the rate of doing work or transferring energy, not just the total amount.
Kinetic energy
Symbols: \(KE\) — kinetic energy; \(m\) — mass; \(v\) — speed.
When to use it: Energy of motion. Combine with gravitational PE for conservation-of-energy problems.
See: Momentum and Energy
Change in gravitational potential energy
Symbols: \(\Delta U\) — change in gravitational PE; \(m\) — mass; \(g\) — gravitational acceleration; \(\Delta h\) — change in height.
When to use it: Near Earth's surface only (uniform field). For orbital-scale distances, use the \(U=-\dfrac{GMm}{r}\) form instead (Gravitation section, below).
See: Momentum and Energy
Work–energy theorem (general)
Symbols: \(W\) — work done; \(\Delta U\) — change in potential energy.
When to use it: Work done against a conservative force (like gravity) converts directly to stored potential energy.
See: Momentum and Energy
Momentum and Collisions¶
Momentum
Symbols: \(\vec{p}\) — momentum; \(m\) — mass; \(\vec{v}\) — velocity.
When to use it: Whenever a problem involves collisions, explosions, or impulse.
See: Momentum and Energy
Impulse–momentum theorem
Symbols: \(\Delta \vec{p}\) — change in momentum; \(\vec{F}_{net}\) — net force; \(\Delta t\) — time interval over which it acts.
When to use it: Connects force and time to a change in momentum — useful when force isn't constant but you know (or can find) the total time it acts.
Conservation of momentum
Symbols: Sum of (mass × velocity) for every object in the system, before and after.
When to use it: Any collision or explosion in an isolated system — this holds true regardless of whether the collision is elastic or inelastic.
See: Momentum and Energy
Kinetic energy conservation (elastic collisions only)
Symbols: Sum of \(\tfrac{1}{2}mv^2\) for every object, before and after.
When to use it: Only holds for elastic collisions. Use it alongside momentum conservation to check whether a collision is elastic, or to solve for an unknown velocity if you're told it is.
See: Momentum and Energy
Circular Motion¶
Orbital/tangential speed
Symbols: \(v\) — speed; \(r\) — radius of the circular path; \(T\) — period (time for one full revolution).
When to use it: Speed of an object moving in a circle, from the circle's radius and how long one lap takes.
See: Circular Motion
Centripetal acceleration
Symbols: \(a_c\) — centripetal acceleration (directed toward the centre); \(v\) — speed; \(r\) — radius.
When to use it: Any object moving in a circle at constant speed has this acceleration, even though its speed isn't changing — only its direction is.
See: Circular Motion
Centripetal force
Symbols: \(F_c\) — centripetal force (net force toward the centre); \(m\) — mass; \(v\) — speed; \(r\) — radius.
When to use it: Whatever is actually supplying the centre-seeking force (tension, gravity, friction, normal force) must add up to this value for the object to maintain circular motion.
See: Circular Motion
Torque
Symbols: \(\tau\) — torque; \(r\) — distance from the pivot to where the force is applied; \(F\) — force magnitude; \(\theta\) — angle between the force and the lever arm.
When to use it: Rotational equivalent of force — how effectively a force turns something around a pivot.
Gravitation and Orbits¶
Newton's law of gravitation
Symbols: \(F\) — gravitational force; \(G\) — universal gravitational constant; \(M\), \(m\) — the two masses; \(r\) — distance between their centres.
When to use it: Force between any two masses — this is the general form; \(F_w=mg\) is just this equation evaluated at Earth's surface.
Gravitational field strength
Symbols: \(g\) — gravitational field strength (acceleration due to gravity); \(G\) — universal gravitational constant; \(M\) — mass of the body creating the field; \(r\) — distance from its centre.
When to use it: Finding "local gravity" at any distance from a mass — not just Earth's surface value of \(9.8\ \text{m s}^{-2}\).
Gravitational potential energy
Symbols: \(U\) — gravitational PE; \(G\) — universal gravitational constant; \(M\), \(m\) — the two masses; \(r\) — separation.
When to use it: For orbital-scale distances, where \(\Delta U = mg\Delta h\) breaks down (that formula assumes a uniform field, which only holds near a planet's surface). Note the negative sign — PE is defined as zero at infinite separation.
See: Orbital Energy
Total orbital energy
Symbols: \(U+KE\) — total mechanical energy of an orbit; \(G\), \(M\), \(m\), \(r\) — as above.
When to use it: For a stable circular orbit specifically — this combines gravitational PE and orbital KE into one expression.
See: Orbital Energy
Kepler's third law
Symbols: \(r\) — orbital radius; \(T\) — orbital period; \(G\) — universal gravitational constant; \(M\) — mass being orbited.
When to use it: Relating orbital radius to orbital period for any object orbiting the same central mass \(M\) — the ratio \(r^3/T^2\) is the same for every satellite of that mass.
Circular orbital velocity
Symbols: \(v_{orb}\) — speed needed for a stable circular orbit; \(G\) — universal gravitational constant; \(M\) — mass being orbited; \(r\) — orbital radius.
When to use it: The one speed that keeps an object in a circular orbit at a given radius — independent of the orbiting object's own mass.
Escape velocity
Symbols: \(v_{esc}\) — minimum speed to escape the gravitational field entirely; \(G\) — universal gravitational constant; \(M\) — mass being escaped; \(r\) — starting distance from its centre.
When to use it: Derived from conservation of energy — the speed at which \(KE\) exactly cancels the (negative) gravitational \(U\), so total energy is zero at launch. Always \(\sqrt{2}\) times the circular orbital velocity at the same radius.
See: Orbital Energy
Waves¶
Wave equation
Symbols: \(v\) — wave speed; \(f\) — frequency; \(\lambda\) — wavelength.
When to use it: Connects any two of speed, frequency and wavelength — the single most-used wave formula.
See: Wave Properties
Frequency–period relation
Symbols: \(f\) — frequency; \(T\) — period.
When to use it: Converting between frequency and period — they're reciprocals of each other.
See: Wave Properties
Refractive index
Symbols: \(n_x\) — refractive index of medium \(x\); \(c\) — speed of light in vacuum; \(v_x\) — speed of light in medium \(x\).
When to use it: Whenever a medium's optical density needs quantifying — higher \(n\) means light travels slower in that medium.
See: Wave Behaviours
Snell's law
Symbols: \(n_1\), \(n_2\) — refractive indices either side of the boundary; \(\theta_1\), \(\theta_2\) — angles of incidence and refraction, measured from the normal.
When to use it: Any time light crosses a boundary between two media at an angle.
See: Wave Behaviours
Critical angle
Symbols: \(\theta_c\) — critical angle; \(n_1\) — refractive index of the denser medium (light starts here); \(n_2\) — refractive index of the less dense medium.
When to use it: Finding the angle beyond which total internal reflection occurs, going from a denser to a less dense medium.
See: Wave Behaviours
Diffraction grating / double-slit interference
Symbols: \(d\) — slit spacing; \(\theta\) — angle to a bright fringe; \(m\) — order (integer: 0, 1, 2, ...); \(\lambda\) — wavelength; \(y\) — fringe position on the screen; \(L\) — distance to the screen.
When to use it: Finding the position or angle of bright (constructive interference) fringes in a diffraction or double-slit pattern.
See: Wave Behaviours
Polarisation intensity (Malus's law)
Symbols: \(I\) — transmitted intensity; \(I_{max}\) — maximum (unpolarised input) intensity; \(\theta\) — angle between the light's polarisation and the polariser's axis.
When to use it: Light passing through a polarising filter at an angle to its own polarisation direction.
Inverse square law for intensity
Symbols: \(I\) — intensity; \(r\) — distance from the source. Subscripts 1, 2 refer to two different distances from the same source.
When to use it: Comparing intensity at two different distances from the same point source (light or sound), without needing to know the source's total power.
See: Light and Sound
Doppler effect
Symbols: \(f'\) — observed frequency; \(f\) — source (emitted) frequency; \(v_{wave}\) — wave speed in the medium; \(v_{observer}\), \(v_{source}\) — velocities of observer/source (positive when moving toward the other party).
When to use it: A source and/or observer moving relative to each other and the medium — frequency appears to shift.
See: Wave Behaviours
Photon energy
Symbols: \(E\) — photon energy; \(h\) — Planck constant; \(f\) — frequency.
When to use it: Converting between a light wave's frequency and the energy of a single photon of that light — the bridge between wave and particle descriptions of light.
Electricity and Magnetism¶
Electrostatics¶
Uniform field between parallel plates
Symbols: \(E\) — electric field strength; \(V\) — potential difference between the plates; \(d\) — plate separation.
When to use it: Specifically for a uniform field between two charged parallel plates — not for a point charge's field, which isn't uniform.
See: Electrostatics
Force on a charge in a field
Symbols: \(\vec{F}\) — force on the charge; \(q\) — charge; \(\vec{E}\) — electric field strength.
When to use it: Finding the force on any charge placed in a known electric field, point-charge or uniform.
See: Electrostatics
Potential difference
Symbols: \(V\) — potential difference; \(\Delta U\) — change in electric potential energy; \(q\) — charge.
When to use it: The definition connecting potential difference to energy per unit charge — the electrical analogue of height in gravitational PE.
See: Electrostatics
Work done by a potential difference
Symbols: \(W\) — work done; \(q\) — charge; \(V\) — potential difference; \(\Delta KE\) — change in kinetic energy.
When to use it: A charge accelerated through a potential difference — e.g. finding the energy or speed gained by an electron in an electric field.
See: Electrostatics
Work done crossing a uniform field
Symbols: \(W\) — work done; \(q\) — charge; \(E\) — field strength; \(d\) — distance moved across the field.
When to use it: A charge moving a known distance through a uniform field (e.g. between parallel plates) — an alternative route to the same work as \(W=qV\).
See: Electrostatics
Coulomb's law
Symbols: \(F\) — force between the charges; \(\varepsilon_0\) — electric permittivity constant; \(q_1\), \(q_2\) — the two charges; \(r\) — separation.
When to use it: Force between two point charges — same inverse-square shape as gravity, but can be attractive or repulsive depending on the signs of \(q_1\), \(q_2\).
See: Electrostatics
Electric field around a point charge
Symbols: \(E\) — field strength; \(\varepsilon_0\) — electric permittivity constant; \(q\) — the source charge; \(r\) — distance from it.
When to use it: Field strength at a distance from a single point charge, before considering what force it would exert on another charge placed there.
See: Electrostatics
Electric Circuits¶
Current
Symbols: \(I\) — current; \(q\) — charge; \(t\) — time.
When to use it: The definition of current — charge flow per unit time.
See: Electric Circuits
Ohm's law
Symbols: \(V\) — voltage (potential difference); \(I\) — current; \(R\) — resistance.
When to use it: Ohmic conductors only — non-ohmic components (like a filament globe) don't have a fixed \(R\), so read values off a \(V\)–\(I\) graph instead.
See: Electric Circuits
Electrical power
Symbols: \(P\) — power; \(V\) — voltage; \(I\) — current; \(R\) — resistance.
When to use it: Two equivalent forms — pick whichever matches the variables you already have (use \(V=IR\) to convert between them if needed).
See: Electric Circuits
Series circuits
Symbols: Voltage/resistance of each component in turn, summed.
When to use it: Components in a single loop, sharing the same current. Voltage divides across them; resistance adds directly.
See: Electric Circuits
Parallel circuits
Symbols: Resistance/current of each parallel branch.
When to use it: Components across separate branches, sharing the same voltage. Current divides between them; resistance combines via reciprocals (always less than the smallest individual resistor).
See: Electric Circuits
Magnetism¶
Field strength around a current-carrying wire
Symbols: \(B\) — magnetic field strength; \(\mu_0\) — magnetic permeability constant; \(I\) — current; \(r\) — distance from the wire.
When to use it: Field strength at a distance from a single straight current-carrying wire. Direction from the right-hand grip rule.
See: Magnetism
Field strength inside a solenoid
Symbols: \(B\) — field strength inside the solenoid; \(\mu_0\) — magnetic permeability constant; \(N\) — number of turns; \(I\) — current; \(L\) — solenoid length.
When to use it: Field inside a coil of wire, which is much stronger and more uniform than a single straight wire's field.
See: Magnetism
Electromagnetic Induction and Motors¶
Force on a moving charge in a magnetic field
Symbols: \(F\) — force on the charge; \(q\) — charge; \(v_\perp\) — velocity component perpendicular to \(B\); \(B\) — magnetic field strength; \(\theta\) — angle between velocity and field.
When to use it: A charged particle moving through a magnetic field — this force is what curves a charged particle's path in a field (e.g. in a mass spectrometer or particle accelerator).
Force on a current-carrying wire
Symbols: \(F\) — force on the wire; \(l\) — length of wire in the field; \(I\) — current; \(B\) — magnetic field strength; \(\theta\) — angle between the wire and the field.
When to use it: The basis of how an electric motor produces force — a current-carrying wire in a magnetic field.
Torque on a current loop
Symbols: \(\tau\) — torque; \(n\) — number of turns; \(I\) — current; \(A\) — loop area; \(B\) — magnetic field strength; \(\theta\) — angle between the loop's normal and the field.
When to use it: How a motor's coil turns — the rotating force on a current loop in a magnetic field.
Magnetic flux
Symbols: \(\Phi\) — magnetic flux; \(B\) — field strength; \(A\) — area; \(\theta\) — angle between the field and the area's normal.
When to use it: Quantifying "how much field passes through a loop" — the quantity that changing produces an induced EMF.
Induced EMF (Faraday's law)
Symbols: \(\varepsilon\) — induced EMF; \(N\) — number of turns; \(\Delta \Phi\) — change in magnetic flux; \(\Delta t\) — time interval.
When to use it: Whenever flux through a coil changes (moving a magnet, changing current, rotating a loop) — this is the principle behind generators.
Transformers¶
Transformer voltage ratio
Symbols: \(V_p\), \(V_s\) — primary/secondary voltage; \(N_p\), \(N_s\) — primary/secondary number of turns.
When to use it: Finding the voltage change across an ideal transformer from its turns ratio.
Transformer power balance
Symbols: \(V_p\), \(I_p\) — primary voltage and current; \(V_s\), \(I_s\) — secondary voltage and current.
When to use it: An ideal (lossless) transformer conserves power — if voltage steps up, current must step down to match.
Speed of light from EM constants
Symbols: \(c\) — speed of light; \(\varepsilon_0\) — electric permittivity constant; \(\mu_0\) — magnetic permeability constant.
When to use it: Rarely needed for calculation (you're given \(c\) directly on the data sheet) — mostly conceptually significant, showing light is an electromagnetic phenomenon.
Quantum, Special Relativity and Nuclear¶
Quantum Physics¶
de Broglie wavelength
Symbols: \(\lambda\) — de Broglie (matter) wavelength; \(h\) — Planck constant; \(m\) — mass; \(v\) — speed.
When to use it: Finding the wavelength associated with a moving particle — the wave-like behaviour of matter.
Photoelectric effect (maximum kinetic energy)
Symbols: \(K_{max}\) — maximum kinetic energy of an emitted electron; \(h\) — Planck constant; \(f\) — frequency of incident light; \(\phi\) — work function of the material.
When to use it: Light hitting a metal surface and ejecting electrons — this is the evidence for light behaving as discrete photons, not just a wave.
Stopping voltage
Symbols: \(K_{max}\) — maximum kinetic energy; \(q\) — electron charge; \(V_0\) — stopping voltage.
When to use it: Combine with the photoelectric equation above to find \(K_{max}\) experimentally, from the voltage needed to stop the fastest emitted electrons.
Wien's law
Symbols: \(\lambda_{max}\) — wavelength of peak emission; \(b\) — Wien's displacement constant; \(T\) — absolute temperature (kelvin).
When to use it: Relating a hot object's temperature to the wavelength it radiates most strongly at (why hotter objects glow bluer, cooler ones redder).
Hydrogen emission spectrum
Symbols: \(\lambda\) — wavelength of emitted/absorbed light; \(R\) — Rydberg constant; \(n_i\), \(n_f\) — initial and final electron energy levels.
When to use it: Predicting the wavelengths in hydrogen's line spectrum, from the electron transition between two specific energy levels.
Special Relativity¶
Time dilation
Symbols: \(t_v\) — time measured by an observer for whom the clock is moving; \(t_0\) — proper time (measured in the clock's own rest frame); \(v\) — relative speed; \(c\) — speed of light.
When to use it: Comparing time intervals measured in different reference frames moving relative to each other, at speeds where relativistic effects matter.
Length contraction
Symbols: \(l_v\) — length measured by an observer for whom the object is moving; \(l_0\) — proper length (measured in the object's own rest frame); \(v\) — relative speed; \(c\) — speed of light.
When to use it: An object's measured length shrinks (along its direction of motion) for an observer it's moving relative to.
Relativistic momentum
Symbols: \(p_v\) — relativistic momentum; \(m_0\) — rest mass; \(v\) — speed; \(c\) — speed of light.
When to use it: At speeds close to \(c\), where the ordinary \(p=mv\) understates momentum — this is why nothing with mass can actually reach \(c\) (momentum would need to be infinite).
Nuclear Physics¶
Mass–energy equivalence
Symbols: \(E\) — energy; \(m\) — mass; \(c\) — speed of light.
When to use it: Converting a mass defect into the energy released (or absorbed) in a nuclear reaction.
Mass defect
Symbols: \(\Delta m\) — mass defect; \(m_i\) — total initial mass; \(m_f\) — total final mass.
When to use it: Finding how much mass "disappears" in a nuclear reaction, before converting it to energy via \(E=mc^2\).
Radioactive decay constant
Symbols: \(\lambda\) — decay constant; \(t_{1/2}\) — half-life.
When to use it: Converting between a radioactive sample's half-life and its decay constant.