THERMODYNAMICS
Temperature conversion: C = (F – 32) × 5/9 F = C × 9/5 + 32 K = C + 273
Heat energy: Q = mcT (Q = heat, m = mass, c = specific heat capacity, T = temperature change)
Heat transfer rate: Q/t = kA(T2 – T1) / d (k = thermal conductivity, A = area, d = thickness)
Ideal Gas Law: PV = nRT (P = pressure, V = volume, n = moles, R = 8.314, T = temperature in Kelvin)
Boyle’s Law: P1V1 = P2V2
Charles’s Law: V1/T1 = V2/T2
First Law of Thermodynamics: Q = U + W (Heat added = change in internal energy + work done)
Efficiency of heat engine: Efficiency = 1 – (Tc / Th) (Tc = cold temperature, Th = hot temperatur
WAVES & OPTICS
Wave speed: v = fλ (v = speed, f = frequency, λ = wavelength)
Period and frequency: T = 1/f
Speed of light: c = 3 × 10⁸ m/s
Snell’s Law (refraction): n1 × sin(θ1) = n2 × sin(θ2)
Refractive index: n = c / v
Mirror equation: 1/f = 1/v + 1/u
Lens equation: 1/f = 1/v – 1/u
Magnification: m = image height / object height = v / u
Diffraction grating: dsin(θ) = nλ
Doppler effect: f = f0 × (v + vo) / (v – vs) (vo = observer velocity, vs = source velocity
ELECTROMAGNETISM
Coulomb’s Law: F = kq1q2 / r² (k = 9 × 10⁹, q = charge, r = distance)
Electric field: E = F / q E = kQ / r²
Electric potential: V = kQ / r
Ohm’s Law: V = IR (V = voltage, I = current, R = resistance)
Power: P = IV = I²R = V²/R
Resistors in series: R = R1 + R2 + R3
Resistors in parallel: 1/R = 1/R1 + 1/R2 + 1/R3
Capacitance: C = Q / V
Energy stored in capacitor: E = ½CV²
Magnetic force on a charge: F = qvB × sin(θ)
Magnetic force on a wire: F = BIL × sin(θ)
Faraday’s Law: EMF = -N × dΦ/dt (N = number of turns, Φ = magnetic flux)
Transformer equation: V1/V2 = N1/N2
MODERN PHYSICS
Einstein’s energy-mass: E = mc²
Photon energy: E = hf (h = 6.626 × 10⁻³⁴ J·s, Planck’s constant)
de Broglie wavelength: λ = h / mv
Photoelectric effect: KE = hf – φ (φ = work function)
Radioactive decay: N = N0 × e^(-λt)
Half life: T½ = 0.693 / λ
Einstein’s special relativity: t = t0 / sqrt(1 – v²/c²) L = L0 × sqrt(1 – v²/c²)
CLASSICAL MECHANICS
MOTION & KINEMATICS
v = u + at (final velocity = initial velocity + acceleration × time)
s = ut + ½at² (displacement = initial velocity × time + half × acceleration × time²)
v² = u² + 2as (final velocity² = initial velocity² + 2 × acceleration × displacement)
s = (u + v) / 2 × t (displacement = average velocity × time)
a = (v – u) / t (acceleration = change in velocity / time)
NEWTON’S LAWS & FORCE
F = ma (Force = mass × acceleration)
Weight = mg (g = 9.8 m/s²)
Action = -Reaction (every force has an equal and opposite force)
F(net) = F1 + F2 + F3… (net force = sum of all forces)
WORK, ENERGY & POWER
W = F × d × cos(θ) (Work = Force × distance × angle)
KE = ½mv² (Kinetic Energy = half × mass × velocity²)
PE = mgh (Potential Energy = mass × gravity × height)
Total Mechanical Energy = KE + PE = constant (when no friction)
Power = W / t (Power = work done / time)
Power = F × v (Power = Force × velocity)
Efficiency = (Useful Output / Total Input) × 100%
MOMENTUM & IMPULSE
p = mv (momentum = mass × velocity)
Impulse = F × t (Impulse = Force × time)
Impulse = change in momentum F × t = mv – mu
Conservation of Momentum: m1u1 + m2u2 = m1v1 + m2v2
GRAVITATION
F = G × m1 × m2 / r² (gravitational force between two masses)
G = 6.674 × 10⁻¹¹ N m² / kg²
g = GM / r² (gravitational field strength)
Escape velocity = sqrt(2GM / r)
Orbital velocity = sqrt(GM / r)
T² = (4π² / GM) × r³ (Kepler’s Third Law)