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A Level Physics > Formulas > Flashcards

Formulas Flashcards

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1
Q

Arc length

A

s = rθ

(s) arc length [m]
(r) radius of circle [m]
(θ) angular displacement [rad]

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2
Q

Angular speed

A

ω = ∆θ / ∆t

(ω) angular speed [rad s⁻¹]
(θ) angular displacement [rad]
(t) time taken [s]

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3
Q

Angular speed equation for one revolution

A

ω = 2π / T

(ω) angular speed [rad s⁻¹]
(2π) angle rotated through by object in one revolution [rad]
(T) period/time to make one revolution [s]

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4
Q

Equation relating speed and angular speed

A

v = ωr

(v) speed [ms⁻¹]
(ω) angular speed [rad s⁻¹]
(r) radius [m]

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5
Q

Acceleration equations in circular motion (2)

A

a = v²/r or a = ω²r

(a) acceleration [ms⁻²]
(v) speed [ms⁻¹]
(r) radius [m]
(ω) angular velocity [rad s⁻¹]

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6
Q

Combining Newton’s second law and acceleration equations in circular motion

A

F = ma
a = v²/r or a = ω²r

∴

Fc = mv²/r or mω²r

(F) force [N]
(a) acceleration [ms⁻²]
(v) speed [ms⁻¹]
(r) radius [m]
(ω) angular velocity [rad s⁻¹]
(Fc) centripetal force [N]
(m) mass [kg]

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7
Q

Calculating orbital speed

A

F = ma
F = mv²/r

∴

ma = mv²/r
a = v²/r

(F) force [N]
(m) mass [kg]
(a) acceleration [ms⁻²]
(v) speed [ms⁻¹]
(r) radius [m]

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8
Q

Angular frequency equation

A

ω = 2πf

(ω) angular frequency [rad s⁻¹]
(f) frequency [Hz]

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9
Q

Equations of s.h.m

A

x = x₀sin ωt or x = x₀cos ωt

sine version used when x (displacement curve) = 0 at t = 0

cosine version used when x (displacement curve) = x₀ at t = 0

(x) displacement [m]
(x₀) max displacement [m]
(ω) angular frequency [rad s⁻¹]
(t) time [s]

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10
Q

Acceleration and displacement formula s.h.m

A

a = -ω²x

(a) acceleration [ms⁻²]
(ω) angular frequency [rad s⁻¹]
(x) displacement [m]

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11
Q

Equation for velocity in s.h.m

A

v = v₀cos ωt

cosine version used as the velocity is at a maximum when t = 0

(v) velocity [ms⁻¹]
(v₀) max velocity [ms⁻¹]
(ω) angular frequency [rad s⁻¹]
(t) time [s]

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12
Q

Speed of an oscillator (2)

A

v = (±)ω √x₀² - x²

v₀ = ωx₀

(v) velocity [ms⁻¹]
(ω) angular frequency [rad s⁻¹]
(x₀) max displacement [m]
(x) displacement [m]
(v₀) max velocity [ms⁻¹]

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13
Q

Total energy of a system undergoing s.h.m

A

E = 1/2mv₀² and v₀ = ωx₀

∴

E = 1/2mω²x₀²

(E) maximum kinetic energy and total energy of system [J]
(m) mass [kg]
(v₀) max velocity [ms⁻¹]
(ω) angular frequency [rad s⁻¹]
(x₀) max displacement [m]

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14
Q

Internal energy

A

∆U = q + w

(U) increase in internal energy [J]
(q) energy supplied by heating [J]
(w) work done on the system [J]

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15
Q

Work done when the volume of a gas changes at constant pressure

A

F = p x A
W = F x d

∴

W = p∆V

(F) force [N]
(p) pressure [kgm⁻³]
(A) area [m²]
(W) work done [J]
(V) volume [m³]

Note:
true if gas is expanding against pressure of atmosphere which changes only very slowly

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16
Q

Conversion between celsius and kelvin

A

θºC = T (K) - 273.15
T(K) = θºC + 273.15

(θ) temperature in ºC
(T) temperature in K

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17
Q

Specific heat capacity (2)

A

E = mc∆θ or Q = mc∆T

or

specific heat capacity = energy supplied / mass temperature change

(E) energy supplied [J]
(m) mass [kg]
(c) specific heat capacity [Jkg⁻¹ºC⁻¹]
(θ) temperature [ºC]
(Q) thermal energy supplied [J]
(T) temperature [K]

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18
Q

Energy formula involving power

A

E = p x t

(E) energy [J]
(p) power [W]
(t) time [s]

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19
Q

Specific latent heat (2)

A

E = mL or Q = mL

or

specific latent heat = rate of supply of energy / rate of loss of mass

(E) energy required to melt or vapourise [J]
(m) mass [kg]
(L) specific latent heat [Jkg⁻¹]
(Q) thermal energy required to melt or vapourise [J]

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20
Q

Number of atoms in specific mass of a substance

A

number of atoms in a substance

specific mass of substance / mass of a single atom of that substance

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21
Q

Number of moles (2)

A

For a specific mass of a substance:
number of atoms in a specific weight of the substance / avogadro constant

Given molar mass:
mass / molar mass

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22
Q

Boyle’s law

A

pV = constant

p₁V₁ = p₂V₂

(p) pressure [kgm⁻³]
(V) volume [m³]

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23
Q

Charles’ law

A

V/T = constant

V₁/T₁ = V₂/T₂

(V) volume [m³]
(T) temperature [K]

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24
Q

Key equation for fixed mass of gas

A

pV/T = constant

p₁V₁/T₁ = p₂V₂/T₂

(p) pressure [kgm⁻³]
(V) volume [m³]
(T) temperature [K]

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25
Q

Equations of state (2)

A

pV = nRT or pV = NkT

(p) pressure [kgm⁻³]
(V) volume [m³]
(n) number of moles [mol]
(R) universal molar gas constant [Jmol⁻¹K⁻¹]
(T) temperature [K]
(N) number of molecules [mol]
(k) Boltzmann constant [JK⁻¹]

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26
Q

Number of molecules

A

number of molecules = number of moles x Avogadro’s constant

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27
Q

Pressure formula derivation

A

F = ∆mv/t
P = F/A

(F) force [N]
(∆mv) change in momentum [kgms⁻¹]
(p) pressure [kgm⁻³]
(A) area [m²]

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28
Q

Pressure of an ideal gas (3)

A

p = 1/3 (Nm/V) < c >²

or

pV = 1/3Nm< c >²

Nm/V is equal to the density of a gas
∴
p = 1/3 p < c >²

(p) pressure [kgm⁻³]
(N) number of molecules [mol]
(m) mass [kg]
(V) volume [m³]
(< c >²) mean square speed of molecules [(m/s)²]

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29
Q

Boltzmann constant equation

A

k = R/Nᴀ

(k) Boltzmann constant
(R) universal molar gas constant [Jmol⁻¹K⁻¹]
(Nᴀ) Avogadro’s constant

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30
Q

Kinetic energy formula from Boltzmann constant

A

1/2m< c> ² = 3/2kT

(m) mass [kg]
(< c >²) mean square speed of molecules [(m/s)²]
(k) Boltzmann constant
(T) temperature [K]

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31
Q

Root-mean-square-speed

A

cᵣ.ₘ.ₛ = √< c >²

(cᵣ.ₘ.ₛ) root-mean-square-speed [ms⁻¹]
(< c >²) mean square speed of

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32
Q

Newton’s law of gravitation

A

F = [ Gm₁m₂ ] / r²

(F) force [N]
(G) gravitational constant [Nm²kg⁻²]
(m) mass [kg]
(r) radius / centre-to-centre separation [m]

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33
Q

Gravitational field due to a point mass

A

g = F / m
F = [ Gm₁m₂ ] / r²

∴

g = GM/r²

(g) gravitational field strength [Nkg⁻¹]
(F) force [N]
(m) mass [kg]
(G) gravitational constant [Nm²kg⁻²]
(r) radius * of larger object / centre-to-centre separation / distance from mass [m]
(M) mass [kg] * of larger object

negative sign may be omitted

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34
Q

Gravitational potential (2)

A

Φ = - GM/r

∆Φ = - GM (1/r₁ - 1/r₂)

(Φ) gravitational potential [Jkg⁻¹]
(G) gravitational constant [Nm²kg⁻²]
(M) mass [kg]
(r) distance from mass [m]

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35
Q

Orbit speed

A

F = mv²/r and F = [ Gm₁m₂ ] / r²

∴

v² = GM / r

(F) force [N]
(m) mass [kg]
(v) speed [ms⁻¹]
(r) radius [m]
(G) gravitational constant [Nm²kg⁻²]
(r) radius / centre-to-centre separation [m]

36
Q

Orbital period

A

v = 2πr/T

∴

v² = (4π²r²/T²) = GM / r

∴

T² = (4π²/GM)r³

(v) speed [ms⁻¹]
(r) radius [m]
(T) period [s]
(G) gravitational constant [Nm²kg⁻²]
(M) mass [kg]

37
Q

Electric field strength

A

E = F/Q

(E) electric field strength [NC⁻¹]
(F) force on the charge [N]
(Q) charge [C]

38
Q

Strength of a uniform field between two parallel metal plates

A

E = ∆V/∆d

(E) electric field strength [Vm⁻¹]
(V) voltage [V]
(d) separation [m]

39
Q

Force on a charge

A

F = QE and F = -QV/d

∴

F = eV/d

(F) force on the charge [N]
(Q) charge [C]
(E) electric field strength [NC⁻¹]
(V) voltage [V]
(d) separation [m]
(e) electron with charge -e [e]

40
Q

Coulomb’s law (3)

A

F = [ kQ₁Q₂ ] /r² and k = 1 / 4πε₀

∴

F = Q₁Q₂ / 4πε₀r²

(F) force between 2 charges [N]
(k) permittivity of free space [Fm⁻¹]
(Q) charge [C]
(r) distance between centres [m]

41
Q

Electric field strength for a radial field

A

E = Q / 4πε₀r²

(E) electric field strength due to a point charge [NC⁻¹]
(Q) charge [C]
(ε₀) electrical constant [8.85 x 10⁻¹² Fm⁻¹]
(r) distance from the point [m]

42
Q

Work done in moving charge

A

W = QV

(W) work done in moving charge [J]
(Q) charge [C]
(V) voltage [V]

43
Q

Electric potential in a radial field due to a point charge

A

V = Q / 4πε₀r

(V) electric potential [V]
(Q) charge [C]
(ε₀) electrical constant [8.85 x 10⁻¹² Fm⁻¹]
(r) distance from the point [m]

44
Q

Potential energy of a pair of point charges

A

Eₚ = Qq / 4πε₀r

(Eₚ) potential energy of the pair of point charges [J or eV]
(Q) point charge [C]
(q) point charge [C]
(ε₀) electrical constant [8.85 x 10⁻¹² Fm⁻¹]
(r) distance between the point charges [m]

45
Q

Potential difference between 2 points from a charge

A

∆V = Q / 4πε₀[1/r₁ - 1/r₂]

(V) electric potential [V]
(Q) charge [C]
(ε₀) electrical constant [8.85 x 10⁻¹² Fm⁻¹]
(r) distance from the point [m]

46
Q

Capacitance

A

C = Q/V

(C) capacitance [F]
(Q) magnitude of charge on each of the capacitor’s plates [C]
(V) potential difference across the capacitor [V]

47
Q

Work done in charging up a capacitor

A

W = 1/2 QV
W = 1/2 CV²
W = 1/2 Q²/C

(W) work done by charging a capacitor [J]
(Q) charge [C]
(V) voltage / potential difference [V]
(C) capacitance [F]

48
Q

Capacitors in parallel including derivation

A

Cₜₒₜₐₗ = C₁ + C₂ + C₃

(C) capacitance [F]

Derivation:
Q = Q₁ + Q₂ = C₁V + C₂V
Q = (C₁ + C₂)V

∴

Cₜₒₜₐₗ = C₁ + C₂ + C₃ …

49
Q

Capacitors in series including derivation

A

1/Cₜₒₜₐₗ = 1/C₁ + 1/C₂ + 1/C₃

(C) capacitance [F]

Derivation:
V₂ = Q / C₁ and V₂ = Q / C₂
V = Q / Cₜₒₜₐₗ

V = V₁ + V₂

Q/Cₜₒₜₐₗ + Q/C₁ + Q/C₂

∴

1/Cₜₒₜₐₗ = 1/C₁ + 1/C₂ + 1/C₃ …

50
Q

Capacitance of isolated bodies (2)
for conducting spheres

A

V = [1/4πε₀] [Q/r]

C = Q / V

∴

C = 4πε₀r

(V) voltage / potential difference [V]
(ε₀) electrical constant [8.85 x 10⁻¹² Fm⁻¹]
(Q) charge [C]
(r) radius [m]
(C) capacitance [F]

51
Q

Time constant for a capacitor discharging

A

τ = RC

(τ) time constant [s]
(R) resistance (Ω)
(C) capacitance [F]

52
Q

Exponential decay of charge on a capacitor (3)

A

I = I₀ exp (-[t/RC])
Q = Q₀ exp (-[t/RC])
V = V₀ exp (-[t/RC])

(I) current [A]
(I₀) initial current [A]
(t) time [s]
(R) resistance (Ω)
(C) capacitance [F]
(Q) charge [C]
(Q₀) initial charge [C]
(V) p.d [V]
(V₀) p.d [V]

exp means take ln from both sides,
side with exp just becomes the fraction {-[t/RC]}, and the other side becomes ln(__).

53
Q

Force on the conductor (only when the conductor is at right-angles to the magnetic field)

A

F = BIL

(F) force on conductor [N]
(B) magnetic flux density of uniform field [T]
(I) current current in conductor [A]
(L) length of conductor in uniform magnetic field [m]

54
Q

Force on a current carrying conductor

A

F = BIL sinθ

(F) force on conductor [N]
(B) magnetic flux density of uniform field [T]
(I) current current in conductor [A]
(L) length of conductor in uniform magnetic field [m]

55
Q

Magnetic force experienced by a charged particle

A

F = BQv sinθ

(F) magnetic force [N]
(B) magnetic flux density of uniform field [T]
(Q) charge on the particle [C]
(v) velocity of particle [ms⁻¹]

56
Q

Orbiting charged particles

A

Fc = mv²/r and BQv = mv²/r

∴

r = mv/BQ and p = BQ*r

(Fc) centripetal force [N]
(m) mass [kg]
(v) speed [ms⁻¹]
(r) radius [m]
(B) magnetic flux density of uniform field [T]
(Q) charge on the particle [C]
(v) velocity of particle [ms⁻¹]
(p) momentum [kgms⁻¹]

Q* charge can be replaced with e, if the charged particle is an electron

57
Q

Charge to mass ratio of electron

A

e V𝒸ₐ = 1/2mₑv² and r = mₑv/Be

∴

e / mₑ = 2V𝒸ₐ / r²B²

(e) elementary charge [C]
(V𝒸ₐ) p.d between the cathode and the anode [V]
(m) mass [m]
(v) velocity [ms⁻¹]
(r) radius of orbit [m]
(B) magnetic flux density field [T]

58
Q

Formula combining magnetic and electric force

A

eE = Bev

∴

v = E/B

E = V/d

∴

v = V/Bd

(e) elementary charge [C]
(E) electric field strength [NC⁻¹]
(B) magnetic flux density field [T]
(v) velocity [ms⁻¹]
(V) voltage [V]
(d) separation [m]

59
Q

Hall voltage equation including derivation

A

Vʜ = BI / ntq

(Vʜ) hall voltage [V]
(B) magnetic flux density of field [T]
(I) current current in conductor [A]
(n) number density of charge carriers
(t) thickness of slice [m]
(q) charge of an individual charge carrier [C]

Derivation:
eE = Bev
eVʜ / d = Bev
eVʜ / d = BeI/nAe
Vʜ = BId/nAe
A = d x t

∴

Vʜ = BI / ntq

60
Q

Magnetic flux linkage (2)

A

Magnetic flux linkage =
NΦ
or
BANcosθ

(N) number of turns for coil
(Φ) magnetic flux [Wb]
(B) magnetic flux density [T]
(A) cross-sectional area [m²]
(θ) angle between normal to the area and magnetic field [º]

61
Q

Induced electromagnetic force (2)

A

E = - (∆(NΦ) / ∆t)

(E) magnitude of induced e.m.f [V]
(N) number of turns for coil
(Φ) magnetic flux [Wb]
(t) time [s]
(-) present due to Lenz’s law, necessary to emphasise principle of conservation of energy

E = BLv

(E) magnitude of induced e.m.f [V]
(B) magnetic flux density [T]
(L) length of wire [m]
(v) speed of wire [ms⁻¹]

62
Q

Transformer formulas (3)

A

Vp / Vs = Np / Ns

Ps = Pp hence
Vp x Ip = Vs x Is

(V) voltage [V]
(p) primary coil
(P) power (W)
(s) secondary coil
(N) number of turns
(I) current [A]

63
Q

Alternating current

A

I = I₀ sin ωt

(I) current at time t [A]
(I₀) peak current [A]
(ω) angular frequency of supply [rad s⁻¹]
(t) time [s]

*calculator must be in radians

64
Q

Alternating voltages

A

V = V₀ sin ωt

(V) voltage at time t [V]
(V₀) peak voltage [V]
(ω) angular frequency of supply [rad s⁻¹]
(t) time [s]

*calculator must be in radians

65
Q

Root-mean-square (r.m.s) value (2)

A

Iᵣ.ₘ.ₛ = I₀ / √2

Vᵣ.ₘ.ₛ = V₀ / √2

(Iᵣ.ₘ.ₛ) root-mean-square value of current [A]
(I₀) peak (maximum) current [A]
(Vᵣ.ₘ.ₛ) root-mean-square value of voltage [V]
(V₀) peak (maximum) voltage [V]

66
Q

Power formulas (4)

A

P = VI
P = I²R
P = V²/R
Pₘₐₓ = Pₐᵥ𝓰 x 2

(P) power [W]
(V) voltage [V]
(I) current [A]
(Pₘₐₓ) maximum power [W]
(Pₐᵥ𝓰) average power [W]

67
Q

Einstein relation (2)

A

E = hf and E = hc/λ

(E) energy of a photon [J]
(h) Planck’s constant [eV]
(f) frequency [Hz]
(c) wave speed [ms⁻¹]
(λ) wavelength [m]

68
Q

Speed of any type of charged particle

A

v = √(2eV/m) or v = √(2Eᴋ/m)

(v) electron speed [ms⁻¹]
(e) electron charge [C]
(V) voltage [V]
(m) mass of particle [kg]
(Eᴋ) kinetic energy [J]

69
Q

Einstein’s photoelectric equation

A

E = hc/λ = hf = Φ + 1/2mvₘₐₓ²

(E) energy of a photon [J]
(h) Planck’s constant [eV]
(f) frequency [Hz]
(c) wave speed [ms⁻¹]
(λ) wavelength [m]
(Φ) work function of the metal [J or eV]
(1/2mvₘₐₓ²) maximum kinetic energy of emitted photoelectron [J]

70
Q

Equations when incident radiation frequency equals threshold frequency (3)

A

hf₀ = Φ
∴
f₀ = Φ/h
∴
λ₀ = hc/Φ

(h) Planck’s constant [Js]
(f₀) threshold frequency [Hz]
(Φ) work function [J or eV]
(λ₀) threshold wavelength [m]
(c) wave speed [ms⁻¹]

71
Q

Momentum of a photon

A

p = E/c

(p) momentum [kgms⁻¹]
(E) energy of the photon [J]
(c) photon speed [ms⁻¹]

72
Q

The energy of a photon, absorbed or emitted, as a result of an electron making a transition between two energy levels E₁ and E₂

A

hf = E₁ - E₂
hc/λ = E₁ - E₂

(h) Planck’s constant [Js]
(f) frequency [Hz]
(c) wave speed [ms⁻¹]
(E) energy levels [J or eV]

73
Q

de Broglie wavelength equation

A

λ = h/p

(λ) wavelength [m]
(h) Planck’s constant [Js]
(p) momentum [kgms⁻¹]

74
Q

Finding wavelength using angle of separation

A

λ = 2d sinθ

(λ) wavelength [m]
(d) spacing of layers [m]
(θ) angle of diffraction [º]

75
Q

Einstein’s mass energy equation

A

E = mc²

(E) energy [J]
(m) mass [kg]
(c) speed of light [ms⁻¹]

76
Q

Activity (2)

A

A = (-)λN = ∆N/∆t

(A) activity [Bq]
(λ) decay constant [s⁻¹]
(N) number of undecayed nuclei
(t) time [s]

77
Q

Radioactive decay formula

A

x = x₀ e⁻*ᵗ

(x) activity [Bq]
(x₀) activity at time t = 0 [Bq]
(*) decay constant (λ) [s⁻¹]
(t) time [s]

78
Q

Half-life and decay constant relationship

A

λ = ln2/t₀.₅
= 0.693 / t₀.₅

(λ) decay constant [s⁻¹]
(t) time [s]

79
Q

Attenuation of x-rays as they pass through a uniform material

A

I = I₀ e⁻*ˣ

(I) transmitted intensity [Wm⁻²]
(I₀) initial intensity [Wm⁻²]
(*) attenuation coefficient (µ) [m⁻¹]
(x) thickness of the material [m]

80
Q

Acoustic impedance

A

Z = ρc

(Z) acoustic impedance [kgm⁻²s⁻¹]
(ρ) density [kgm⁻³]
(c) speed of sound [ms⁻¹]

81
Q

Intensity reflection fraction of the boundary between two materials

A

Iᵣ/I₀ = [ (Z₁ - Z₂) / (Z₁ + Z₂) ]²

(Iᵣ) reflected intensity [Wm⁻²]
(I₀) incident intensity [Wm⁻²]
(Z) acoustic impedances of materials [kgm⁻²s⁻¹]

82
Q

Attenuation of ultrasound

A

I = I₀ e⁻*ˣ

(I) transmitted intensity [Wm⁻²]
(I₀) initial intensity [Wm⁻²]
(*) absorption coefficient (a) [m⁻¹]
(x) thickness of the material [m]

83
Q

A-scan formulas (2)

A

thickness of bone = distance travelled by ultrasound / 2

= c∆t / 2

(c) speed of ultrasound [ms⁻¹]
(t) time interval between pulses [s]

84
Q

Number of photons

A

energy available / energy of a photon

85
Q

Radiant flux intensity

A

F = L / 4πd²

(F) radiant flux intensity [Wm⁻²]
(L) luminosity, power of star, [W]
(4πd²) surface area of sphere [m²]

  • (d) diameter [m]
86
Q

Hubble’s law

A

v = H₀d

(v) speed [ms⁻¹]
(H₀) Hubble constant [s⁻¹]
(d) distance of the galaxy [m]

87
Q

Doppler redshift

A

∆λ / λ
≈
∆f / f
≈
v / c

(λ) wavelength of the electromagnetic waves from the source [m]
(f) frequency of the electromagnetic waves from the source
(v) recession speed of source [s⁻¹]
(c) speed of light in vacuum [ms⁻¹]

A Level Physics (6 decks)

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