All Equations (inc Formula Booklet - currently not indicated) Flashcards
*Hooke’s Law (F)
F = kx
force = spring constant * extension
Newtons, N
*Hooke’s Law (E)
E = ¹/₂Fx = ¹/₂kx^2
elastic energy = ¹/₂ * force * extension
elastic energy = ¹/₂ * spring constant * extension^2
Joules, J
Multiple springs in parallel
K(total) = K(1) + K(2) + K(3) …
Multiple springs in series
1/K(total) = 1/K(1) + 1/K(2) + 1/K(3) …
*Stress
σ = F / A
Stress = Force/Area
Pascals, Pa OR Nm^-2
*Strain
ε = x/L
Strain = Extension/Original Length
No units, A ratio
*Young Modulus
E = σ/ε = (FL)/(Ax)
Young Modulus = Stress/Strain
Pascals, Pa OR Nm^-2
Tensile Strength
Tensile Strength = Breaking Force/Cross-sectional Area
Pascals, Pa OR Nm^-2
Fracture Energy
Fracture Energy = energy needed to break/Cross-Sectional Area
Jm^-2
Relation between Drift Velocity and Current
I = nAev
I = Current
n = number of charge carriers
A = Cross-Sectional Area
e = charge on charge carrier
v = drift velocity
Amps, A
Lens Power
Lens Power = 1/f
Lens Power = 1/focal length
Dioptres, D
Curvature of a Wave
Curvature of a Wave = 1/r
Curvature of a Wave = 1/radius of wave
Curvature of a wave leaving a Lens
= Curvature of wave entering + Curvature added by the Lens
*1/v
1/v = 1/u + 1/f
v = image distance (+ve)
u = object distance (-ve)
n.b. derived from 1/f = 1/v + (- 1/u)
metres, m
Magnification
M = v/u = image size/object size
Ratio, no unit
*Shannon’s Criteria
b = log2 (V(total)/V(noise))
V(total) = total range of data
Transmission Rate
Transmission Rate = total info sent / time taken
Charge
Q = nq
Charge = number of electrons * charge on one electron
Coulomb, C
*Current
I = Q/t
Current = charge / time
Ampere, A
*Potential Difference (Volts)
V = W/Q
Volt, V
Resistance
R = V/I (or V=IR)
Ohm, Ω
Conductance
G = 1/R = I/V
Siemen, S
*Power
P = W/t = IV = I^2 * R = (V^2)/R = F*v
Watt, W
*Work Done
W = P/t = ItV = F*s
Work = Force * Displacement
Joules, J OR Nm OR kgm^2s^-2
*Resistance (wires)
R = ρL/A
L = length of wire
ρ = resistivity (Ωm)
A = Area
*Conductance (wires)
G = σA/L
L = length of wire
σ = conductivity
A = area
*Potential Divider equations
Vout = (R1/(R1+R2))*Vin
V1/V2 = R1/R2
where ε = Vin and the voltage recorded across R2 is Vout
*EMF
ε = V + I*r
EMF = terminal p.d + current * internal resistance
EMF off of graph
A graph of V against I (V = y-axis)
Frequency (wave)
f = 1/T
frequency = 1 / Time Period
Hertz, Hz or s^-1
Diffraction (grating)
nλ = dSinθ
n = order of maxima
θ = angle of separation (from n = 0)
d = distance between individual slits
λ = wavelength of source
Critical angle
Sin C = n2 / n1
C = critical angle
n2 = refractive index light is going into
n1 = refractive index light is leaving
Youngs Double Slit
nλ = (xd)/L
n = order of maxima
d = distance between individual slits
λ = wavelength of source
x = distance between the fringe (from n = 0)
L = distance between the slit and the ‘screen’ the fringes are projected on
*Capitance
C = Q/V
Capitance = Charge / Voltage
Farad, F
*Energy stored in a capacitor (some in booklet)
E = 1/2QV (= 1/2CV^2 = Q^2/(2*C))
The area under a pd charge graph (pd = y-axis)
Current (capacitor/capacitance)
I = Q / (R*C)
Current = Charge / (Resistance * Capitance)
*dQ/dt
dQ/dt = -Q/RC
rate of change of charge is proportional to charge remaining
Time Constant
Time Constant = R*C
Resistance * Capitance
RC = how long it takes for the charge to fall to 37% of its original value (e^-1)
Charge left on a capacitor
Q = Qo * e^(-t/RC)
Qo = Initial charge
t = time
RC = time constant
Current left on a capacitor
I = Io * e^(-t/RC)
Io = Initial current
t = time
RC = time constant
Potential Difference left on a capacitor
V = Vo * e^(-t/RC)
Vo = Initial pd
t = time
RC = time constant
Energy of a photon (general)
E = h*f
Energy = Planck’s constant * frequency
Energy gained by an electron (p-n junction)
E = q*V
q - electron charge
V - striking voltage
Momentum (de Broglie)
p = h/λ
momentum = Planck’s constant / wavelength
(can be linked with E = h*f)
SUVAT (only one not given)
s = 1/2t(u + v)
Momentum
ρ = m*v
kgms^-1
Rate of change of momentum
F = (mv - mu)/t
Work done
Work = F*s
Work = Force * Displacement
Joules, J OR Nm OR kgm^2s^-2
KE
KE = 1/2mv^2
GPE
mgh
Efficiency
useful/total * 100
Displacement SHM (Ideal)
x = A * cos (ω*t)
A = amplitude
Velocity SHM (Ideal)
v = -ω * A * sin(ω*t)
A = amplitude
Acceleration SHM (Ideal)
a = -ω^2 * x = -ω^2 * A * cos(ωt)
Angular Velcocity
ω = 2πf = θ/t
rads^-1
Potential Energy (SHM)
PE = 1/2Fx = 1/2kx^2
Time Period (SHM)
T = 2π√(l/g) = 2π√(m/k)
SEE NOTES FOR DERIVATION PROCESS
T = 1/f
T^2 = (4π^2l)/g
Frequency (SHM)
f = 1/2π √(g/l) = 1/2π√(k/m)
SEE NOTES FOR DERIVATION PROCESS
f = 1/T
f^2 = g/(4π^2*l)
Linear Velocity
v = (rθ)/t = rω
Angular Acceleration
a = vω = rω^2 = v^2/r
Centripetal force
F = ma
(insert angular acc)
Gravitational field strength
g = F/m = (-G*M)/r^2
G = gravitational force constant
M = mass of the big object/only object
Force (in a gravitational field)
F = (-GMm)/r^2
G = gravitational force constant
M = mass of the big object/only object
m = mass of the small object/only object
Gravitational potential
Vg = gh = (-GM)/r
G = gravitational force constant
M = mass of the big object/only object
Gravitational potential energy (gravitational field)
GPE = Eg = (-GMm)/r
G = gravitational force constant
M = mass of the big object/only object
m = mass of the small object
RADAR to measure relative velocity away/towards Earth
v = ∆d/(t1-t2)
RADAR to measure distance
wave speed = d/t
Doppler effect
z ≈ v/c ≈ ∆f/f ≈ ∆λ/λ
The Lorentz factor
γ = 1/√(1 - v^2/c^2)
v = velocity of moving observer
c = speed of light
γ = the Lorenz Factor
Time Dilation
t = γ * t0
t = time observed outside of the inertial frame of reference
γ = the Lorenz factor
t0 = time observed inside the inertial frame of reference
Length Contraction
l = 1/γ * l0
l = apparent length
l0 = actual length
γ = Lorentz factor
Mass Increase (relativity)
m = γ *m0
m = apparent mass
m0 = actual mass
γ = Lorentz factor
Hubble’s constant
t0 = 1/H0
t0 = the time that the galaxies have been receding from us (age of universe)
H0 = Hubble’s Constant
Energy (Specific Heat Capacity)
E = mc∆θ
m = mass
c = specific heat capacity (Jkg^-1K^1)
∆θ = change in temperature (K)
Pressure
P = F/A
Area can be surface area or other
Brownian Motion
d ∝ √N
d ∝ √t
distance travelled in N steps
distance travelled in t seconds
The mean square speed, <c>^2
All the speeds squared and then averaged
<c> ^2
Average KE ∝ T
1/2m<c>^2 = kT
OR 1/2m<c>^2 = a/2 * kT
k = Boltzmann Constant
<c>^2 = mean square speed
a = degrees of freedom of movement (typically 3)
m = mass of molecule
T = Temp (K)
√(Mean Square Speed), cr
cr = √(<c>^2) = √((3*k*T)/m)
k = Boltzmann constant
m = mass of molecule
T = Temp (K)</c>
Charles Law
At constant pressure
V ∝ T
V1/T1 = V2/T2
Pressure Law
At a constant volume
P ∝ T
P1/T1 = P2/T2
Boyles Law
At a constant temperature
P ∝ 1/V
P1V1 = P2V2
Combined Equations (Kinetic Theory)
PV = nRT = NkT
P = Pressure
V = Volume
n = number of moles
R = Universal gas constant
N = number of identical molecules
k = Boltzmann constant
T = Temperature (K)
Process occurs at an appreciable rate
Using ε/(k*T)
If it is between 15 and 30 then the process occurs at an appreciable rate. Less than15 is too fast to be properly observed and more than 30 is too slow to be any use at all.
ε = activation energy
The number of particles with energy E
E => Nf
2E => Nf^2
3E => N*f^3 ect
E = particle energy
N = number of particles
f = fraction with extra energy
Boltzmann Factor
f = e^(-ε/kT)
f = fraction with extra energy
ε = activation energy
k = Boltzmann constant
T = Temperature (K)
Magnetic Flux
Φ = BA = ΛNI
B = magnetic flux density
A = surface area OR (length of wire*distance it travels)
Λ = permeance
N = number of coils
I = current
Permeance
Λ = (μ*A)/l
μ = permittivity
Size force acting (mag field)
F = B* I *L
B = mag field strength
I = Current
l = length conductor in field (at right angles to mag field)
EMF (mag fields)
ε = BLv
B = magnetic flux density
L = length of wire at right angles to the field
v = velocity of movement
Max EMF (graph of flux against time)
negative max gradient = positive max EMF
positive max gradient = negative max EMF
(greatest rate of change of the graph)
Transformers (relation between output and input)
For an ideal transformer
Vp/Vs = Np/Ns = Is/Ip
REMEMBER CURRENT IS INVERSE REALTIONSHIP!
Electric field strength
E = F/Q = (k*Q)/r^2
Potential Difference (electric fields)
V = (k*Q)/r
Volts, V OR JC^-1
Electric Potential Energy
Eelec = (kqQ)/r
Force (electric fields)
F = (kqQ)/r^2
Uniform Electric Field (field strength)
E = V/d
Repulsive force between nuclei
F = (q*Q)/(k *r^2)
k = electric force constant
Millikans (stationary)
Q = (mgd)/V
m = mass of droplet
g = gravitational field strength
d = distance between the plates
V = pd between the plates
Deflection of electrons
F = BQv
(or motion not perp to field F = BQv*sinθ
Radius in a cyclotron
r = (mv)/(BQ) = p/(B*Q)
Frequency of voltage, cyclotron
f = (BQ)/(2π*m)
Rest Energy
ΔE = Δm*c^2
Δm = rest mass (the mass of the particle when not in motion and not undergoing any relativistic effects)
Particle Energy
E = m*c^2
m = mass of particle (can be undergoing relativistic effect as in motion)
Energy of particles at high energy
E ≈ pc
p = momentum
c = speed of light
Standing wave model
En = n^2 * E1
En = energy at level n
n = energy level
E1 = energy at level 1
INACCURATE!!!
Electron model
En = 1/n^2 *E1
En = the total energy required to be liberated from level n
n = energy level
E1 = energy at level 1
MUCH MORE ACCURATE!!
(KE +PE)
The angle to the first minima of the diffraction pattern formed by an electron and a nucleus
sinθ = (1.22*λ)/d
d = diameter of nucleus
λ = wavelength
Correlation between R^3 and A
R^3 ∝ A
R = radius
A = nucleon number
R = r0*A^(1/3)
r0 = radius of a proton
Activity
A = dN/dt = -λ*N = A0 e^(-λt)
λ = decay constant
N = number of parent nuclei
A0 = starting activity
t = time
Becquerel, Bq
Half life
t1/2 = ln2 / λ
t1/2 = half life
Number nuclei left
N = N0 e^(-λt)
N = number of nuclei left
N0 = starting nuclei
λ = decay constant
t = time
HVT - Half Value Thickness
x1/2 = ln2/μ
μ = linear absorption
x1/2 = material thickness
Intensity (HVT)
I = I0 e^(-μx)
I = intensity
I0 = Initial intensity
μ = linear absorption
x = material thickness
Wm^-2
Absorbed Dose, D
D = E/m
E = energy
m = mass
Gray, Gy OR Jkg^-1
Equivalent Dose, H
H = D*Q
D = Absorbed dose
Q = quality factor
Sievert, Sv
Keplar’s Third Law
T^2 = r^3 * (4π^2 / GM)
