Physics a Level Equations

7/30/2019 Physics a Level Equations

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Advancing Physics Revision Guide CD-ROM

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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=

+

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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)

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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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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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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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Physics a Level Equations

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