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physics — all 48 formulas

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Motion in a Straight Line3 formulas

First Equation of Motion

v=u+atv = u + at

Final velocity after time t

Units: m/s

Second Equation of Motion

s=ut+12at2s = ut + \frac{1}{2}at^2

Displacement in time t

Units: m

Third Equation of Motion

v2=u2+2asv^2 = u^2 + 2as

Velocity–displacement relation

Units: m/s

Laws of Motion2 formulas

Newton's Second Law

F=maF = ma

Net force equals mass × acceleration

Units: N

Friction Force

f=μNf = \mu N

µ = coefficient of friction, N = normal force

Units: N

Work, Energy & Power4 formulas

Kinetic Energy

KE=12mv2KE = \frac{1}{2}mv^2

Energy of a moving body

Units: J

Work Done

W=Fscos⁡θW = Fs\cos\theta

Work by force F over displacement s

Units: J

Power

P=Wt=FvP = \frac{W}{t} = Fv

Rate of doing work

Units: W

Conservation of Energy

KE+PE=constantKE + PE = \text{constant}

Total mechanical energy is conserved

Units: J

System of Particles & Rotational Motion2 formulas

Centripetal Force

Fc=mv2r=mrω2F_c = \frac{mv^2}{r} = mr\omega^2

Force directed toward centre of circle

Units: N

Angular Velocity

ω=2πT=2πf\omega = \frac{2\pi}{T} = 2\pi f

Angular speed of circular motion

Units: rad/s

Gravitation4 formulas

Newton's Law of Gravitation

F=Gm1m2r2F = \frac{Gm_1 m_2}{r^2}

Gravitational force between two masses

Units: N

Acceleration due to Gravity

g=GMR2g = \frac{GM}{R^2}

g at Earth's surface

Units: m/s²

Escape Velocity

ve=2GMRv_e = \sqrt{\frac{2GM}{R}}

Minimum speed to escape Earth's gravity

Units: m/s

Orbital Velocity

vo=GMrv_o = \sqrt{\frac{GM}{r}}

Speed of satellite at radius r

Units: m/s

Oscillations3 formulas

Time Period — Spring

T=2πmkT = 2\pi\sqrt{\frac{m}{k}}

Oscillation period of spring-mass system

Units: s

Time Period — Pendulum

T=2πLgT = 2\pi\sqrt{\frac{L}{g}}

Oscillation period of simple pendulum

Units: s

SHM Displacement

x=Asin⁡(ωt+ϕ)x = A\sin(\omega t + \phi)

Position in simple harmonic motion

Units: m

Waves2 formulas

Wave Speed

v=fλv = f\lambda

Speed = frequency × wavelength

Units: m/s

Speed of Sound in Gas

v=γRTMv = \sqrt{\frac{\gamma RT}{M}}

γ = adiabatic index, M = molar mass

Units: m/s

Thermodynamics3 formulas

Ideal Gas Law

PV=nRTPV = nRT

P=pressure, V=volume, n=moles, T=temp

Units: Pa·m³

First Law of Thermodynamics

ΔU=Q−W\Delta U = Q - W

Change in internal energy

Units: J

Efficiency of Carnot Engine

η=1−T2T1\eta = 1 - \frac{T_2}{T_1}

Max efficiency between temperatures T₁ > T₂

Units: %

Electric Charges & Fields2 formulas

Coulomb's Law

F=kq1q2r2F = \frac{kq_1 q_2}{r^2}

k = 9×10⁹ N·m²/C²

Units: N

Electric Field

E=Fq=kQr2E = \frac{F}{q} = \frac{kQ}{r^2}

Field due to point charge Q

Units: N/C

Electrostatic Potential & Capacitance2 formulas

Electric Potential

V=kQrV = \frac{kQ}{r}

Potential due to point charge Q

Units: V

Capacitance

C=QV=ε0AdC = \frac{Q}{V} = \frac{\varepsilon_0 A}{d}

Charge stored per unit voltage (parallel plate)

Units: F

Current Electricity3 formulas

Ohm's Law

V=IRV = IR

Voltage = Current × Resistance

Units: V

Power (Electrical)

P=VI=I2R=V2RP = VI = I^2R = \frac{V^2}{R}

Electrical power dissipated

Units: W

Resistivity

R=ρLAR = \frac{\rho L}{A}

ρ = resistivity, L = length, A = cross-section

Units: Ω

Moving Charges & Magnetism3 formulas

Lorentz Force

F=qvBsin⁡θF = qvB\sin\theta

Force on charge moving in magnetic field

Units: N

Force on Current-Carrying Wire

F=BILsin⁡θF = BIL\sin\theta

Force on wire of length L in field B

Units: N

Magnetic Moment

M=nIAM = nIA

n=turns, I=current, A=area

Units: A·m²

Electromagnetic Induction3 formulas

Faraday's Law (EMF)

ε=−dΦdt\varepsilon = -\frac{d\Phi}{dt}

Induced EMF = rate of change of flux

Units: V

Magnetic Flux

Φ=BAcos⁡θ\Phi = BA\cos\theta

Flux through area A at angle θ to field B

Units: Wb

Motional EMF

ε=BLv\varepsilon = BLv

EMF of conductor moving at speed v

Units: V

Ray Optics & Optical Instruments5 formulas

Mirror Formula

1f=1v+1u\frac{1}{f} = \frac{1}{v} + \frac{1}{u}

Focal length from image/object distances

Units: m

Magnification (Mirror)

m=−vum = -\frac{v}{u}

Linear magnification (negative = inverted)

Units: —

Lens Formula

1f=1v−1u\frac{1}{f} = \frac{1}{v} - \frac{1}{u}

Thin lens equation

Units: m

Snell's Law

n1sin⁡θ1=n2sin⁡θ2n_1 \sin\theta_1 = n_2 \sin\theta_2

Refraction at interface

Units: —

Lens Power

P=1fP = \frac{1}{f}

Power of a lens (f in metres)

Units: D (dioptre)

Dual Nature of Radiation & Matter2 formulas

Photoelectric Effect

E=hf=ϕ+12mvmax2E = hf = \phi + \frac{1}{2}mv^2_{max}

h = 6.626×10⁻³⁴ J·s, φ = work function

Units: J

de Broglie Wavelength

λ=hmv=hp\lambda = \frac{h}{mv} = \frac{h}{p}

Matter wave wavelength

Units: m

Atoms2 formulas

Energy of nth Orbit (H-atom)

En=−13.6n2 eVE_n = -\frac{13.6}{n^2}\text{ eV}

Energy levels of hydrogen atom

Units: eV

Radius of nth Orbit (H-atom)

rn=0.529×n2 A˚r_n = 0.529 \times n^2 \text{ Å}

Bohr radius for hydrogen

Units: Å

Nuclei3 formulas

Mass-Energy Equivalence

E=mc2E = mc^2

c = 3×10⁸ m/s

Units: J

Radioactive Decay

N=N0e−λtN = N_0 e^{-\lambda t}

N = remaining nuclei after time t

Units: atoms

Half-Life

t1/2=0.693λt_{1/2} = \frac{0.693}{\lambda}

Time for half the nuclei to decay

Units: s

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