Physics HSC Reference Sheet — Explained

$v$ — final velocity (m s⁻¹); $u$ — initial velocity (m s⁻¹); $a$ — acceleration (m s⁻²); $t$ — time (s).

Use when you know three of the four variables and need the fourth — and displacement $s$ is not involved.

$s$ — displacement (m); $u$ — initial velocity (m s⁻¹); $a$ — acceleration (m s⁻²); $t$ — time (s).

Use when final velocity is unknown and you need displacement (or vice-versa), given time.

$v$ — final velocity (m s⁻¹); $u$ — initial velocity (m s⁻¹); $a$ — acceleration (m s⁻²); $s$ — displacement (m).

Use when time is not given or not required — links velocity and displacement directly.

$s$ — displacement (m); $u$ — initial velocity (m s⁻¹); $v$ — final velocity (m s⁻¹); $t$ — time (s).

Use when you know both initial and final velocities and the time elapsed but not the acceleration.

$F_{\text{net}}$ — net (resultant) force (N); $m$ — mass (kg); $a$ — acceleration (m s⁻²).

Use whenever a net force causes acceleration. Draw a free-body diagram first to identify all forces.

$p$ — momentum (kg m s⁻¹); $m$ — mass (kg); $v$ — velocity (m s⁻¹).

Use in collision and explosion problems. Momentum is always conserved when no external force acts.

$J$ — impulse (N s); $F$ — (average) force (N); $\Delta t$ — time interval (s); $\Delta p = mv - mu$ — change in momentum (kg m s⁻¹).

Use when a force acts for a short time (collision, kick, rocket burst) and you want the change in momentum or the average force.

$W$ — work (J); $F$ — force (N); $s$ — displacement (m); $\theta$ — angle between force and displacement.

Use when a force is applied at an angle to the direction of motion. If force and displacement are parallel, $\theta = 0$ and $W = Fs$.

$P$ — power (W); $W$ — work (J); $t$ — time (s); $F$ — force (N); $v$ — velocity (m s⁻¹).

Use $P = W/t$ for total energy delivered over a time. Use $P = Fv$ for instantaneous power when force and velocity are parallel.

$E_k$ — kinetic energy (J); $m$ — mass (kg); $v$ — speed (m s⁻¹).

Use to find energy stored in a moving object, or to relate speed before/after a collision or energy conversion.

$E_p$ — gravitational PE (J); $m$ — mass (kg); $g$ — gravitational field strength (m s⁻²); $h$ — height above reference level (m).

Use near Earth's surface (constant $g$) when an object changes height. The reference level ($h = 0$) is your choice — pick the most convenient point.

$a_c$ — centripetal acceleration (m s⁻²); $v$ — tangential speed (m s⁻¹); $r$ — radius (m); $T$ — period (s).

Use for any object moving in a circle at constant speed. The acceleration points toward the centre.

$F_c$ — centripetal force (N); $m$ — mass (kg); $v$ — tangential speed (m s⁻¹); $r$ — radius (m); $T$ — period (s).

Use to find the net inward force required to keep an object moving in a circle — or to identify what provides it (gravity, friction, tension, normal force).

$x$ — horizontal displacement (m); $v_x$ — horizontal speed (constant, m s⁻¹); $v_0$ — launch speed (m s⁻¹); $\theta$ — launch angle; $t$ — time (s).

Horizontal motion is uniform (constant velocity) — no horizontal acceleration. Apply throughout flight.

$y$ — vertical displacement (m, upward positive); $v_0$ — launch speed (m s⁻¹); $\theta$ — launch angle; $g$ — gravitational acceleration (m s⁻²); $t$ — time (s).

Vertical motion has constant downward acceleration $g$. Use to find height at any time or time of flight.

$F_g$ — gravitational force (N); $G = 6.67 \times 10^{-11}$ N m² kg⁻²; $m_1, m_2$ — masses (kg); $r$ — centre-to-centre distance (m).

Use to find the gravitational force between any two masses, or the gravitational field strength $g = GM/r^2$ at distance $r$.

$U$ — gravitational PE (J, always negative); $G$ — gravitational constant; $m_1, m_2$ — masses (kg); $r$ — separation (m).

Use for objects far from Earth's surface where $g$ is not constant — satellites, planetary motion, escape velocity.

$v$ — orbital speed (m s⁻¹); $G$ — gravitational constant; $M$ — mass of central body (kg); $r$ — orbital radius (m).

Use for circular orbits. Derived by equating gravitational force to centripetal force.

$r$ — orbital radius (m); $T$ — orbital period (s); $G$ — gravitational constant; $M$ — mass of central body (kg).

Use to find period, radius, or central body mass for any circular orbit. Ratios form is useful: $r_1^3/T_1^2 = r_2^3/T_2^2$.

$v$ — wave speed (m s⁻¹); $f$ — frequency (Hz); $\lambda$ — wavelength (m).

Use for any wave — sound, light, water — relating speed, frequency, and wavelength.

$f'$ — observed frequency (Hz); $f$ — source frequency (Hz); $v_w$ — speed of sound in the medium (m s⁻¹); $v_o$ — speed of observer (m s⁻¹, positive when moving toward source); $v_s$ — speed of source (m s⁻¹, positive when moving toward observer).

Use when a sound source or observer is moving relative to the medium. Use $v_w = 340$ m s⁻¹ unless otherwise stated. Sign convention: velocities are positive when directed toward each other.

$T$ — period (s); $f$ — frequency (Hz = s⁻¹).

Converts between period and frequency — essential first step in most wave problems.

$q$ — charge (C); $I$ — current (A); $t$ — time (s).

Use to find total charge delivered by a steady current over a time interval, or to find average current when charge and time are known.

$W$ — work done on the charge (J); $q$ — charge (C); $V$ — potential difference (V).

Use to find the energy gained or lost by a charge moving through a potential difference — fundamental to all circuit energy calculations.

$F_e$ — electrostatic force (N); $k = 8.99 \times 10^9$ N m² C⁻²; $q_1, q_2$ — charges (C); $r$ — separation (m); $\varepsilon_0$ — permittivity of free space.

Use to find the force between two point charges. Like charges repel, unlike attract.

$E$ — electric field (N C⁻¹ = V m⁻¹); $F$ — force on test charge (N); $q$ — test charge (C); $k$ — Coulomb constant; $Q$ — source charge (C); $r$ — distance (m).

Use to find the force per unit charge at a point, or to find the force on a charge placed in a known field ($F = qE$).

$V$ — potential difference (V); $I$ — current (A); $R$ — resistance ($\Omega$).

Use for any ohmic (constant resistance) conductor. Rearrange for current or resistance as required.

$P$ — power (W); $V$ — voltage (V); $I$ — current (A); $R$ — resistance ($\Omega$).

Use to find energy dissipation rate in a circuit component. Which form to use depends on which two quantities are known.

$F$ — force (N); $B$ — magnetic flux density (T); $I$ — current (A); $l$ — length of conductor in field (m); $\theta$ — angle between conductor and field direction.

Use for the force on a straight wire in a uniform magnetic field. If wire is perpendicular to $B$, $\theta = 90°$ and $F = BIl$.

$F$ — magnetic force (N); $q$ — charge (C); $v$ — speed (m s⁻¹); $B$ — magnetic flux density (T); $\theta$ — angle between velocity and field.

Use for individual charged particles moving through a magnetic field — cathode rays, cyclotrons, mass spectrometers.

$\Phi$ — magnetic flux (Wb = T m²); $B$ — magnetic flux density (T); $A$ — area of loop (m²); $\theta$ — angle between $B$ and normal to the loop.

Use as the first step in any electromagnetic induction problem. Flux is what changes to induce an EMF.

$\mathcal{E}$ — induced EMF (V); $N$ — number of turns; $\Delta\Phi$ — change in flux (Wb); $\Delta t$ — time interval (s).

Use whenever flux through a coil changes — moving magnets, changing current in a nearby coil, rotating generators.

$V_p$ — primary voltage (V); $V_s$ — secondary voltage (V); $N_p$ — primary turns; $N_s$ — secondary turns.

Use for ideal transformers to step voltage up or down. Combined with $V_p I_p = V_s I_s$ for current.

$E$ — photon energy (J); $h = 6.626 \times 10^{-34}$ J s — Planck's constant; $f$ — frequency (Hz); $c$ — speed of light (m s⁻¹); $\lambda$ — wavelength (m).

Use to find the energy of a single photon. The $hc/\lambda$ form is useful when wavelength is given directly.

$E_k^{\max}$ — maximum kinetic energy of ejected photoelectrons (J); $hf$ — photon energy (J); $W = hf_0$ — work function of the metal (J); $f_0$ — threshold frequency (Hz).

Use whenever a photon ejects an electron from a metal surface. Below the threshold frequency, no electrons are emitted regardless of intensity.

$\lambda$ — de Broglie (matter) wavelength (m); $h$ — Planck's constant (J s); $p = mv$ — momentum (kg m s⁻¹).

Use to find the wave-like wavelength of any particle. Larger momentum means shorter wavelength — electrons in an electron microscope have shorter wavelengths than visible light.

$\lambda_{\text{max}}$ — peak wavelength (m); $b = 2.898 \times 10^{-3}$ m K — Wien's displacement constant; $T$ — absolute temperature of the black body (K).

Use to find the wavelength at which a black body emits most intensely, or to infer a star's surface temperature from its colour. Module 8 (The Universe and the Atom).

$t$ — dilated time measured by stationary observer (s); $t_0$ — proper time (in the moving frame, s); $v$ — relative speed (m s⁻¹); $c$ — speed of light (m s⁻¹); $\gamma$ — Lorentz factor.

Use when an event is observed from two frames moving relative to each other. The clock in the moving frame runs slower as seen from the stationary frame.

$L$ — contracted length (m, measured in the frame in which the object is moving); $L_0$ — proper length (m, measured in the object's rest frame); $\gamma$ — Lorentz factor; $v$ — relative speed (m s⁻¹).

Use when measuring the length of an object that is moving relative to you. Moving objects appear shorter along the direction of motion.

$E$ — energy (J); $m$ — mass (kg); $c = 3.00 \times 10^8$ m s⁻¹ — speed of light.

Use to convert between mass and energy in nuclear reactions, pair production/annihilation, and binding energy calculations.

$N(t)$ — number of undecayed nuclei at time $t$; $N_0$ — initial number; $t_{1/2}$ — half-life (s or years); $t$ — elapsed time.

Use to find the remaining activity or number of nuclei after a given number of half-lives. Also works for activity $A$ and mass $m$ in place of $N$.

$p$ — photon momentum (kg m s⁻¹); $E$ — photon energy (J); $c$ — speed of light (m s⁻¹); $h$ — Planck's constant (J s); $\lambda$ — wavelength (m).

Use in Compton scattering and radiation pressure problems where photons transfer momentum to matter.

$E$ — total energy (J); $p$ — momentum (kg m s⁻¹); $c$ — speed of light (m s⁻¹); $m_0$ — rest mass (kg).

Use for particles moving at relativistic speeds. For photons ($m_0 = 0$) this gives $E = pc$. For a particle at rest ($p = 0$) it gives $E = m_0 c^2$.