Physics Formulas

Kinematics

v = v₀ + at—Velocity

x = x₀ + v₀t + ½at²—Displacement

v² = v₀² + 2a(x-x₀)—No time

x = ½(v₀+v)t—Average velocity

Free fall: a = g = 9.8 m/s²—Near Earth surface

Range = v₀²sin(2θ)/g—Projectile range

Max height = v₀²sin²θ/(2g)—Projectile

Forces & Newton's Laws

F = ma—Newton's 2nd law

W = mg—Weight

f = μN—Friction force

F₁₂ = -F₂₁—Newton's 3rd law

ΣF = 0 → equilibrium—Newton's 1st law

F_c = mv²/r—Centripetal force

F = -kx—Hooke's law (spring)

F = Gm₁m₂/r²—Universal gravitation

Energy & Work

W = Fd cos θ—Work done

KE = ½mv²—Kinetic energy

PE = mgh—Gravitational PE

PE = ½kx²—Elastic PE (spring)

W_net = ΔKE—Work-energy theorem

KE₁+PE₁ = KE₂+PE₂—Conservation of energy

P = W/t = Fv—Power

Efficiency = useful out / total in—

Momentum & Collisions

p = mv—Momentum

J = FΔt = Δp—Impulse

Σp_before = Σp_after—Conservation of momentum

Elastic: KE conserved—

Inelastic: KE not conserved—

Perfectly inelastic: objects stick—m₁v₁=(m₁+m₂)v_f

Thermodynamics

Q = mcΔT—Heat transfer

Q = mL—Latent heat (phase change)

PV = nRT—Ideal gas law

ΔU = Q - W—1st law of thermodynamics

ΔS ≥ 0 (isolated system)—2nd law

η = 1 - T_cold/T_hot—Carnot efficiency

k_B = 1.38×10⁻²³ J/K—Boltzmann constant

KE_avg = (3/2)k_BT—Kinetic theory

Waves & Sound

v = fλ—Wave speed

f = 1/T—Frequency

v_sound ≈ 343 m/s (air, 20°C)—

dB = 10 log₁₀(I/I₀)—Sound intensity level

I₀ = 10⁻¹² W/m²—Threshold of hearing

Doppler: f' = f(v±v_obs)/(v∓v_src)—

Standing wave: L = nλ/2—Fixed both ends

Beats: f_beat = |f₁-f₂|—

Electricity

V = IR—Ohm's law

P = IV = I²R = V²/R—Electrical power

F = kq₁q₂/r²—Coulomb's law

E = F/q = kQ/r²—Electric field

V = kQ/r—Electric potential

C = Q/V = ε₀A/d—Capacitance

Series R: R_T = R₁+R₂+...—

Parallel R: 1/R_T = 1/R₁+1/R₂+...—

Series C: 1/C_T = 1/C₁+1/C₂+...—

Parallel C: C_T = C₁+C₂+...—

Magnetism & EM

F = qvB sin θ—Force on moving charge

F = BIL sin θ—Force on current-carrying wire

Φ_B = BA cos θ—Magnetic flux

EMF = -dΦ_B/dt—Faraday's law

B = μ₀I/(2πr)—Field around wire

c = 1/√(μ₀ε₀) = 3×10⁸ m/s—Speed of light

E = hf—Photon energy

Optics

n = c/v—Index of refraction

n₁ sin θ₁ = n₂ sin θ₂—Snell's law

θ_c = arcsin(n₂/n₁)—Critical angle (TIR)

1/f = 1/dₒ + 1/dᵢ—Thin lens / mirror eq

M = -dᵢ/dₒ = hᵢ/hₒ—Magnification

dsinθ = mλ—Diffraction grating

Nuclear & Constants

E = mc²—Mass-energy equivalence

N = N₀e⁻λt—Radioactive decay

t₁/₂ = ln2/λ—Half-life

g = 9.81 m/s²—Gravity

G = 6.674×10⁻¹¹ Nm²/kg²—Gravitational const

k = 8.99×10⁹ Nm²/C²—Coulomb's const

e = 1.602×10⁻¹⁹ C—Electron charge

h = 6.626×10⁻³⁴ J·s—Planck's const

c = 2.998×10⁸ m/s—Speed of light

μ₀ = 4π×10⁻⁷ T·m/A—Permeability

ε₀ = 8.854×10⁻¹² F/m—Permittivity

R = 8.314 J/(mol·K)—Gas constant

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