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Physics (OCR B) > All Equations (inc Formula Booklet - currently not indicated) > Flashcards

All Equations (inc Formula Booklet - currently not indicated) Flashcards

1
Q

*Hooke’s Law (F)

A

F = kx
force = spring constant * extension
Newtons, N

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2
Q

*Hooke’s Law (E)

A

E = ¹/₂Fx = ¹/₂kx^2
elastic energy = ¹/₂ * force * extension
elastic energy = ¹/₂ * spring constant * extension^2
Joules, J

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3
Q

Multiple springs in parallel

A

K(total) = K(1) + K(2) + K(3) …

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4
Q

Multiple springs in series

A

1/K(total) = 1/K(1) + 1/K(2) + 1/K(3) …

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5
Q

*Stress

A

σ = F / A
Stress = Force/Area
Pascals, Pa OR Nm^-2

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6
Q

*Strain

A

ε = x/L
Strain = Extension/Original Length
No units, A ratio

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7
Q

*Young Modulus

A

E = σ/ε = (FL)/(Ax)
Young Modulus = Stress/Strain
Pascals, Pa OR Nm^-2

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8
Q

Tensile Strength

A

Tensile Strength = Breaking Force/Cross-sectional Area
Pascals, Pa OR Nm^-2

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9
Q

Fracture Energy

A

Fracture Energy = energy needed to break/Cross-Sectional Area
Jm^-2

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10
Q

Relation between Drift Velocity and Current

A

I = nAev
I = Current
n = number of charge carriers
A = Cross-Sectional Area
e = charge on charge carrier
v = drift velocity
Amps, A

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11
Q

Lens Power

A

Lens Power = 1/f
Lens Power = 1/focal length
Dioptres, D

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12
Q

Curvature of a Wave

A

Curvature of a Wave = 1/r
Curvature of a Wave = 1/radius of wave

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13
Q

Curvature of a wave leaving a Lens

A

= Curvature of wave entering + Curvature added by the Lens

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14
Q

*1/v

A

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

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15
Q

Magnification

A

M = v/u = image size/object size
Ratio, no unit

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16
Q

*Shannon’s Criteria

A

b = log2 (V(total)/V(noise))
V(total) = total range of data

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17
Q

Transmission Rate

A

Transmission Rate = total info sent / time taken

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18
Q

Charge

A

Q = nq
Charge = number of electrons * charge on one electron
Coulomb, C

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19
Q

*Current

A

I = Q/t
Current = charge / time
Ampere, A

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20
Q

*Potential Difference (Volts)

A

V = W/Q
Volt, V

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21
Q

Resistance

A

R = V/I (or V=IR)
Ohm, Ω

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22
Q

Conductance

A

G = 1/R = I/V
Siemen, S

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23
Q

*Power

A

P = W/t = IV = I^2 * R = (V^2)/R = F*v
Watt, W

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24
Q

*Work Done

A

W = P/t = ItV = F*s
Work = Force * Displacement
Joules, J OR Nm OR kgm^2s^-2

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25
Q

*Resistance (wires)

A

R = ρL/A
L = length of wire
ρ = resistivity (Ωm)
A = Area

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26
Q

*Conductance (wires)

A

G = σA/L
L = length of wire
σ = conductivity
A = area

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27
Q

*Potential Divider equations

A

Vout = (R1/(R1+R2))*Vin
V1/V2 = R1/R2
where ε = Vin and the voltage recorded across R2 is Vout

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28
Q

*EMF

A

ε = V + I*r
EMF = terminal p.d + current * internal resistance

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29
Q

EMF off of graph

A

A graph of V against I (V = y-axis)

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30
Q

Frequency (wave)

A

f = 1/T
frequency = 1 / Time Period
Hertz, Hz or s^-1

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31
Q

Diffraction (grating)

A

nλ = dSinθ
n = order of maxima
θ = angle of separation (from n = 0)
d = distance between individual slits
λ = wavelength of source

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32
Q

Critical angle

A

Sin C = n2 / n1
C = critical angle
n2 = refractive index light is going into
n1 = refractive index light is leaving

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33
Q

Youngs Double Slit

A

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

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34
Q

*Capitance

A

C = Q/V
Capitance = Charge / Voltage
Farad, F

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35
Q

*Energy stored in a capacitor (some in booklet)

A

E = 1/2QV (= 1/2CV^2 = Q^2/(2*C))
The area under a pd charge graph (pd = y-axis)

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36
Q

Current (capacitor/capacitance)

A

I = Q / (R*C)
Current = Charge / (Resistance * Capitance)

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37
Q

*dQ/dt

A

dQ/dt = -Q/RC
rate of change of charge is proportional to charge remaining

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38
Q

Time Constant

A

Time Constant = R*C
Resistance * Capitance
RC = how long it takes for the charge to fall to 37% of its original value (e^-1)

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39
Q

Charge left on a capacitor

A

Q = Qo * e^(-t/RC)
Qo = Initial charge
t = time
RC = time constant

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40
Q

Current left on a capacitor

A

I = Io * e^(-t/RC)
Io = Initial current
t = time
RC = time constant

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41
Q

Potential Difference left on a capacitor

A

V = Vo * e^(-t/RC)
Vo = Initial pd
t = time
RC = time constant

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42
Q

Energy of a photon (general)

A

E = h*f
Energy = Planck’s constant * frequency

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43
Q

Energy gained by an electron (p-n junction)

A

E = q*V
q - electron charge
V - striking voltage

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44
Q

Momentum (de Broglie)

A

p = h/λ
momentum = Planck’s constant / wavelength
(can be linked with E = h*f)

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45
Q

SUVAT (only one not given)

A

s = 1/2t(u + v)

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46
Q

Momentum

A

ρ = m*v
kgms^-1

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47
Q

Rate of change of momentum

A

F = (mv - mu)/t

48
Q

Work done

A

Work = F*s
Work = Force * Displacement
Joules, J OR Nm OR kgm^2s^-2

49
Q

KE

A

KE = 1/2mv^2

50
Q

GPE

A

mgh

51
Q

Efficiency

A

useful/total * 100

52
Q

Displacement SHM (Ideal)

A

x = A * cos (ω*t)
A = amplitude

53
Q

Velocity SHM (Ideal)

A

v = -ω * A * sin(ω*t)
A = amplitude

54
Q

Acceleration SHM (Ideal)

A

a = -ω^2 * x = -ω^2 * A * cos(ωt)

55
Q

Angular Velcocity

A

ω = 2πf = θ/t
rads^-1

56
Q

Potential Energy (SHM)

A

PE = 1/2Fx = 1/2kx^2

57
Q

Time Period (SHM)

A

T = 2π√(l/g) = 2π√(m/k)
SEE NOTES FOR DERIVATION PROCESS
T = 1/f
T^2 = (4π^2l)/g

58
Q

Frequency (SHM)

A

f = 1/2π √(g/l) = 1/2π√(k/m)
SEE NOTES FOR DERIVATION PROCESS
f = 1/T
f^2 = g/(4π^2*l)

59
Q

Linear Velocity

A

v = (rθ)/t = rω

60
Q

Angular Acceleration

A

a = vω = rω^2 = v^2/r

61
Q

Centripetal force

A

F = ma
(insert angular acc)

62
Q

Gravitational field strength

A

g = F/m = (-G*M)/r^2
G = gravitational force constant
M = mass of the big object/only object

63
Q

Force (in a gravitational field)

A

F = (-GMm)/r^2
G = gravitational force constant
M = mass of the big object/only object
m = mass of the small object/only object

64
Q

Gravitational potential

A

Vg = gh = (-GM)/r
G = gravitational force constant
M = mass of the big object/only object

65
Q

Gravitational potential energy (gravitational field)

A

GPE = Eg = (-GMm)/r
G = gravitational force constant
M = mass of the big object/only object
m = mass of the small object

66
Q

RADAR to measure relative velocity away/towards Earth

A

v = ∆d/(t1-t2)

67
Q

RADAR to measure distance

A

wave speed = d/t

68
Q

Doppler effect

A

z ≈ v/c ≈ ∆f/f ≈ ∆λ/λ

69
Q

The Lorentz factor

A

γ = 1/√(1 - v^2/c^2)
v = velocity of moving observer
c = speed of light
γ = the Lorenz Factor

70
Q

Time Dilation

A

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

71
Q

Length Contraction

A

l = 1/γ * l0
l = apparent length
l0 = actual length
γ = Lorentz factor

72
Q

Mass Increase (relativity)

A

m = γ *m0
m = apparent mass
m0 = actual mass
γ = Lorentz factor

73
Q

Hubble’s constant

A

t0 = 1/H0
t0 = the time that the galaxies have been receding from us (age of universe)
H0 = Hubble’s Constant

74
Q

Energy (Specific Heat Capacity)

A

E = mc∆θ
m = mass
c = specific heat capacity (Jkg^-1K^1)
∆θ = change in temperature (K)

75
Q

Pressure

A

P = F/A
Area can be surface area or other

76
Q

Brownian Motion

A

d ∝ √N
d ∝ √t
distance travelled in N steps
distance travelled in t seconds

77
Q

The mean square speed, <c>^2

A

All the speeds squared and then averaged
<c> ^2

78
Q

Average KE ∝ T

A

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)

79
Q

√(Mean Square Speed), cr

A

cr = √(<c>^2) = √((3*k*T)/m)
k = Boltzmann constant
m = mass of molecule
T = Temp (K)</c>

80
Q

Charles Law

A

At constant pressure
V ∝ T
V1/T1 = V2/T2

81
Q

Pressure Law

A

At a constant volume
P ∝ T
P1/T1 = P2/T2

82
Q

Boyles Law

A

At a constant temperature
P ∝ 1/V
P1V1 = P2V2

83
Q

Combined Equations (Kinetic Theory)

A

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)

84
Q

Process occurs at an appreciable rate

A

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

85
Q

The number of particles with energy E

A

E => Nf
2E => Nf^2
3E => N*f^3 ect
E = particle energy
N = number of particles
f = fraction with extra energy

86
Q

Boltzmann Factor

A

f = e^(-ε/kT)
f = fraction with extra energy
ε = activation energy
k = Boltzmann constant
T = Temperature (K)

87
Q

Magnetic Flux

A

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

88
Q

Permeance

A

Λ = (μ*A)/l
μ = permittivity

89
Q

Size force acting (mag field)

A

F = B* I *L
B = mag field strength
I = Current
l = length conductor in field (at right angles to mag field)

90
Q

EMF (mag fields)

A

ε = BLv
B = magnetic flux density
L = length of wire at right angles to the field
v = velocity of movement

91
Q

Max EMF (graph of flux against time)

A

negative max gradient = positive max EMF
positive max gradient = negative max EMF
(greatest rate of change of the graph)

92
Q

Transformers (relation between output and input)

A

For an ideal transformer
Vp/Vs = Np/Ns = Is/Ip
REMEMBER CURRENT IS INVERSE REALTIONSHIP!

93
Q

Electric field strength

A

E = F/Q = (k*Q)/r^2

94
Q

Potential Difference (electric fields)

A

V = (k*Q)/r
Volts, V OR JC^-1

95
Q

Electric Potential Energy

A

Eelec = (kqQ)/r

96
Q

Force (electric fields)

A

F = (kqQ)/r^2

97
Q

Uniform Electric Field (field strength)

A

E = V/d

98
Q

Repulsive force between nuclei

A

F = (q*Q)/(k *r^2)
k = electric force constant

99
Q

Millikans (stationary)

A

Q = (mgd)/V
m = mass of droplet
g = gravitational field strength
d = distance between the plates
V = pd between the plates

100
Q

Deflection of electrons

A

F = BQv
(or motion not perp to field F = BQv*sinθ

101
Q

Radius in a cyclotron

A

r = (mv)/(BQ) = p/(B*Q)

102
Q

Frequency of voltage, cyclotron

A

f = (BQ)/(2π*m)

103
Q

Rest Energy

A

ΔE = Δm*c^2
Δm = rest mass (the mass of the particle when not in motion and not undergoing any relativistic effects)

104
Q

Particle Energy

A

E = m*c^2
m = mass of particle (can be undergoing relativistic effect as in motion)

105
Q

Energy of particles at high energy

A

E ≈ pc
p = momentum
c = speed of light

106
Q

Standing wave model

A

En = n^2 * E1
En = energy at level n
n = energy level
E1 = energy at level 1
INACCURATE!!!

107
Q

Electron model

A

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)

108
Q

The angle to the first minima of the diffraction pattern formed by an electron and a nucleus

A

sinθ = (1.22*λ)/d
d = diameter of nucleus
λ = wavelength

109
Q

Correlation between R^3 and A

A

R^3 ∝ A
R = radius
A = nucleon number
R = r0*A^(1/3)
r0 = radius of a proton

110
Q

Activity

A

A = dN/dt = -λ*N = A0 e^(-λt)
λ = decay constant
N = number of parent nuclei
A0 = starting activity
t = time
Becquerel, Bq

111
Q

Half life

A

t1/2 = ln2 / λ
t1/2 = half life

112
Q

Number nuclei left

A

N = N0 e^(-λt)
N = number of nuclei left
N0 = starting nuclei
λ = decay constant
t = time

113
Q

HVT - Half Value Thickness

A

x1/2 = ln2/μ
μ = linear absorption
x1/2 = material thickness

114
Q

Intensity (HVT)

A

I = I0 e^(-μx)
I = intensity
I0 = Initial intensity
μ = linear absorption
x = material thickness
Wm^-2

115
Q

Absorbed Dose, D

A

D = E/m
E = energy
m = mass
Gray, Gy OR Jkg^-1

116
Q

Equivalent Dose, H

A

H = D*Q
D = Absorbed dose
Q = quality factor
Sievert, Sv

117
Q

Keplar’s Third Law

A

T^2 = r^3 * (4π^2 / GM)

Physics (OCR B) (2 decks)

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