Formulae Flashcards
acceleration due to gravity
9.81 m s-2
on formula sheet
elementary charge
1.60 * 10^-19 C
on formula sheet
speed of light in a vacuum
3.00 * 10^8 m s-1
on formula sheet
Planck’s constant
6.63 * 10^-34 J s
on formula sheet
Avogadro’s constant
6.02 * 10^23 mol-1
on formula sheet
molar gas constant
8.31 J mol-1 K-1
on formula sheet
Boltzmann constant
1.38 * 10^-23 J K-1
on formula sheet
gravitational constant
6.67 * 10^-11 N m2 kg-2
on formula sheet
permittivity of free space
8.85 * 10^-12 C2 N-1 m-2 (F m-1)
on formula sheet
electron rest mass
9.11 * 10^-31 kg
on formula sheet
proton rest mass
1.673 * 10^-27 kg
on formula sheet
neutron rest mass
1.675 * 10^-27 kg
on formula sheet
alpha particle rest mass
6.646 * 10^-27 kg
on formula sheet
Stefan constant
5.67 * 10^-8 W m-2 K-4
on formula sheet
up quark charge
+2/3e
on formula sheet
down quark charge
-1/3e
on formula sheet
strange quark charge
-1/3e
on formula sheet
unified atomic mass unit to kg
1 u = 1.661 * 10^-27 kg
on formula sheet
electronvolt to J
1 eV = 1.60 * 10^-19 J
on formula sheet
day to s
1 day = 8.64 * 10^4 s
on formula sheet
year to s
1 year ≈ 3.16 * 10^7 s
on formula sheet
light year to m
1 light year ≈ 9.5 * 10^15 m
on formula sheet
parsec to m
1 parsec ≈ 3.1 * 10^16 m
on formula sheet
arc length
r𝜃
on formula sheet
circumference of a circle
2πr
on formula sheet
area of a circle
πr^2
on formula sheet
curved surface area of a cylinder
2πrh
on formula sheet
surface area of a sphere
4πr^2
on formula sheet
area of a trapezium
1/2(a + b)h
on formula sheet
volume of a cylinder
πr^2h
on formula sheet
volume of a sphere
4/3πr^3
on formula sheet
Pythagoras’ theorem
a^2 = b^2 + c^2
on formula sheet
cosine rule
a^2 = b^2 + c^2 - 2cos(A)
on formula sheet
sine rule
a/sin(A) = b/sin(B) = c/sin(C)
on formula sheet
logarithms multiplication rule
log(AB) = log(A) + log(B)
on formula sheet
logarithms division rule
log(A/B) = log(A) - log(B)
on formula sheet
logarithms powers rule
log(x^n) = n*log(x)
on formula sheet
vectors trigonometry
Fx = Fcos(𝜃)
Fy = Fsin(𝜃)
on formula sheet
suvat equations
v = u + a*t s = 1/2*(u + v)*t s = u*t + 1/2 *a*t^2 v^2 = u^2 + 2*a*s s = displacement (m) u = initial velocity (m s-1) v = final velocity (m s-1) a = acceleration (m s-2) t = time (s) on formula sheet
force (using momentum)
F = Δp/Δt F = force (N) Δp = change in momentum (kg m s-1) Δt = change in time on formula sheet
force (using acceleration)
F = m*a F = force (N) m = mass (kg) a = acceleration (m s-2) NOT ON FORMULA SHEET
momentum (using mass)
p = m*v p = momentum (kg m s-1) m = mass (kg) v = velocity (m s-1) on formula sheet
moment
moment = F*x
F = force (N)
x = perpendicular distance from pivot (m)
on formula sheet
torque
torque = F*d
F = force (N)
d = distance between forces across the pivot (m)
on formula sheet
density
ρ = m/V ρ = density (kg m-3) m = mass (kg) V = volume (m3) on formula sheet
pressure (using force)
p = F/A p = pressure (N m-2) F = force (N) A = area (m2) on formula sheet
pressure (using fluid density)
p = h*ρ*g p = pressure (N m-2) h = depth (m) ρ = fluid density (kg m-3) g = acceleration due to gravity (9.81 m s-2) on formula sheet
work (using an angle)
W = F*x*cos(𝜃) W = work (J) F = force (N) x = displacement (m) 𝜃 = angle between the force and the direction of motion (°) on formula sheet
efficiency
efficiency = (useful energy output)/(total energy input) * 100%
on formula sheet
power (using work done)
P = W/t P = power (W) W = work done (J) t = time (s) on formula sheet
power (using force and velocity)
P = F*v P = power (W) F = force (N) v = velocity (m s-1) on formula sheet
Hooke’s law
F = k*x F = force (N) k = force constant (N m-1) x = extension (m) on formula sheet (not labelled)
energy (using force and extension)
E = 1/2*F*x E = elastic potential energy (J) F = force (N) x = extension (m) on formula sheet
energy (using the force constant)
E = 1/2*k*x^2 E = elastic potential energy (J) k = force constant (N m-1) x = extension (m) on formula sheet
stress
σ = F/A σ = stress (N m-2) F = force (N) A = area (m2) on formula sheet (not labelled)
strain
ε = x/L ε = strain (no units) x = extension (m) L = original length (m) on formula sheet (not labelled)
Young’s modulus (using stress and strain)
E = σ/ε E = Young's modulus (N m-2) σ = stress (N m-2) ε = strain (no units) on formula sheet (not labelled)
Young’s modulus (using force and extension)
E = (F*L)/(A*x) E = Young's modulus (N m-2) F = force (N) L = original length (m) A = area (m2) x = extension (m) NOT ON FORMULA SHEET but easy to find from information you are given
charge
ΔQ = I*Δ*t ΔQ = change in charge (C) I = current (A) Δt = chage in time (s) on formula sheet
current (using cross-sectional area)
I = Ane*v
I = current (A)
A = cross-sectional area of wire (m2)
n = number of electrons per unit volume (m-3)
e = charge of an electron (1.602 * 10^-19 C)
v = mean drift velocity of the electrons (m s-1)
on formula sheet
work done (using potential difference and charge)
W = V*Q W = work done (J) V = potential difference (V) Q = charge (C) on formula sheet
work done (using e.m.f and charge)
W = ε*Q W = work done (J) ε = e.m.f (V) Q = charge (C) on formula sheet
work done (using potential difference, current and time)
W = V*I*t W = work done (J) V = potential difference (V) I = current (A) t = time (s) on formula sheet
resistors in series
R = R1 + R2 +…
R = total resistance (Ω)
Rn = resistance of component n (Ω)
on formula sheet (not labelled as ‘in series’)
resistors in parallel
1/R = 1/R1 + 1/R2 +…
R = total resistance (Ω)
Rn = resistance of component n (Ω)
on formula sheet (not labelled as ‘in parallel’)
resistance (using resistivity)
R = (ρ*L)/A R = resistance (Ω) ρ = resistivity (Ω m) L = length of wire (m) A = cross-sectional area (m2) on formula sheet
power (using potential difference and current)
P = V*I P = power (W) V = potential difference (V) I = current (A) on formula sheet
power (using current and resistance)
P = I^2 * R P = power (W) I = current (A) R = resistance (Ω) on formula sheet
power (using potential difference and resistance)
P = V^2 / R P = power (W) V = potential difference (V) R = resistance (Ω) on formula sheet
e.m.f (using Resistance)
ε = I*(R+r) ε = e.m.f (V) I = current (A) R = external resistance (Ω) r = internal resistance (Ω) on formula sheet
e.m.f (using potential difference)
ε = V + I*r ε = e.m.f (V) V = potential difference (V) I = current (A) r = internal resistance (Ω) on formula sheet
potential divider formula (using Vin and Vout)
Vout = (R2/(R1 + R2))*Vin
Vout = potential difference measured across R2 (V)
R1 = resistance of component 1 (Ω)
R2 = resistance of component 2 (Ω)
Vin = potential difference across R1 and R2 (V)
on formula sheet
potential divider formula (using V1 and V2)
V1/V2 = R1/R2 V1 = potential difference across R1 (V) V2 = potential difference across R2 (V) R1 = resistance of componenet 1 (Ω) R2 = resistance of componenet 2 (Ω) on formula sheet
current (using potential difference and resistance)
I = V/R I = current (A) V = potential difference (V) R = resistance (Ω) NOT ON FORMULA SHEET
potential difference (using current and resistance)
V = IR V = potential difference (V) I = current (A) R = resistance (Ω) NOT ON FORMULA SHEET
resistance (using potential difference and current)
R = V/I R = resistance (Ω) V = potential difference (V) I = current (A) NOT ON FORMULA SHEET
wave velocity
v = f*λ v = wave velocity (m s-1) f = frequency (Hz) λ = wavelength (m) on formula sheet
frequency
f = 1/T
f = frequency (Hz)
T = time period (s)
on formula sheet
Intensity
I = P/A I = intensity (W m-2) P = power (W) A = area (m2) on formula sheet
wavelength (using double slit experiment)
λ = (a*x)/D λ = wavelength (m) a = slit separation (m) x = fringe separation (m) D = distance between the slits and the screen (m) on formula sheet
wavelength (using diffraction grating)
n*λ = d*sin(𝜃) n = order of the maximum (no unit) λ = wavelength (m) d = slit separation (m) 𝜃 = angle between normal to the grating and the beam of light (°) NOT ON FORMULA SHEET
refraction (using the speed of light)
n = c/v n = refravtive index (no units) c = speed of light in a vacuum (3.00 * 10^8 m s-1) v = speed of light in material (m s-1) on formula sheet
refraction (using a constant)
n*sin(𝜃) = constant n = refravtive index (no units) 𝜃 = angle between normal to the material and the beam of light (°) constant = n2*sin(𝜃2) on formula sheet
refraction (using the critical angle)
sin(C) = 1/n
C = critical angle, point at which total internal reflection begins (°)
n = refractive index (no units)
on formula sheet
energy of a photon (using frequency)
E = h*f E = energy of a photon (J) h = Planck's constant (6.626 * 10^-34 J s) f = frequency (Hz) on formula sheet
energy of a photon (using wavelength)
E = (h*c)/λ
E = energy of a photon (J)
h = Planck’s constant (6.626 * 10^-34 J s)
c = speed of light in a vacuum (3.00 * 10^8 m s-1)
λ = wavelength (m)
on formula sheet
wavelength (using Planck’s constant)
λ = h/p λ = wavelength (m) h = Planck's constant (6.626 * 10^-34 J s) p = momentum (kg m s-1) on formula sheet
energy of a photon (using kinetic energy)
E = h*f h*f = Φ + KEmax E = energy of a photon (J) h = Planck's constant (6.626 * 10^-34 J s) f = frequency (Hz) Φ = work function (J) KEmax = kinetic energy of electrons once released (J) on formula sheet
force (using acceleration due to gravity)
F = m*g F = force (N) m = mass (kg) g = acceleration due to gravity (9.81 m s-2) NOT ON FORMULA SHEET
acceleration (using force)
a = F/m a = acceleration (m s-2) F = force (N) m = mass (kg) NOT ON FORMULA SHEET
mass (using acceleration)
m = F/a m = mass (kg) F = force (N) a = acceleration (m s-2) NOT ON FORMULA SHEET
Drag
Fd = 1/2ρCdAv
Fd = drag (N)
ρ = fluid density (kg m-3)
Cd = coefficient of drag (no units)
A = cross-sectional area of the moving object (m2)
v = velocity of the moving object (m s-1)
NOT ON FORMULA SHEET
Kinetic energy (using velocity)
KE = 1/2*m*v^2 KE = kinetic energy (J) m = mass (kg) v = velocity (m s-1) NOT ON FORMULA SHEET
thinking distance
thinking distance (m) = reaction time (s) * velocity of the car (m s-1) NOT ON FORMULA SHEET
relationship between braking distance and velocity
braking distance ∝ (velocity)^2
NOT ON FORMULA SHEET
stopping distance
stopping distance = thinking distance + braking distance
NOT ON FORMULA SHEET
thermal energy
E = m*c*ΔT E = thermal energy (J) m = mass (kg) c = specific heat capacity (J kg °C-1) ΔT = change in temperature (K or °C) NOT ON FORMULA SHEET
nuclear energy
E = m*c^2 E = nuclear energy (J) m = mass (kg) c = speed of light in a vacuum (3.00 * 10^8 m s-1) NOT ON FORMULA SHEET
weight (using acceleration due to gravity)
w = m*g w = weight (N) m = mass (kg) g = acceleration due to gravity (m s-2) NOT ON FORMULA SHEET
gravitational potential energy
GPE = m*g*Δh m = mass (kg) g = acceleration due to gravity (m s-2) Δh = change in height (m) NOT ON FORMULA SHEET
relationship between gravitational potential energy and kinetic energy
kinetic energy (J) ↓ , gravitational potential energy (J) ↑ kinetic energy (J) ↑ , gravitational potential energy (J) ↓ NOT ON FORMULA SHEET
relationship between intensity and amplitude
intensity (W m-2) ∝ (amplitude (m))^2
NOT ON FORMULA SHEET
energy (using power)
E = P*t E = energy (J) P = power (W) t = time (s) NOT ON FORMULA SHEET
impulse
I = F*Δt I = impulse (N s) F = force (N) Δt = change in time (s) NOT ON FORMULA SHEET
power (using force and distance)
P = (F*d)/t P = power (W) F = force (N) d = distance (m) t = time (s) NOT ON FORMULA SHEET
work done (using force and distance)
W = F*d W = work done (J) F = force (N) d = distance (m) NOT ON FORMULA SHEET this is the same as W = F*d*cos(θ) but θ is 0° so cos(θ) = 1
work done (using acceleration due to gravity)
W = m*g*h W = work done (J) m = mass (kg) g = acceleration due to gravity (9.81 m s-1) h = height (m) NOT ON FORMULA SHEET
e.m.f (using energy transferred)
e.m.f (V) = energy transferred (J) / charge (C)
NOT ON FORMULA SHEET
energy (using work done)
energy (J) = work done (J)
NOT ON FORMULA SHEET
potential difference (using work done)
V = W/Q V = potential difference (V) W = work done (J) Q = charge (C) NOT ON FORMULA SHEET
relationship between resistivity and temperature
ρT = ρ0[1 + ∝(T - T0)]
ρT = resistivity of material at temperature T (Ω m)
ρ0 = resistivity of material at temperature T0
∝ = the temperature coefficient
T = temperature of the material (K or °C)
T0 = reference temperature at which the resistivity of the material is quoted (K or °C)
NOT ON FORMULA SHEET
percentage uncertainty from absolute uncertainty
percentage uncertainty = (absolute uncertainty / measured value)*100%
NOT ON FORMULA SHEET
y = a*b
% uncertainty of y from % uncertainties of a and b
% uncertainty of y = % uncertainty of a + % uncertainty of b
NOT ON FORMULA SHEET
y = a/b
% uncertainty of y from % uncertainties of a and b
% uncertainty of y = % uncertainty of a + % uncertainty of b
NOT ON FORMULA SHEET
y = a^n
% uncertainty of y from % uncertainty of a
% uncertainty of y = % uncertainty of a * n
NOT ON FORMULA SHEET
percentage uncertainty from a gradient
percentage uncertainty = (absolute uncertainty / gradient of line of best fit)*100%
NOT ON FORMULA SHEET
percentage uncertainty from a y-intercept
percentage uncertainty = (absolute uncertainty / ‘best’ y-intercept)*100%
NOT ON FORMULA SHEET
absolute uncertainty form gradients
absolute uncertainty = gradient of best fit line - gradient of worst fit line
NOT ON FORMULA SHEET
absolute uncertainty form y-intercepts
absolute uncertainty = best y-intercept - worst y-intercept
NOT ON FORMULA SHEET
average speed
average speed (m s-1) = distance (m) / time (s) NOT ON FORMULA SHEET
average velocity
average velocity (m s-1) = total displacement (m) / time (s) NOT ON FORMULA SHEET
acceleration (using change in velocity)
acceleration (m s-2) = change in velocity (m s-1) / time (s)
NOT ON FORMULA SHEET
this can be found by rearranging v =u + a*t
1 kilowatt-hour
1 kilowatt-hour = 1000 watts * 3600 seconds
1 kilowatt-hour = 3600 000 Joules
NOT ON FORMULA SHEET
cost of energy
cost = number of kilowatt-hours * cost per kilowatt-hour
NOT ON FORMULA SHEET
distance between nodes in a stationary wave
λ/2
λ = wavelength (m)
NOT ON FORMULA SHEET
distance between anti-nodes in a stationary wave
λ/2
λ = wavelength (m)
NOT ON FORMULA SHEET
distance between nodes and anti-nodes in a stationary wave
λ/4
λ = wavelength (m)
NOT ON FORMULA SHEET
Kirchhoff’s first law
ΣIin = ΣIout
sum of currents entering a junction (A) = sum of currents exiting a junction (A)
NOT ON FORMULA SHEET
Kirchhoff’s second law
Σε = ΣI*R
sum of the e.m.f (V) = sum of the products of current and resistance of each component in series (V)
NOT ON FORMULA SHEET
maximum kinetic energy of electrons emitted as a result of the photoelectric effect
maximum kinetic energy (J) = charge of an electron (1.602 * 10^-19 C) * stopping potential (V)
NOT ON FORMULA SHEET
Snell’s law
n1 * sin(θ1) = n2 * sin(θ2)
n1 = refractive index of material 1 (no units)
θ1 = angle between normal to material 1 and the beam of light in material 1 (°)
n2 = refractive index of material 2 (no units)
θ2 = angle between normal to material 2 and the beam of light in material 2 (°)
critical angle between two materials
sin(C) = n1/n2 C = critical angle (°) n1 = refractive index of material 1 (no units) n2 = refractive index of material 2 (no units)
In the suvat equations, what does s denote?
Displacement (m)
In the suvat equations, what does u denote?
Initial Velocity (m s-1)
In the suvat equations, what does v denote?
Final Velocity (m s-1)
In the suvat equations, what does a denote?
Acceleration (m s-2)
In the suvat equations, what does t denote?
Time (s)
What equation would you use to find final velocity given initial velocity, acceleration and time?
v = u + a*t
What equation would you use to find final velocity given initial velocity, acceleration and displacement?
v^2 = u^2 + 2as
What equation would you use to find displacement given initial velocity, final velocity and time?
s = 1/2(u + v)t
What equation would you use to find displacement given initial velocity, acceleration and time?
s = ut + 1/2a*t^2
Rearrange v = u + a*t for u
u = v - a*t
Rearrange v = u + a*t for a
a = (v - u)/t
Rearrange v = u + a*t for t
t = (v - u)/a
Rearrange v^2 = u^2 + 2as for u^2
u^2 = v^2 - 2as
Rearrange v^2 = u^2 + 2as for a
a = (v^2 - u^2)/(2*s)
Rearrange v^2 = u^2 + 2as for s
s = (v^2 - u^2)/(2*a)
Rearrange s = 1/2(u + v)t for u
u = (s/t)*2 - v
Rearrange s = 1/2(u + v)t for v
v = (s/t)*2 - u
Rearrange s = 1/2(u + v)t for t
t = (2*s)/(u + v)
Rearrange s = ut + 1/2a*t^2 for u
u = (s - 1/2at^2)/t
Rearrange s = ut + 1/2a*t^2 for a
a = 2(s - ut)/t^2
Rearrange s = ut + 1/2a*t^2 for t
t = ((2as + u^2)^(1/2) - u)/a