# Equations - G484 and G485

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F = Δp/Δt

Rate of change of momentum - F = Force (N); p = momentum (Ns); t = time (s)

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v = 2πr/T

Angular Velocity - v = velocity (m/s); r = radius (m); T = period (s)

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a = v²/r

Angular Acceleration - a = acceleration (m/s²); v = velocity (m/s); r = radius (m)

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F = mv²/r

Centripetal Force - F = Force (N); m = mass (kg); v = velocity (m/s); r = radius (m)

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F = GMm/r²

Gravitational Force Between Two Bodies - F = Force (N); G = 6.67e-11 (Nm²/kg²); M = (larger or orbited) mass (kg); m = (smaller) mass (kg); r = radius (m)

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g = F/m

Gravitational Field Strength - g = acceleration due to free fall (m/s²); F = Force (N); m = mass (kg)

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g = GM/r²

Gravitational Field Strength - g = acceleration due to free fall (m/s²); G = 6.67e-11 (Nm²/kg²); M = (larger or orbited) mass (kg); r = radius (m)

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T² = (4π²/GM)r³

Orbital Period - T = period (s); G = 6.67e-11 (Nm²/kg²); M = (larger or orbited) mass (kg); r = radius (m)

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f = 1/T

Definition of Frequency - f = frequency (Hz); T = period (s)

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ω = 2π/T = 2πf

Angular Frequency - ω = angular frequency (Hz); T = period (s); f = frequency (Hz)

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a = -(2πf)²x

Definition of Simple Harmonic Motion - a = acceleration (m/s²); f = frequency (Hz); x = displacement (m)

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x = Acos(2πft)x

Solution to Simple Harmonic Motion - x = displacement (m); A = amplitude (m); f = frequency (Hz); t = time (s)

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Vmax = (2πf)A

Max Velocity of Simple Harmonic Motion - Vmax = maximum velocity (m/s); A = amplitude (m); f = frequency (Hz)

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E = mcΔθ

Energy to raise a mass by θ°c/K - E = energy (J); c = specific heat capacity; θ = temperature (K)

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pV = NkT

Ideal Gas Law - p = pressure (N/m²); V = volume (m³); N = number of molecules in the gas; k = 1.38e-23; T = temperature (K)

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pV = nRT

Ideal Gas Law - p = pressure (N/m²); V = volume (m³); n = number of moles of gas; R = 8.31 (J/mol K); T = temperature (K)

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E = (3/2)kT

Mean Kinetic Energy of a Molecule - E = energy (J); k = 1.38e-23; T = temperature (K)

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E = F/Q

Electric Field Strength - E = Electric Field Strength (N/C); F = Force (N); Q = Charge (C)

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F = Qq/4πεr²

Coulomb's Law - F = force (N); Q = charge (C); q = test charge (C); ε = 8.85e-12 (C²/Nm²); r = radius (m)

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E = Q/4πεr²

Coulomb’s Law - E = Electric Field Strength (N/C); Q = charge (C); ε = 8.85e-12 (C²/Nm²); r = radius (m)

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E = V/d

Electric Field Strength - E = Electric Field Strength (N/C); V = voltage or p.d. (V); d = distance (m)

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F = BILsinθ

Force Produced by a Current in a Magnetic Field - F = force (N); B = magnetic flux density (T); I = current (A); L = length (m)

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F = BQv

Force on a Particle in a Uniform Magnetic Field - F = force (N); B = magnetic flux density (T); Q = charge (C); v = velocity (m/s)

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ϕ = BAcosθ

Magnetic Flux - ϕ = magnetic flux (Wb); B = magnetic flux density (T); A = area (m²)

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induced e.m.f. = - rate of change of magnetic flux linkage

Lenz's Law

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Vs/Vp = ns/np

Ideal Transformer - Vs = voltage on secondary coil (V); Vp = voltage on primary coil (V); ns = turns on secondary coil; np = turns on primary coil

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Q = VC

Charge of a Capacitor - Q = charge (C); V = voltage or p.d. (V); C = capacitance (F)

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W = (1/2)QV = (1/2)CV²

Work of a Capacitor - W = work (J); Q = charge (C); V = voltage or p.d. (V); C = capacitance (F)

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time constant = CR

Time Constant of a Capacitor - C = capacitance (F); R = resistance (Ω)

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x = x0e^(-1/CR)

Exponential Decay of a Capacitor - x = placeholder for Q or I or V; x0 = initial value of Q or I or V; t = time (s); C = capacitance (F); R = resistance (Ω)

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C = C1 + C2 + C3

Capacitors in Parallel - C = capacitance (F)

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1/C = 1/C1 + 1/C2 + 1/C3

Capacitors in Series - C = capacitance (F)

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A = λN

Activity of a Radioactive Source - A = activity (Bq); λ = decay constant; N = number of undecayed atoms

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A = A0e^(-λt)

Activity of Radioactive Decay - A = activity (Bq); λ = decay constant; t = time (s)

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N = N0e^(-λt)

Number of Undecayed Nuclei - N = number of undecayed atoms; N = number of undecayed atoms

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λ*(t1/2) = 0.693

Half-life - λ = decay constant; t1/2 = half life

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ΔE = Δmc²

Einstein’s Mass-Energy Equivalence - E = energy (J); m = mass (kg); c = speed of light (m/s)

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I = I0e^(-μx)

Attenuation of X-Ray Intensity - I = intensity; I0 = incident intensity; μ = linear attenuation coefficient; x = displacement

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Z = ρc

Specific Acoustic Impedance - Z = Specific acoustic impedance; ρ = density (kg/m³); c = speed of light (m/s)

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Ir/I0 = (Z2 - Z1)²/(Z2 + Z1)²

Intensity Reflection Coefficient - Ir = reflected intensity; I0 = incident intensity; Z = specific acoustic impedance

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Δλ/λ = v/c

Doppler Effect - λ = decay constant; v = velocity (m/s); c = speed of light (m/s)

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age of universe = 1/H0

Hubble Age or Characteristic Expansion Time - H0 = Hubble constant

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ρ0 = 3H0²/8πG

Critical Density of the Universe - ρ0 = critical density of the universe; H0 = Hubble constant; G = 6.67e-11 (Nm²/kg²)

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## Other cards in this set

### Card 2

#### Front

Angular Velocity - v = velocity (m/s); r = radius (m); T = period (s)

#### Back

v = 2πr/T

### Card 3

#### Front

Angular Acceleration - a = acceleration (m/s²); v = velocity (m/s); r = radius (m)

#### Back

### Card 4

#### Front

Centripetal Force - F = Force (N); m = mass (kg); v = velocity (m/s); r = radius (m)

#### Back

### Card 5

#### Front

Gravitational Force Between Two Bodies - F = Force (N); G = 6.67e-11 (Nm²/kg²); M = (larger or orbited) mass (kg); m = (smaller) mass (kg); r = radius (m)

#### Back

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