Physics Formula Reference Sheet
Comprehensive Reference for Secondary and Senior Secondary Physics (Grades 10 – 12)
1. Mechanics & Kinematics
Equations of Motion (Constant \(a\))
$$
v = u + at
$$
$$
s = ut + \frac{1}{2}at^2
$$
$$
v^2 = u^2 + 2as
$$
$$
s_n = u + \frac{a}{2}(2n – 1)
$$
Newton’s Laws & Momentum
$$
\vec{F}_{\text{net}} = \frac{d\vec{p}}{dt} = m\vec{a}
$$
$$
\vec{p} = m\vec{v}
$$
$$
\vec{J} = \Delta \vec{p} = \int \vec{F}\,dt = \vec{F}_{\text{avg}}\Delta t
$$
Friction & Circular Motion
$$
f_s \le \mu_s N, \quad f_k = \mu_k N
$$
$$
a_c = \frac{v^2}{r} = \omega^2 r
$$
$$
v_{\text{banked}} = \sqrt{r g \left(\frac{\mu + \tan\theta}{1 – \mu\tan\theta}\right)}
$$
2. Work, Energy & Rotation
Work, Energy & Power
$$
W = \int \vec{F} \cdot d\vec{r} = F d \cos\theta
$$
$$
K = \frac{1}{2}m v^2 = \frac{p^2}{2m}
$$
$$
U_g = mgh, \quad U_s = \frac{1}{2}kx^2
$$
$$
P = \frac{dW}{dt} = \vec{F}\cdot\vec{v}
$$
Rotational Mechanics
$$
\tau = \vec{r} \times \vec{F} = I\alpha
$$
$$
L = \vec{r} \times \vec{p} = I\omega
$$
$$
K_{\text{rot}} = \frac{1}{2}I\omega^2
$$
$$
I_{\text{parallel}} = I_{\text{cm}} + M d^2
$$
3. Gravitation & Fluids
Gravitation
$$
F = G\frac{m_1 m_2}{r^2}, \quad g = \frac{GM}{R^2}
$$
$$
U_g = -\frac{GMm}{r}, \quad v_e = \sqrt{\frac{2GM}{R}}
$$
$$
v_o = \sqrt{\frac{GM}{r}}, \quad T^2 = \left(\frac{4\pi^2}{GM}\right)r^3
$$
Fluid Mechanics
$$
P = P_0 + \rho g h
$$
$$
A_1 v_1 = A_2 v_2
$$
$$
P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}
$$
$$
F_v = 6\pi\eta r v \quad (\text{Stokes’ Law})
$$
4. Thermal Physics
Thermal Properties & Expansion
$$
\Delta L = L_0 \alpha \Delta T, \quad \Delta V = V_0 \gamma \Delta T
$$
$$
Q = mc\Delta T = mL
$$
$$
\frac{dQ}{dt} = -kA\frac{dT}{dx} = \sigma e A (T^4 – T_0^4)
$$
Thermodynamics & Kinetic Theory
$$
PV = nRT = N k_B T
$$
$$
v_{\text{rms}} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3k_B T}{m}}
$$
$$
\Delta Q = \Delta U + W, \quad W_{\text{iso}} = nRT\ln\left(\frac{V_f}{V_i}\right)
$$
$$
\eta = 1 – \frac{Q_C}{Q_H} = 1 – \frac{T_C}{T_H} \quad (\text{Carnot})
$$
5. Oscillations & Waves
Simple Harmonic Motion (SHM)
$$
\frac{d^2x}{dt^2} + \omega^2 x = 0 \implies x(t) = A\sin(\omega t + \phi)
$$
$$
T_{\text{spring}} = 2\pi\sqrt{\frac{m}{k}}, \quad T_{\text{pendulum}} = 2\pi\sqrt{\frac{L}{g}}
$$
$$
E_{\text{total}} = \frac{1}{2}kA^2 = \frac{1}{2}m\omega^2 A^2
$$
Wave Mechanics & Sound
$$
y(x,t) = A\sin(kx – \omega t), \quad v = \frac{\omega}{k} = f\lambda
$$
$$
v_{\text{string}} = \sqrt{\frac{T}{\mu}}, \quad v_{\text{sound}} = \sqrt{\frac{\gamma P}{\rho}}
$$
$$
f’ = f\left(\frac{v \pm v_o}{v \mp v_s}\right) \quad (\text{Doppler Effect})
$$
6. Electrostatics & Capacitance
Coulomb’s Law & Electric Potential
$$
\vec{F} = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r^2}\hat{r}
$$
$$
\Phi_E = \oint \vec{E}\cdot d\vec{A} = \frac{q_{\text{enclosed}}}{\varepsilon_0}
$$
$$
V = \frac{1}{4\pi\varepsilon_0}\frac{q}{r}, \quad \vec{E} = -\vec{\nabla}V
$$
Capacitors
$$
C = \frac{Q}{V} = \frac{\kappa\varepsilon_0 A}{d}
$$
$$
U_C = \frac{1}{2}CV^2 = \frac{Q^2}{2C} = \frac{1}{2}QV
$$
$$
C_{\text{parallel}} = \sum C_i, \quad \frac{1}{C_{\text{series}}} = \sum \frac{1}{C_i}
$$
7. Current & Magnetism
Current Electricity
$$
I = \frac{dQ}{dt} = n e A v_d, \quad V = IR
$$
$$
R = \rho\frac{L}{A}, \quad P = VI = I^2 R = \frac{V^2}{R}
$$
$$
\sum I_{\text{node}} = 0, \quad \sum \Delta V_{\text{loop}} = 0
$$
Magnetic Fields & Forces
$$
\vec{F}_B = q(\vec{v}\times\vec{B}), \quad \vec{F}_I = I(\vec{L}\times\vec{B})
$$
$$
d\vec{B} = \frac{\mu_0 I}{4\pi}\frac{d\vec{l}\times\hat{r}}{r^2}
$$
$$
\oint \vec{B}\cdot d\vec{l} = \mu_0 I_{\text{enclosed}}
$$
8. Induction & Alternating Current
Electromagnetic Induction
$$
\Phi_B = \int \vec{B}\cdot d\vec{A}
$$
$$
\mathcal{E} = -\frac{d\Phi_B}{dt} = (\vec{v}\times\vec{B})\cdot\vec{L}
$$
$$
U_L = \frac{1}{2}L I^2, \quad \mathcal{E}_L = -L\frac{dI}{dt}
$$
AC Circuits
$$
X_L = \omega L, \quad X_C = \frac{1}{\omega C}
$$
$$
Z = \sqrt{R^2 + (X_L – X_C)^2}
$$
$$
\omega_0 = \frac{1}{\sqrt{LC}}, \quad P_{\text{avg}} = V_{\text{rms}}I_{\text{rms}}\cos\phi
$$
9. Optics & Modern Physics
Ray & Wave Optics
$$
\frac{1}{f} = \frac{1}{v} + \frac{1}{u}, \quad \frac{1}{f} = (\mu – 1)\left(\frac{1}{R_1} – \frac{1}{R_2}\right)
$$
$$
n_1 \sin\theta_1 = n_2 \sin\theta_2, \quad \beta = \frac{\lambda D}{d}
$$
Quantum, Atomic & Nuclear
$$
E = hf = \frac{hc}{\lambda}, \quad hf = \Phi_0 + K_{\text{max}}
$$
$$
E_n = -\frac{13.6\,\text{eV}}{n^2}Z^2, \quad \lambda_{\text{dB}} = \frac{h}{p}
$$
$$
N(t) = N_0 e^{-\lambda t}, \quad T_{1/2} = \frac{\ln 2}{\lambda}
$$
10. Fundamental Physical Constants
| Constant | Symbol | Standard Value (SI Units) |
|---|---|---|
| Speed of light in vacuum | \(c\) | \(2.998 \times 10^{8}\,\text{m}\,\cdotp\,\text{s}^{-1}\) |
| Elementary charge | \(e\) | \(1.602 \times 10^{-19}\,\text{C}\) |
| Planck’s constant | \(h\) (\(\hbar = h/2\pi\)) | \(6.626 \times 10^{-34}\,\text{J}\,\cdotp\,\text{s}\) |
| Gravitational constant | \(G\) | \(6.674 \times 10^{-11}\,\text{N}\,\cdotp\,\text{m}^2\,\cdotp\,\text{kg}^{-2}\) |
| Permittivity of free space | \(\varepsilon_0\) | \(8.854 \times 10^{-12}\,\text{F}\,\cdotp\,\text{m}^{-1}\) |
| Permeability of free space | \(\mu_0\) | \(4\pi \times 10^{-7}\,\text{T}\,\cdotp\,\text{m}\,\cdotp\,\text{A}^{-1}\) |
| Boltzmann constant | \(k_B\) | \(1.381 \times 10^{-23}\,\text{J}\,\cdotp\,\text{K}^{-1}\) |
| Universal gas constant | \(R\) | \(8.314\,\text{J}\,\cdotp\,\text{mol}^{-1}\,\cdotp\,\text{K}^{-1}\) |
| Electron rest mass | \(m_e\) | \(9.109 \times 10^{-31}\,\text{kg} \approx 0.511\,\text{MeV}/c^2\) |
