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Every equation in the catalogue, one row per product.

  1. Adiabram, the Slow-Change Shepherd MugMug \[T_{\text{change}} \gg \frac{\hbar}{\Delta E}\]
  2. Aliasyne, the Undersampled Twin MugMug \[f_s > 2 f_{\max}\]
  3. Arnold's Cat – Cat Map Chaos Physics T-ShirtT-Shirt \[\Gamma:\ (x, y) \mapsto (x + y,\ x + 2y) \bmod 1\]\[A = \begin{pmatrix}1 & 1\\ 1 & 2\end{pmatrix},\quad \det A = 1,\quad \lambda_\pm = \frac{3 \pm \sqrt{5}}{2}\]\[\Pi(124) = 15\]
  4. Asymptor, the Last-Step Knight MugMug \[\lim_{T \to 0} \Delta S = 0\]
  5. Atom Smashers Pixel Sticker Sheet – 12 Physics StickersPaper products \[Q = \left(M_{\text{initial}} - M_{\text{final}}\right)c^{2}\]\[\begin{gathered} V(r) = -\frac{g^{2}}{4\pi}\,\frac{e^{-r/R}}{r} \\ R = \frac{\hbar}{m c} \end{gathered}\]\[\begin{gathered} E_N = \hbar\omega\left(N + \tfrac{3}{2}\right) \\ \begin{aligned} g_N &= (N+1)(N+2) \\ &= 2,\,6,\,12,\,\ldots \end{aligned} \\ \Rightarrow\; \text{shells close at } 2,\,8,\,20 \end{gathered}\]\[\alpha = \left(\frac{A-1}{A+1}\right)^2\]\[V(\phi) = -\mu^2|\phi|^2 + \lambda|\phi|^4\]\[m_{\bar{X}} = m_X,\quad \tau_{\bar{X}} = \tau_X\]\[\sin^{2}\theta_W \approx 0.231\ \ (\overline{\mathrm{MS}},\ \mu = M_Z),\quad e = g\sin\theta_W\]\[\mu = \frac{m_p}{m_e} = 1836.152\,673\,426(32)\]\[p + {}^{7}\mathrm{Li} \rightarrow 2\,\alpha + 17.3\ \mathrm{MeV}\]\[h = \frac{\mathbf{s}\cdot\mathbf{p}}{|\mathbf{s}|\,|\mathbf{p}|} = -1\]\[\omega_c^{2} = \omega_+^{2} + \omega_z^{2} + \omega_-^{2}\]
  6. Avergail, the Mean-Field Courtier MugMug \[B_{\text{eff}} = B + \lambda M\]\[\chi = \frac{C}{T - T_c}\]
  7. Azurwake – Cherenkov Radiation / Light-Speed in Water Physics StickerPaper products \[\cos\theta = \frac{1}{n\beta}, \qquad \beta > \frac{1}{n}\]\[\begin{aligned} \frac{d^2N}{dx\,d\lambda} &= \frac{2\pi\alpha z^2}{\lambda^2} \\ &\quad\times\left(1-\frac{1}{\beta^2 n^2}\right) \end{aligned}\]
  8. Backglowen, the Sky-Limited Lantern MugMug \[\text{SNR} \propto \sqrt{t} \quad \text{(sky-limited)}\]
  9. Backrowena, the Broken-Symmetry Usher MugMug \[V(\phi) = -\mu^{2}|\phi|^{2} + \lambda |\phi|^{4}\]\[|\phi_0|^{2} = \frac{\mu^{2}}{2\lambda}\]
  10. Barrierwyn, the Escape-Rate Climber MugMug \[k \propto e^{-\Delta E / k_B T}\]
  11. Beaconess, the Laser-Star Maker MugMug \[E = \frac{hc}{\lambda}\]\[\lambda_{\text{Na D}_2} \approx 589\ \text{nm} \;\Rightarrow\; E \approx 2.1\ \text{eV}\]
  12. Bifurcor – Stern–Gerlach Experiment / Spin Quantization Physics StickerPaper products \[F_z = \mu_z\,\frac{\partial B_z}{\partial z}\]\[\begin{gathered} \mu_z = -g_s\,\mu_B\,m_s \\ m_s = \pm\tfrac{1}{2} \end{gathered}\]
  13. Bose-Einstein Condensate 1995 TeeT-Shirt \[\lambda_{\mathrm{dB}} = \frac{h}{\sqrt{2\pi m k_B T}}\]\[n\,\lambda_{\mathrm{dB}}^{3} = \zeta(3/2) \approx 2.612\]\[k_B T_c = \frac{2\pi\hbar^{2}}{m}\left(\frac{n}{\zeta(3/2)}\right)^{2/3}\quad\text{(uniform gas)}\]\[k_B T_c \approx 0.94\,\hbar\bar\omega\,N^{1/3}\quad\text{(harmonic trap)}\]
  14. Boundraith, the Mismatched Border Wraith MugMug \[R_K \propto T^{-3}\]
  15. Bremsella – Bremsstrahlung (Braking Radiation) Physics StickerPaper products \[P = \frac{q^2 a^2}{6\pi\varepsilon_0 c^3}\]
  16. Broadling, the Short-Lived Herald MugMug \[\Gamma = \frac{\hbar}{\tau}\]
  17. C. V. Raman Sticker – Most Pass Free. A Few Pay A Toll. | Physics StickerPaper products \[\begin{gathered} h\nu_s = h\nu_0 - h\nu_{\text{vib}} \\ (\text{Stokes}) \end{gathered}\]\[\begin{gathered} h\nu_s = h\nu_0 + h\nu_{\text{vib}} \\ (\text{anti-Stokes}) \end{gathered}\]\[\Delta\tilde\nu = \frac{1}{\lambda_0} - \frac{1}{\lambda_s}\]
  18. Casimira – The Casimir Effect Pixel StickerPaper products \[\frac{F}{A} = -\frac{\pi^2\hbar c}{240\,d^4}\]
  19. Cecilia Payne-Gaposchkin Sticker – Almost Certainly Real. | Physics StickerPaper products \[\begin{aligned} \frac{n_{i+1}\,n_e}{n_i} &= \frac{2}{\Lambda^{3}}\,\frac{g_{i+1}}{g_i} \\ &\quad\times\exp\!\left(-\frac{\chi_i}{k_B T}\right) \\ \Lambda &= \frac{h}{\sqrt{2\pi m_e k_B T}} \end{aligned}\]\[\begin{gathered} X + Y + Z = 1 \\ (\text{Sun's surface today:} \\ X\approx0.74,\ Y\approx0.25, \\ Z\approx0.013) \end{gathered}\]
  20. Chandrasekhar Limit Tee: 1.4 M☉T-Shirt \[M_{\mathrm{Ch}} = \frac{\omega_3^{0}\sqrt{3\pi}}{2}\left(\frac{\hbar c}{G}\right)^{3/2}\frac{1}{(\mu_e m_H)^{2}} \approx \frac{5.8\,M_\odot}{\mu_e^{2}}\]\[\mu_e = 2 \;\Rightarrow\; M_{\mathrm{Ch}} \approx 1.44\,M_\odot\ \text{(ideal)},\ \approx 1.4\,M_\odot\ \text{(real white dwarfs)}\]
  21. Chien-Shiung Wu Sticker – She Broke Symmetry. And Records. | Physics StickerPaper products \[{}^{60}\mathrm{Co} \to {}^{60}\mathrm{Ni}^{*} + e^{-} + \bar\nu_e\]\[\begin{gathered} \hat P:\ \vec J \to \vec J,\ \ \vec p_e \to -\vec p_e \\ \Rightarrow\; \langle \vec J\cdot\vec p_e\rangle \ne 0 \\ \text{violates parity} \end{gathered}\]
  22. Chimella, the Hot-Chocolate Bell MugMug \[\frac{1}{\rho c^{2}} = \frac{1-\phi}{\rho_l c_l^{2}} + \frac{\phi}{\rho_g c_g^{2}}\]\[f \propto c\]
  23. Chivelle, the Too-Good-Fit Inquisitor MugMug \[\frac{\chi^{2}}{\nu} \approx 1\]
  24. Christiaan Huygens Sticker – Every Point A Source | Physics StickerPaper products \[r = v\,\Delta t\]\[\text{new front} = \text{envelope of the wavelets}\]
  25. Classic Lab Experiments Pixel Sticker Sheet – 12 Physics StickersPaper products \[F \propto -\,I_{\mathrm{coil}}\,I_{\mathrm{ring}}\]\[f = \frac{n}{2L}\sqrt{\frac{T}{\mu}}\]\[\gamma = \frac{4\pi^{2} m V}{A^{2} p\,T^{2}}\]\[W = J\,Q\]\[\delta_{\mathrm{beam}} = 2\theta\]\[B \propto q\,v\]\[Q = \frac{m}{e}\,\frac{v_0 L}{R}\]\[F = \pi r^{2}\,\Delta p\]\[E > E_c \;\rightarrow\; \text{rotation}\]\[G = 6.674\,30(15)\times10^{-11}\ \mathrm{m^{3}\,kg^{-1}\,s^{-2}}\]
  26. Classical Physics Vol. 1 Pixel Sticker Sheet – 10 Physics StickersPaper products \[J = \oint p\,\mathrm{d}q\]\[\frac{\partial p}{\partial r} = \frac{\rho v_\theta^{2}}{r}\]\[\lambda_{\mathrm{IR}} > \lambda_{\mathrm{red}} \approx 0.7\ \mu\mathrm{m}\]\[k_{\mathrm{eff}} = \tfrac{k}{2}\ (\text{series}) \;\rightarrow\; k_{\mathrm{eff}} = 2k\ (\text{parallel})\]\[z = \frac{\omega^{2} r^{2}}{2g}\]\[h_2 \propto h_1\]\[\mathbf{a}' = -2\,\boldsymbol{\Omega}\times\mathbf{v}' - \boldsymbol{\Omega}\times(\boldsymbol{\Omega}\times\mathbf{r}')\]\[\phi = U\left(r + \frac{a^{3}}{2r^{2}}\right)\cos\theta \;\Rightarrow\; F_{\mathrm{drag}} = 0\]\[p(z) = p_\infty\left(1 - e^{-z/\lambda}\right),\quad \lambda = \frac{R}{2\mu K}\]\[r_{L2} \approx R\left(\frac{M_2}{3M_1}\right)^{1/3}\]
  27. Classical Physics Vol. 2 Pixel Sticker Sheet – 10 Physics StickersPaper products \[\mathbf{F}_M = \alpha\,\boldsymbol{\omega}\times\mathbf{v}\]\[f = \frac{n}{2L}\sqrt{\frac{T}{\mu}}\]\[\omega_{\text{prec}} = \Omega_\oplus \sin\varphi\]\[L = I\omega\]\[m\frac{dv}{dt} = mg - \tfrac12\rho C_d A\,v^2\]\[V = -N\,\frac{\mathrm{d}\Phi}{\mathrm{d}t}\]\[\mathbf{J}_d = \varepsilon_0\,\frac{\partial \mathbf{E}}{\partial t}\]\[\beta = V B d\]\[\delta_{\mathrm{beam}} = 2\theta\]\[Q = \frac{m}{e}\,\frac{v_0 L}{R}\]
  28. Classical Physics Vol. 4 Pixel Sticker Sheet – 10 Physics StickersPaper products \[\mathrm{Fr} = \frac{v}{\sqrt{g h}}\]\[f = \mathrm{St}\,\frac{U}{D}, \qquad \mathrm{St} \approx 0.2\]\[N_1 = \tau_{11} - \tau_{22} > 0\]\[\tau = \nabla_s \gamma\]\[I_e \propto \exp\!\left[\frac{e\,(V - V_p)}{k_B T_e}\right]\]\[\Phi_v = K_m \int V(\lambda)\,\Phi_{e,\lambda}\,\mathrm{d}\lambda,\quad K_{cd} = 683\ \mathrm{lm/W}\]\[D_{\min} = 2\arcsin\!\left(n\sin 30^\circ\right) - 60^\circ\]\[n_o > n_{\mathrm{balsam}} > n_e\]\[\Delta\nu_{\mathrm{FSR}} = \frac{c}{2nL}\]\[\mathbf{F}_{\mathrm{grad}} \propto \nabla I\]
  29. Clustrelle, the Cheerios-Effect Gatherer MugMug \[\ell_c = \sqrt{\frac{\gamma}{\rho g}}\]\[F(\ell) \propto K_1\!\left(\frac{\ell}{\ell_c}\right)\]
  30. Condensa – Bose–Einstein Condensate Physics StickerPaper products \[\frac{N_0}{N} = 1 - \left(\frac{T}{T_c}\right)^{3/2}\quad(T\le T_c)\]\[kT_c = \frac{2\pi\hbar^2}{m}\left(\frac{n}{\zeta(3/2)}\right)^{2/3}\]
  31. Constants & Units Pixel Sticker Sheet – 12 Physics StickersPaper products \[m g v = U I\]\[I = e f\]\[c^{2} = \frac{\gamma k_B T}{m}\]\[\Phi_0 = \frac{h}{2e} \approx 2.067\,833\,848\times10^{-15}\ \mathrm{Wb}\]\[\mu_B = \frac{e\hbar}{2m_e} = 9.274\,010\,0657(29)\times10^{-24}\ \mathrm{J/T}\]\[a_0 = \frac{4\pi\varepsilon_0\hbar^{2}}{m_e e^{2}} = 5.291\,772\,105\,44(82)\times10^{-11}\ \mathrm{m}\]\[G = 6.674\,30(15)\times10^{-11}\ \mathrm{m^{3}\,kg^{-1}\,s^{-2}}\]\[\sin^{2}\theta_W \approx 0.231\ \ (\overline{\mathrm{MS}},\ \mu = M_Z),\quad e = g\sin\theta_W\]\[G = \frac{2e^{2}}{h}\sum_n T_n,\quad G_0 = \frac{2e^{2}}{h} \approx 7.748\,091\,729\times10^{-5}\ \mathrm{S}\]\[\mu = \frac{m_p}{m_e} = 1836.152\,673\,426(32)\]\[\sigma_T = \frac{8\pi}{3}\,r_e^{2} = 6.652\,458\,7051(62)\times10^{-29}\ \mathrm{m}^{2}\]\[\Phi_v = K_m \int V(\lambda)\,\Phi_{e,\lambda}\,\mathrm{d}\lambda,\quad K_{cd} = 683\ \mathrm{lm/W}\]
  32. Corekeeper – Strong Nuclear Force / Nuclear Binding Physics T-ShirtT-Shirt \[V(r) = -\frac{g^{2}}{4\pi}\frac{e^{-r/\lambda}}{r}, \qquad \lambda = \frac{\hbar}{m_\pi c}\]\[B = \left(Z m_p + N m_n - M_{\text{nuc}}\right)c^{2}\]
  33. Coriolix – Coriolis Effect Physics StickerPaper products \[\mathbf{a}' = -2\,\boldsymbol{\Omega}\times\mathbf{v}' - \boldsymbol{\Omega}\times(\boldsymbol{\Omega}\times\mathbf{r}')\]\[x' = vt\cos\Omega t,\qquad y' = -vt\sin\Omega t\]\[\Delta\varphi = \frac{\Omega R}{v}\]
  34. Cosmic Extremes Pixel Sticker Sheet – 11 Physics StickersPaper products \[T_H = \frac{\hbar c^{3}}{8\pi G M k_B}\]\[\begin{aligned} M_{\text{Ch}} &= \frac{\omega_3^{0}\sqrt{3\pi}}{2}\left(\frac{\hbar c}{G}\right)^{3/2} \\ &\quad\times\frac{1}{(\mu_e m_H)^{2}} \\ &\approx \frac{5.73}{\mu_e^{2}}\,M_\odot \end{aligned}\]\[\sigma^2 \sim \frac{GM}{R}\]\[v(r)^{2} = \frac{G M(r)}{r}\]\[\bar\rho \gtrsim \frac{3\pi}{G P^{2}}\]\[T(z) = T_0\,(1+z)\]\[Y_p \simeq \frac{2\,(n/p)}{1 + n/p}\]\[h \approx \frac{\Delta L}{L}\]\[\Delta t = \gamma\,\tau, \qquad L = \frac{L_0}{\gamma}\]\[R_{\mathrm{Cl}}^{\mathrm{meas}} = 2.56 \pm 0.16 \pm 0.16\ \mathrm{SNU} \quad \text{vs} \quad R_{\mathrm{Cl}}^{\mathrm{pred}} = 7.6^{+1.3}_{-1.1}\ \mathrm{SNU}\]
  35. Counterterra, the Renormalising Smith MugMug \[m = m_0 + \delta m\]\[e = \sqrt{Z_3}\, e_0\]
  36. Creamward, the Milk-First Alchemist MugMug \[\frac{dT}{dt} = -k\,(T - T_{\text{env}})\]
  37. Cryo Fault – Ductile-to-Brittle Transition Physics T-ShirtT-Shirt \[\sigma_f = \sqrt{\frac{2E\gamma_s}{\pi a}}\]\[K_I = Y\sigma\sqrt{\pi a} \ \ge\ K_{Ic} \;\Rightarrow\; \text{fracture}\]
  38. Cryoselle, Abbess of the Twenty Millikelvin MugMug \[\bar n = \frac{1}{e^{hf/kT} - 1}\]\[f = 5\ \text{GHz},\ T = 20\ \text{mK}:\quad \frac{hf}{kT} \approx 12,\quad \bar n \approx 6 \times 10^{-6}\]
  39. Dark Matter Host – Gravitational Lensing / Invisible Mass Physics T-ShirtT-Shirt \[v(r)^{2} = \frac{G M(r)}{r} \;\Rightarrow\; M(r) = \frac{v^{2} r}{G}\]\[\theta_E = \sqrt{\frac{4GM}{c^{2}}\,\frac{D_{LS}}{D_L D_S}}\]
  40. Decay Dancer – Weak Nuclear Force / Beta Decay Physics T-ShirtT-Shirt \[n \to p + e^{-} + \bar\nu_e\]\[d \to u + W^{-} \to u + e^{-} + \bar\nu_e\]\[Q = \left(m_n - m_p - m_e\right)c^{2} \approx 0.782\ \text{MeV}\]
  41. Decoherex – The Interference / Quantum Decoherence Physics T-ShirtT-Shirt \[\rho_{01}(t) = \rho_{01}(0)\,e^{-t/\tau_D}\]
  42. Decouplarch, the Two-Timescale Diplomat MugMug \[\Psi(\mathbf{r},\mathbf{R}) \approx \psi_{\mathbf{R}}(\mathbf{r})\, \chi(\mathbf{R})\]
  43. Degreeda, the Equipartition Dreamer MugMug \[\langle E \rangle = \tfrac{1}{2} k_B T \quad \text{per quadratic degree of freedom}\]
  44. Densara, the Final-State Cartographer MugMug \[\Gamma = \frac{2\pi}{\hbar}\, |M|^{2}\, \rho(E_f)\]
  45. Diagonix – Malus’s Law / Three-Polarizer Effect Physics StickerPaper products \[I = I_0\cos^2\theta\]\[I_{\text{out}} = \frac{I_0}{2}\cos^2 45^\circ\,\cos^2 45^\circ\]\[I_{\text{out}} = \frac{I_0}{8}\]
  46. Discoveries That Changed Physics Pixel Sticker Sheet – 11 Physics StickersPaper products \[v = \frac{E}{B}\]\[\frac{d\sigma}{d\Omega} = \left(\frac{zZe^2}{16\pi\varepsilon_0 E}\right)^2\frac{1}{\sin^4(\theta/2)}\]\[p + {}^{7}\mathrm{Li} \rightarrow 2\,\alpha + 17.3\ \mathrm{MeV}\]\[\rho_{\mathrm{N_2}}^{\mathrm{air}} \approx 1.005\,\rho_{\mathrm{N_2}}^{\mathrm{chem}}\]\[\lambda_{\mathrm{IR}} > \lambda_{\mathrm{red}} \approx 0.7\ \mu\mathrm{m}\]\[\theta \approx \frac{v}{c} \approx 20.5''\]\[\Delta t = \frac{\Delta d}{c}\]\[R_{\mathrm{Cl}}^{\mathrm{meas}} = 2.56 \pm 0.16 \pm 0.16\ \mathrm{SNU} \quad \text{vs} \quad R_{\mathrm{Cl}}^{\mathrm{pred}} = 7.6^{+1.3}_{-1.1}\ \mathrm{SNU}\]\[d = \tfrac{1}{2}g t^{2}\]
  47. Dissipar, the Fidgeting Oracle MugMug \[\langle V^{2} \rangle = 4 k_B T R\, \Delta f\]
  48. Distalis, the Far-Field Back-Row Watcher MugMug \[U(x,y) \propto \iint A(\xi,\eta)\, e^{-i\frac{2\pi}{\lambda z}(x\xi + y\eta)}\, d\xi\, d\eta\]\[z \gg \frac{a^{2}}{\lambda}\]
  49. Driftgale, the Thermal-Drift Wind Spirit MugMug \[\Delta L = \alpha L\, \Delta T\]\[\alpha_{\text{Al}} \approx 23 \times 10^{-6}\ \text{K}^{-1}:\quad L = 1\ \text{m},\ \Delta T = 1\ \text{K} \Rightarrow \Delta L \approx 23\ \mu\text{m}\]
  50. Drycrest, the Water-Vapour Hermit MugMug \[\text{PWV} = \frac{1}{\rho_w g}\int_0^{p_s} q\, dp\]\[\text{median PWV} \approx 1.86\ \text{mm (Mauna Kea 13N)}\]
  51. Duskward, the Astronomical-Twilight Warden MugMug \[h_\odot = -18^\circ \quad \text{(end of astronomical twilight)}\]\[-18^\circ \le h_\odot < -12^\circ\]
  52. Émilie du Châtelet Sticker – 2× The Speed. 4× The Dent. | Physics StickerPaper products \[\begin{gathered} E_k = \tfrac{1}{2} m v^{2} \\ (\text{vis viva: } m v^{2}) \end{gathered}\]\[v = \sqrt{2 g h}\;\Rightarrow\; h \propto v^{2}\]\[\begin{gathered} m g h \approx F d\;\Rightarrow\; d \propto v^{2} \\ (\text{idealised: constant} \\ \text{clay resistance}) \end{gathered}\]\[\begin{gathered} m_1 h_1 = m_2 h_2 \\ \Leftrightarrow\; m_1 v_1^{2} = m_2 v_2^{2} \\ \Rightarrow\; \text{equal dents} \\ (\text{'s Gravesande}) \end{gathered}\]
  53. Emmy Noether Sticker – Symmetry In. Conservation Out. | Physics StickerPaper products \[Q = \sum_i \frac{\partial L}{\partial \dot q_i}\,\delta q_i\]\[\delta L = 0 \;\Rightarrow\; \frac{dQ}{dt} = 0\]\[\begin{gathered} E = \sum_i \dot q_i\,\frac{\partial L}{\partial \dot q_i} - L \\ \frac{\partial L}{\partial t} = 0 \;\Rightarrow\; \frac{dE}{dt} = 0 \end{gathered}\]\[\begin{aligned} t \to t+\epsilon \;&\Rightarrow\; E \text{ conserved} \\ \vec x \to \vec x+\vec\epsilon \;&\Rightarrow\; \vec p \\ \theta \to \theta+\epsilon \;&\Rightarrow\; \vec L \end{aligned}\]
  54. Endoreva, the Max-Power Engine MugMug \[\eta = 1 - \sqrt{\frac{T_c}{T_h}}\]
  55. Enrico Fermi Sticker – Within An Order | Physics StickerPaper products \[f(E)=\frac{1}{e^{(E-\mu)/kT}+1}\]\[f(\mu)=\tfrac12\quad(T>0)\]
  56. Epochra, the Precession Navigator MugMug \[p_A \approx 5028.796195''\ \text{per Julian century} \approx 50.3''\,\text{yr}^{-1}\]\[P = \frac{360^\circ}{p_A} \approx 25\,800\ \text{yr}\]
  57. Ernest Rutherford Sticker – Some Came Back | Physics StickerPaper products \[\frac{d\sigma}{d\Omega} = \left(\frac{zZe^2}{16\pi\varepsilon_0 E}\right)^2\frac{1}{\sin^4(\theta/2)}\]\[\tan\frac{\theta}{2} = \frac{d}{2b},\qquad d = \frac{zZe^2}{4\pi\varepsilon_0 E}\]
  58. Eventide Prophet – Black Hole Information Paradox Physics T-ShirtT-Shirt \[T_H = \frac{\hbar c^{3}}{8\pi G M k_B}\]\[S_{BH} = \frac{k_B c^{3} A}{4 G \hbar}\]\[\begin{gathered} S_{\text{rad}}(t) \le S_{BH}(t) \\ \text{unitary evaporation} \\ (\text{Page 1993}) \end{gathered}\]
  59. Everyday Physics Pixel Sticker Sheet – 12 Physics StickersPaper products \[\ell_c = \sqrt{\frac{\gamma}{\rho g}}\]\[\tau = \nabla_s \gamma\]\[\frac{\partial p}{\partial r} = \frac{\rho v_\theta^{2}}{r}\]\[I_s \propto \frac{1}{\lambda^4}\]\[D_{\min} = 2\arcsin\!\left(n\sin 30^\circ\right) - 60^\circ\]\[m\frac{dv}{dt} = mg - \tfrac12\rho C_d A\,v^2\]\[\mathbf{F}_M = \alpha\,\boldsymbol{\omega}\times\mathbf{v}\]\[\mathrm{Fr} = \frac{v}{\sqrt{g h}}\]\[\frac{\Delta f}{f} \approx \frac{\Delta\Phi}{c^2} - \frac{v^2}{2c^2}\]\[\mathcal{E} = -\frac{d\Phi_B}{dt}\]\[L = I\omega\]\[f = \mathrm{St}\,\frac{U}{D}, \qquad \mathrm{St} \approx 0.2\]
  60. Exclusor – Pauli Exclusion Principle / Degeneracy Pressure Physics T-ShirtT-Shirt \[\psi(x_1,x_2) = \frac{1}{\sqrt{2}}\begin{vmatrix} \phi_a(x_1) & \phi_b(x_1) \\ \phi_a(x_2) & \phi_b(x_2) \end{vmatrix}\]\[\psi(x_2,x_1) = -\,\psi(x_1,x_2)\]\[\phi_a = \phi_b \;\Rightarrow\; \psi = 0\]\[P = \frac{(3\pi^{2})^{2/3}}{5}\,\frac{\hbar^{2}}{m_e}\,n_e^{5/3}\]
  61. Expulsieur – Meissner Effect / Flux Expulsion Physics StickerPaper products \[\mathbf{B}_{\text{inside}} = 0\]\[B(x) = B_0\,e^{-x/\lambda_L}\]\[\lambda_L = \sqrt{\frac{m}{\mu_0 n_s e^2}}\]
  62. Fields Forever Pixel Sticker Sheet – 12 Physics StickersPaper products \[V(t) = V_0\sin(\omega t)\]\[\nabla\cdot\vec E = \frac{\rho}{\varepsilon_0}, \quad \nabla\cdot\vec B = 0\]\[\oint_S \vec E\cdot d\vec A = \frac{Q_{\text{enc}}}{\varepsilon_0}\]\[\mathcal{E} = -\frac{d\Phi_B}{dt}\]\[q v B = \frac{m v^2}{r} \;\Rightarrow\; r = \frac{m v}{q B}\]\[\mathbf{J}_d = \varepsilon_0\,\frac{\partial \mathbf{E}}{\partial t}\]\[F \propto -\,I_{\mathrm{coil}}\,I_{\mathrm{ring}}\]\[P = \frac{q^2 a^2}{6\pi\varepsilon_0 c^3}\]\[\cos\theta = \frac{1}{n\beta}, \qquad \beta > \frac{1}{n}\]\[\omega_c^{2} = \omega_+^{2} + \omega_z^{2} + \omega_-^{2}\]\[\Delta E = \frac{1}{2}\,\frac{C_1 C_2}{C_1 + C_2}\,(V_1 - V_2)^{2}\]
  63. Flickermoth, the Pink-Noise Moth Queen MugMug \[S(f) \propto \frac{1}{f^{\alpha}}, \qquad \alpha \approx 1\]\[S_y(f) \propto \frac{1}{f} \;\Rightarrow\; \sigma_y(\tau) = \text{const}\]\[\text{white FM: } \sigma_y(\tau) \propto \tau^{-1/2}\]
  64. Flukessa, the Second-Law Rebel MugMug \[\frac{P(\Sigma_t = A)}{P(\Sigma_t = -A)} = e^{A t}\]
  65. Forces & Fields Vol. 1 Pixel Sticker Sheet – 7 Physics StickersPaper products \[\cos\theta = \frac{1}{n\beta}, \qquad \beta > \frac{1}{n}\]\[P = \frac{q^2 a^2}{6\pi\varepsilon_0 c^3}\]\[\Delta E = \frac{1}{2}\,\frac{C_1 C_2}{C_1 + C_2}\,(V_1 - V_2)^{2}\]\[I = I_0\cos^2\theta\]\[q v B = \frac{m v^2}{r} \;\Rightarrow\; r = \frac{m v}{q B}\]\[m g v = U I\]\[\mathcal{E} = -\frac{d\Phi_B}{dt}\]
  66. Forces & Fields Vol. 2 Pixel Sticker Sheet – 7 Physics StickersPaper products \[p_{\mathrm{Minkowski}} = \frac{n\hbar\omega}{c},\quad p_{\mathrm{Abraham}} = \frac{\hbar\omega}{n c}\]\[\omega_c^{2} = \omega_+^{2} + \omega_z^{2} + \omega_-^{2}\]\[\frac{\sin\theta_1}{v_1} = \frac{\sin\theta_2}{v_2}\]\[I_s \propto \frac{1}{\lambda^4}\]\[\sigma_T = \frac{8\pi}{3}\,r_e^{2} = 6.652\,458\,7051(62)\times10^{-29}\ \mathrm{m}^{2}\]\[G = 6.674\,30(15)\times10^{-11}\ \mathrm{m^{3}\,kg^{-1}\,s^{-2}}\]\[\alpha = \left(\frac{A-1}{A+1}\right)^2\]
  67. Fritz Zwicky Sticker – Too Fast To Be Lit | Physics StickerPaper products \[\sigma^2 \sim \frac{GM}{R}\]\[M_{\mathrm{vir}} \approx \frac{\sigma^2 R}{G}\]
  68. Galileo Galilei Sticker – Telescope. Tea. Trouble with the Church. | Physics StickerPaper products \[d = \tfrac{1}{2}g t^{2}\]\[d_1 : d_2 : d_3 : \dots = 1 : 3 : 5 : \dots\]
  69. Graviton Whisper – Quantum Gravity / Force Carrier Physics T-ShirtT-Shirt \[\Box\,\bar h_{\mu\nu} = -\frac{16\pi G}{c^{4}}\,T_{\mu\nu}\]\[E = hf, \qquad m_{g} = 0 \ (\text{if it exists}),\ \ s = 2\]\[m_g \le 2.42\times10^{-23}\ \mathrm{eV}/c^{2}\quad\text{(LIGO–Virgo–KAGRA, GWTC-3, 90\% credible)}\]
  70. Gyrolla – Cyclotron Motion / Lorentz Force Physics StickerPaper products \[q v B = \frac{m v^2}{r} \;\Rightarrow\; r = \frac{m v}{q B}\]\[f_c = \frac{q B}{2\pi m}\]\[\frac{f_c}{B} \approx 15.2\ \text{MHz/T}\ (\text{proton})\]
  71. Hadron Brawler – Strong Nuclear Force / Quantum Chromodynamics Physics T-ShirtT-Shirt \[V(r) = -\frac{4}{3}\frac{\alpha_s \hbar c}{r} + \sigma r\]
  72. Harmonel, the Green-Pointer Imp MugMug \[\omega_{\text{out}} = 2\,\omega_{\text{in}} \;\Leftrightarrow\; \lambda_{\text{out}} = \frac{\lambda_{\text{in}}}{2}\]\[\frac{1064\ \text{nm}}{2} = 532\ \text{nm}\]
  73. Henrietta Swan Leavitt Sticker – The Blink Is the Ruler | Physics StickerPaper products \[M_V = -2.43\,(\log_{10} P - 1) - 4.05\]\[m - M = 5\log_{10}\frac{d}{10\,\mathrm{pc}}\]
  74. Hideki Yukawa Sticker – Heavy Ball. Short Game. | Physics StickerPaper products \[\begin{gathered} V(r) = -\frac{g^{2}}{4\pi}\,\frac{e^{-r/R}}{r} \\ R = \frac{\hbar}{m c} \end{gathered}\]\[\begin{aligned} R &= \frac{1}{\lambda} = 2\ \text{fm} \\ \Rightarrow\; mc^{2} &= \frac{\hbar c}{R} \approx 99\ \text{MeV} \\ &\approx 2\times10^{2}\,m_e c^{2} \end{aligned}\]
  75. Interfera – The Path Unchosen / Quantum Interference Physics T-ShirtT-Shirt \[P = \lvert\psi_1 + \psi_2\rvert^{2} = \lvert\psi_1\rvert^{2} + \lvert\psi_2\rvert^{2} + 2\,\mathrm{Re}\!\left(\psi_1^{*}\psi_2\right)\]\[\Delta y = \frac{\lambda L}{d}, \qquad \lambda = \frac{h}{p}\]
  76. Invertia – Negative Absolute Temperature / Population Inversion Physics StickerPaper products \[\frac{1}{T} = \frac{\partial S}{\partial E} < 0\]\[\frac{N_{\uparrow}}{N_{\downarrow}} = e^{-\Delta E/k_B T}\]\[T < 0 \;\Rightarrow\; N_{\uparrow} > N_{\downarrow}\]
  77. Isaac Newton Sticker – Gravity Hits Different | Physics StickerPaper products \[\vec F = \frac{d\vec p}{dt}\]\[F = \frac{G m_1 m_2}{r^{2}}\]
  78. Islandine, the Coulomb-Blockade Gatekeeper MugMug \[E_C = \frac{e^{2}}{2C} \gg k_B T\]
  79. It's All Spin Pixel Sticker Sheet – 12 Physics StickersPaper products \[t_{\mathrm{echo}} = 2\tau\]\[L = \frac{2 m_e\,\mu}{g\,e}\]\[M \propto \Omega\]\[\mu_B = \frac{e\hbar}{2m_e} = 9.274\,010\,0657(29)\times10^{-24}\ \mathrm{J/T}\]\[h = \frac{\mathbf{s}\cdot\mathbf{p}}{|\mathbf{s}|\,|\mathbf{p}|} = -1\]\[\bar n(\varepsilon) = \frac{1}{e^{(\varepsilon-\mu)/(k_B T)} - 1}\]\[\Delta B \approx \frac{\hbar}{g\,\mu_B\,\tau}\]\[F_z = \mu_z\,\frac{\partial B_z}{\partial z}\]\[\begin{aligned} R(2\pi)\,\psi &= e^{-i\,2\pi\,\hat{n}\cdot\boldsymbol{\sigma}/2}\,\psi \\ &= -\psi \end{aligned}\]\[\psi(1,2)=\frac1{\sqrt2}\bigl[\phi_a(1)\phi_b(2)-\phi_a(2)\phi_b(1)\bigr]\]\[V = -N\,\frac{\mathrm{d}\Phi}{\mathrm{d}t}\]\[L = I\omega\]
  80. James Clerk Maxwell Sticker – Field Goals Achieved | Physics StickerPaper products \[\nabla\cdot\vec E = \frac{\rho}{\varepsilon_0}, \quad \nabla\cdot\vec B = 0\]\[\nabla\times\vec E = -\frac{\partial\vec B}{\partial t}, \quad \nabla\times\vec B = \mu_0\vec J + \mu_0\varepsilon_0\frac{\partial\vec E}{\partial t}\]\[c = \frac{1}{\sqrt{\mu_0\varepsilon_0}}\]
  81. Jocelyn Bell Burnell Sticker – She Found Pulsars. They Gave Her Silence. | Physics StickerPaper products \[\bar\rho \gtrsim \frac{3\pi}{G P^{2}}\]\[\Delta t = \frac{e^{2}}{8\pi^{2}\varepsilon_0 m_e c}\,\mathrm{DM}\left(f_1^{-2} - f_2^{-2}\right)\]
  82. Lenzor – Lenz’s Law / Eddy-Current Braking Physics StickerPaper products \[\mathcal{E} = -\frac{d\Phi_B}{dt}\]\[m g = F_{\text{eddy}}(v_t) \propto \sigma\,v_t\]
  83. Libratrix – Lagrange Points / Three-Body Equilibrium Physics StickerPaper products \[r_{L2} \approx R\left(\frac{M_2}{3M_1}\right)^{1/3}\]\[r_{L2} \approx 1.5\times10^{6}\ \text{km}\]\[\frac{M_1}{M_2} > \frac{25+\sqrt{621}}{2} \approx 24.96\]
  84. Light & Optics Pixel Sticker Sheet – 12 Physics StickersPaper products \[I_s \propto \frac{1}{\lambda^4}\]\[\frac{\sin\theta_1}{v_1} = \frac{\sin\theta_2}{v_2}\]\[I = I_0\cos^2\theta\]\[\cos\theta = \frac{1}{n\beta}, \qquad \beta > \frac{1}{n}\]\[D_{\min} = 2\arcsin\!\left(n\sin 30^\circ\right) - 60^\circ\]\[n_o > n_{\mathrm{balsam}} > n_e\]\[\Delta\nu_{\mathrm{FSR}} = \frac{c}{2nL}\]\[\mathbf{F}_{\mathrm{grad}} \propto \nabla I\]\[\Delta n \propto E\]\[\lambda_{\mathrm{IR}} > \lambda_{\mathrm{red}} \approx 0.7\ \mu\mathrm{m}\]\[\Delta\alpha = \frac{2\omega D}{c}\]\[r = v\,\Delta t\]
  85. Light, Time & Relativity Pixel Sticker Sheet – 9 Physics StickersPaper products \[\Delta t = \gamma\,\tau, \qquad L = \frac{L_0}{\gamma}\]\[\frac{\Delta f}{f} \approx \frac{\Delta\Phi}{c^2} - \frac{v^2}{2c^2}\]\[\tau = 0\]\[\mathcal{E} = v B L\]\[\Delta\alpha = \frac{2\omega D}{c}\]\[\Delta t = \frac{\Delta d}{c}\]\[\theta \approx \frac{v}{c} \approx 20.5''\]\[p_{\mathrm{Minkowski}} = \frac{n\hbar\omega}{c},\quad p_{\mathrm{Abraham}} = \frac{\hbar\omega}{n c}\]\[h \approx \frac{\Delta L}{L}\]
  86. Lise Meitner Sticker – Split Happens | Physics StickerPaper products \[Q = \left(M_{\text{initial}} - M_{\text{final}}\right)c^{2}\]\[E_C = \frac{Z_1 Z_2 e^{2}}{4\pi\varepsilon_0\,d}\]
  87. Ludwig Boltzmann Sticker – There Are More Ways To Be A Mess. | Physics StickerPaper products \[S = k_B \ln W\]\[\begin{gathered} k_B = 1.380\,649\times10^{-23}\ \text{J/K} \\ (\text{exact since 2019}) \end{gathered}\]
  88. Lunelock, the Tidally Locked Speaker MugMug \[P_{\text{rot}} = P_{\text{orb}}\]
  89. Magnara – Magnus Effect Physics StickerPaper products \[\mathbf{F}_M = \alpha\,\boldsymbol{\omega}\times\mathbf{v}\]\[m\dot{\mathbf{v}} = m\mathbf{g} - b\mathbf{v} + \alpha\,\boldsymbol{\omega}\times\mathbf{v}\]
  90. Magnetron Twins – Electromagnetism / Polarity Lock Physics T-ShirtT-Shirt \[U = -\frac{\mu_0}{4\pi r^{3}}\left[3(\vec m_1\cdot\hat r)(\vec m_2\cdot\hat r) - \vec m_1\cdot\vec m_2\right]\]
  91. Magnidra, the Pogson Scale Keeper MugMug \[m_1 - m_2 = -2.5 \log_{10}\!\left(\frac{F_1}{F_2}\right)\]\[\Delta m = 5 \;\Leftrightarrow\; \frac{F_1}{F_2} = 100\]
  92. Maria Goeppert Mayer Sticker – A Full Floor Is Magic. | Physics StickerPaper products \[\begin{gathered} E_N = \hbar\omega\left(N + \tfrac{3}{2}\right) \\ \begin{aligned} g_N &= (N+1)(N+2) \\ &= 2,\,6,\,12,\,\ldots \end{aligned} \\ \Rightarrow\; \text{shells close at } 2,\,8,\,20 \end{gathered}\]\[\begin{gathered} V_{\ell s} = -C(r)\,\vec\ell\cdot\vec s \\ j = \ell\pm\tfrac12,\ \text{degeneracy } 2j+1 \\ \Rightarrow\ 28,\,50,\,82,\,126 \end{gathered}\]
  93. Marie Curie Sticker – She Literally Glowed Up | Physics StickerPaper products \[N(t) = N_0 e^{-\lambda t}\]\[t_{1/2} = \frac{\ln 2}{\lambda}, \qquad A = \lambda N\]
  94. Max Planck Sticker – He Quantized the Vibe | Physics StickerPaper products \[E = h\nu\]\[B_\nu(\nu,T) = \frac{2h\nu^{3}}{c^{2}}\,\frac{1}{e^{h\nu/(k_B T)} - 1}\]
  95. Michael Faraday Sticker – All Quiet In Here. | Physics StickerPaper products \[\oint_S \vec E\cdot d\vec A = \frac{Q_{\text{enc}}}{\varepsilon_0}\]\[\begin{gathered} \vec E_{\text{inside}} = 0 \\ (\text{empty cavity in a closed} \\ \text{conductor, electrostatic} \\ \text{equilibrium}) \end{gathered}\]
  96. Moderon – Neutron Moderation / Elastic Scattering Physics StickerPaper products \[\alpha = \left(\frac{A-1}{A+1}\right)^2\]\[\xi = 1 + \frac{\alpha\ln\alpha}{1-\alpha}\]\[n_{\text{coll}} \approx \frac{\ln(E_0/E_{\text{th}})}{\xi}\]
  97. Muonaut – Muon Time Dilation / Length Contraction Physics StickerPaper products \[\Delta t = \gamma\,\tau, \qquad L = \frac{L_0}{\gamma}\]\[\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}\]\[c\tau \approx 659\ \text{m}\]
  98. Neutrina Fade – Neutrino Ghost Matter Physics T-ShirtT-Shirt \[\cos\theta_C = \frac{1}{n\beta}\]\[P_{\nu_a\to\nu_b} = \sin^{2}(2\theta)\,\sin^{2}\!\left(\frac{\Delta m^{2}c^{4}L}{4\hbar c E}\right)\]
  99. Niels Bohr Sticker – Said Nothing Clearly. Explained Everything. | Physics StickerPaper products \[\begin{gathered} E_n = -\frac{R_\infty hc}{n^{2}} \\ R_\infty hc = 13.605\,693\,122\,990\ \text{eV} \end{gathered}\]\[h\nu = E_i - E_f\]
  100. Nightglowe, the Airglow Sleepwalker MugMug \[\text{H} + \text{O}_3 \to \text{OH}(v \le 9) + \text{O}_2\]\[\text{OH}(v') \to \text{OH}(v'') + h\nu\]
  101. Nikola Tesla Sticker – AC Slays DC Pixel Art | Physics StickerPaper products \[V(t) = V_0\sin(\omega t)\]\[\frac{V_s}{V_p} = \frac{N_s}{N_p}\]\[P_{\text{loss}} = I^{2}R\]
  102. Nimbryn, the Mie-Scattering Grey Lady MugMug \[x = \frac{2\pi r}{\lambda} \gg 1 \;\Rightarrow\; Q_{\text{ext}} \to 2\]
  103. Null Beacon – Cosmic Event Horizon / Causal Disconnect Physics T-ShirtT-Shirt \[d_{\text{EH}}(t) = a(t)\int_{t}^{\infty} \frac{c\,dt^{\prime}}{a(t^{\prime})}\]\[d_{\text{EH}} \to \frac{c}{H_\Lambda} \quad (\text{pure de Sitter})\]