🏋️ Physics

Physics, quick reference

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Official NZQA Physics resource booklet (formulae & constants: supplied in the exam) Opens the official NZQA subject page, download the current resource/formula sheet there Physics, Formula & Reference Sheet L3 · Study Hub

The formulas you get (and don’t get) on the day, grouped by topic. Print for a clean revision sheet.

Circular & rotational motion

Angular \omega=\frac{2\pi}{T}=2\pi f\qquad v=r\omega Centripetal a=\frac{v^2}{r}=\omega^2 r\qquad F=\frac{mv^2}{r}=m\omega^2 r Torque & rotation \tau=Fr=I\alpha\qquad L=I\omega\qquad E_k=\tfrac12 I\omega^2 Rotational kinematics \omega=\omega_0+\alpha t\qquad \omega^2=\omega_0^2+2\alpha\theta

Simple harmonic motion

Defining a=-\omega^2 y Motion y=A\cos\omega t\qquad v=\pm\omega\sqrt{A^2-y^2}\qquad v_{max}=\omega A Periods T_{spring}=2\pi\sqrt{\frac{m}{k}}\qquad T_{pend}=2\pi\sqrt{\frac{L}{g}} Energy E=\tfrac12 kA^2=\tfrac12 mv^2+\tfrac12 ky^2

Gravitation & orbits

Force / field F=\frac{Gm_1m_2}{r^2}\qquad g=\frac{GM}{r^2} Orbit v=\sqrt{\frac{GM}{r}}\qquad T^2=\frac{4\pi^2r^3}{G(m_1+m_2)} G 6.67×10⁻¹¹ N m² kg⁻²

Waves

Wave v=f\lambda\qquad T=\frac{1}{f} Interference / grating d\sin\theta=n\lambda\qquad x=\frac{\lambda L}{d} Standing waves f_{open}=\frac{nv}{2L}\qquad f_{closed}=\frac{nv}{4L}\ (n\ \text{odd}) Beats / Doppler f_beat = |f₁−f₂| ; f' = f(v±v_o)/(v∓v_s) Refraction n_1\sin\theta_1=n_2\sin\theta_2\qquad \sin\theta_c=\frac{n_2}{n_1}\qquad n=\frac{c}{v}

DC & capacitors

Ohm / power V=IR\qquad P=VI=I^2R=\frac{V^2}{R} Capacitor C=\frac{Q}{V}\qquad E=\tfrac12 CV^2=\tfrac12 QV Combinations \text{parallel: }C_T=\textstyle\sum C_i\qquad\text{series: }\frac{1}{C_T}=\sum\frac{1}{C_i} Charging \tau=RC\qquad Q=Q_0e^{-t/RC}\qquad Q=Q_0\left(1-e^{-t/RC}\right)

AC & inductors

Inductor \varepsilon=-L\frac{\Delta I}{\Delta t}\qquad E=\tfrac12 LI^2 RMS V_{rms}=\frac{V_{peak}}{\sqrt2}\qquad I_{rms}=\frac{I_{peak}}{\sqrt2} Reactance X_C=\frac{1}{2\pi fC}\qquad X_L=2\pi fL Impedance / resonance Z=\sqrt{R^2+(X_L-X_C)^2}\qquad f_0=\frac{1}{2\pi\sqrt{LC}} Phase ELI the ICE man (I lags E in L; I leads E in C)

Modern physics

Photon E=hf=\frac{hc}{\lambda}\quad(h=6.63\times10^{-34}\,\mathrm{J\,s}) Photoelectric hf = W + E_k(max) ; eV_s = E_k(max) Nuclear E=mc^2\qquad N=N_0\left(\tfrac12\right)^{t/t_{1/2}}