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7/30/2019 Physics a Level Equations
1/15
Advancing Physics Revision Guide CD-ROM
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7/30/2019 Physics a Level Equations
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Advancing Physics Revision Guide CD-ROM
Formulae, Symbols, Units and DataContents
Formulae and relationships
Quantities, symbols and units
Useful data
Formulae and relationshipsA booklet containing the values of physical data and mathematical formulae is supplied byOCR forAdvancing Physics examinations. It is available from the OCR Web site, or from theAdvancing Physics Web site at:
http://advanc ingph y sics.io p .org/s u pp o rt_ materia ls /stu dent/PhysicsEquatio n s .pdf
Imaging and signalling
log2(V
) or 2 focal length 1 11=
+
Advancing Physics2
http://advancingphysics.iop.org/support_materials/student/PhysicsEquations.pdfhttp://advancingphysics.iop.org/support_materials/student/PhysicsEquations.pdfhttp://advancingphysics.iop.org/support_materials/student/PhysicsEquations.pdfhttp://advancingphysics.iop.org/support_materials/student/PhysicsEquations.pdf7/30/2019 Physics a Level Equations
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Advancing Physics Revision Guide CD-ROM
refractive index=
speedvacuo speedmedium
noiselimitation onmaximum bitspersample
V
voltage variation Vtotal
, noise
Electricity
current
=Q
(currentI, charge flow Q,time interval t)
potential differenceEV= Q
(potential difference V, energyE, charge Q)
powerP=IV=I
2
R(powerP, potential difference V,
currentI
, resistance R)V
load
= Ir (emf,internal resistance r)
resistanceandconductance
R=V
G =II
(resistance R, conductance G,
potential difference V, currentI)
G = G
1
+ G
2
+ .......(conductors in parallel)
R= R
1
+ R
2
+ .......(resistors in series)
conductivityand resistivity A lG =
l
R=
A
(conductivity , resistivity , cross
sectionA, length l)
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capacitanceC= Q
(potential difference V, chargeQ, capacitance C)
1 1
2
discharge
ofcapacitor
Q = Q e
t RC0
(initial charge Q
0
, time constant RC,
time t)
(time constant )
Materials
density = M
(density , mass M, volume V)
Hooke's law F=kx
(tension F, spring constantk, extensionx)
stress, strainand the Youngmodulus
tension stress =cross - sectionalarea
extension strain =original length
stressYoung modulus =
elastic strain energy =1
kx2
2
Energy and thermal effects
efficiencyefficiency =
useful energy
output
energy E=
mc
(change in energy E, mass m,
specific thermal capacityc, temperature change)
Boltzmann factor ( E
kT
)
e
(energy difference E, kelvin
temperature T, Boltzmannconstant
Waves
v=
f(wave speed v, frequencyf, wavelength )
n = dsin (on a distant screen from adiffraction grating or double slit; slitspacing d,
ordern, wavelength , angles
of maxima )
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Oscillations
d2x k 2
dt2 m (time t, acceleration a,force per unit displacement k, massm,displacementx, frequency f)
x=A cos 2 ft
x=A sin 2 ft
(amplitudeA, time t)
T = 2 m k(periodic time T)
1
(frequency f)
total energy
1 2 1 2 1
2
= a = x = (2f) x
Gases
ideal gas equation pV=nRT
(pressurep, volume V, numberof moles n, molar gas constantR,
kinetic theoryof gases pV =
1
Nmc
2
3
(pressurep, volume V, numberof molecules N, mass ofmolecule m,
c2
Motion and forces
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equationsforuniformlyaccelerated
s = ut+ 1 at2
v = u + at
v2 = u 2 + 2as
(initial speed u, final speed v,time taken t, acceleration a,distance travelled s)
momentum p = (momentump, mass m, velocity
power = (force F, velocity v)
force = rate of change ofimpulse = Ft (force F)
2
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components ofa vector in twoperpendiculardirections
F
Fcos
work =Fx
(force F, component ofdisplacement in the directionof
forcircularmotion
2v2
F=
mva =
r r(radius of circle r)
Special relativityrelativistic factor
=
1 (speed of object v, speed of light c)
relativisticmomentu
p =
mv
(momentump, relativistic factor,
mass m, velocity v)
relativistic energy Etotal
= Erest
Etotal
= mc2
(total energy Etotal
, relativistic factor
,
rest energy Erest
)
Atomic and nuclear physics
radioactive decay N (numberN, decay constant , time t)
t
(initial numberN0
)
T =
ln
2
1
(half-life T1/2
)
absorbed dose =energy deposited per
unit mass
dose equivalent =absorbed dose qualityfactor
risk = probability
consequence
expected random variation
mass-energy
Erest
=
mc2
(rest energy Erest
, mass m, speed of
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light c)
energy-frequencyrelationship for
E=hf
(photon energy E, Planck constanth, frequency f)
= hp
(wavelength , Planck constant h,
momentump;
NOTEp = mvfor slow movingparticles,p = E/ cfor photonsand particles moving close tospeed of light)
Field and potential
for all fieldsfield strength =
dV
Vdr r
(potential V, distance r,potential gradient dV/ dr)
gravitational fields
F
(gravitational field strengthg, gravitational force F, massm )
V = GM F=
GMm
(gravitational potential Vgrav
, radial
constant G, masses m andM, distance r)
electric fields
=F
(electric field strength E, electricforceF, charge q )
V = kQ F=kQq
(electric potential Velec
, radial
component of force F, electricforce constant k, charges q andQ,
grav
r
r2
component of force F, gravitational
elec
r r2
Electromagnetism
force on a currentcarrying
F=ILB (flux density B, currentI, length L )
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Quantities, symbols and unitsThe following list illustrates the symbols and units which are used inAdvancing Physics, andin the AS and A2 question papers.
Quantity Usual symbols Usual unit
absolute temperature T K
acceleration am s
2
acceleration of free fall gm s
2
activity of radioactive source A Bq
angle , rad
angular displacement , rad
angular frequency rad s
1
angular speed
rad s1
amount of substance n mol
area Am
2
atomic massm
akg, u
Avogadro constant L, NA mol
1
Boltzmann constant k
J K
1
capacitance C F
Celsius temperature C
conductance G S
conductivity
S m1
decay constant
s1
density
kg m3
displacement xors m
distance d, r,x m
electric charge Q, q C
electric current I A
electric field strength EN C
1
, V m1
electric potential V V
electric potential difference V V
electromotive force (emf) V
electron mass
me kg, u
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Advancing Physics Revision Guide CD-ROM
Quantity Usual symbols Usual unit
elementary charge e C
energy E, W J
energy transferred thermally (heating) Q J
force F N
frequency f Hz
gravitational constant GN kg
2
m2
gravitational field strength gN kg
1
half-lifet1/2
s
kinetic energyE
KJ
length l m
magnetic flux Wb
magnetic flux density B T
mass m kg
molar gas constant RJ K
1
mol1
momentum pkg m s
1
neutron mass mn
kg, u
neutron number N
nucleon number A
number N, n, m
number density (number per unit volume) nm
3
period T s
permeability of free space 0 H m
1
permittivity of free space 0 F m
1
Planck constant h J s or J Hz
1
potential energy EP
J
power P W
pressure p Pa
proton massm
pkg, u
proton number Z
resistance R W
resistivity W m
specific thermal capacity corCJ kg
1
K1
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Quantity Usual symbols Usual unit
specific latent heat LJ kg
1
speed u, v, cm s
1
speed of electromagnetic waves cm s
1
spring constant kN m
1
strain fraction or per cent
stress Pa
time t s
time constant s
velocity u, v, cm s
1
volume Vm
3
wavelength m
work W J
work function energy W J, eV
Young modulus E Pa
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Useful dataThis list of data is more comprehensive than lists issued with examination papers.Values are given to three significant figures, except where more or less are useful.
Physical constants
speed of light c3.00 10
8
ms1
permittivity of free space n 8.85 10
12
C2
N1
m2
(or F m1
)
electric force constant
1k=
0
8.98 10
9
N m
2
C
2
permeability of free space 0
4 107 N A2 (or H m1)
charge on electron e1.60 10
19
C
mass of electronm
e 9.11 1031
kg = 0.000 55 u
mass of proton
mp 1.673 10
27
kg = 1.007 3 u
mass of neutron mn 1.675 10
27
kg = 1.008 7 u
mass of alpha particle m
6.646 1027
kg = 4.001 5 u
Avogadro constantL, N
A 6.02 1023
mol1
Planck constant h 6.63 1034
J s
Boltzmann constant k1.38 10
23
J K1
molar gas constant R8.31 J mol
1
K1
gravitational force constant G6.67 10
11
N m2
kg2
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Other data
standard temperature
and pressure (stp)
273 K (0 C), 1.01 105
Pa (1 atmosphere)
molar volume of a gasat stp
Vm 22.4 dm
3
= 2.24 102
m3
gravitational fieldstrength at the Earth'ssurface inthe UK
g9.81 N kg
1
(or m s2
)
Conversion factors
unified atomic mass unit 1 u= 1.661 10
27
kg
1 day= 8.64 10
4
s
1 year 3.16 107 s
1 light year 1016 m
Mathematical constants and equations
e = 2.72 = 3.14 1 radian = 57.3
arc = r circumference of circle = 2r
sin tan and cos 1 for small
area of circle = r2
curved surface area of cylinder= 2rh
ln(x
n
) = n lnx
volume of cylinder= r2h
ln(e
kx
) = kx
surface area of sphere = 4r2
volume of sphere =
4
r3
3
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