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)

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