a level physics key terms - cheatography.com

A-Level Physics Key Terms Cheat Sheetby 0llieC (0llieC) via cheatography.com/38321/cs/11952/

Mechanics

Scalar A quantity without direct ion. Length /Di stance, Speed, Mass, Temper ature, Time,Energy

Vector A quantity with both direction and magnit ude Displa cement, Velocity, Force (inc. Weight), Accele ration,Momentum

Equili brium When all forces acting on an object are balanced andcancel each other out. There is no resultant force

Free-bodyDiagram

A diagram of all the forces acting on a body, but not theforces it exerts on other things. The arrows indicatemagnitude and direction.

Principle ofMoments

For a body to be in equili brium, the sum of the clockwisemoments equals the sum of the anticl ockwise moments.

Moment The product of the size of the force and the perpen diculardistance between the turning point and the line of actionof the force.

Couple A pair of forces with equal size which act parallel to eachother but in opposite direction. E.g. turning a car's steeringwheel.

Centre ofMass

The single point from which the body's weight actsthrough. The object will always balance around this point. To calculate for uniform objects: Σmx = Mx̄

SUVAT(ConstantAccele ration)

v = u + at s = 1/2 (u+v)tv = u + 2ass = ut + 1/2 ats = vt - 1/2 at

Mechanics (cont)

Displa cem ent -Time Graph

Displa cement (y) against Time (x). Gradient = Velocity Accele ration = Δgradi ent

Veloci ty-Time Graph

Velocity (y) against Time (x) Gradient = Accele ration ΔGradient = ΔAccel eration Area = Displa cement

VariableAccele ration

Differentiate

x v a

Δa Integrate

Accele rat ion -Time Graph

Accele ration (y) against Time (x). Gradient = ΔAccel era tion 0 Gradient = No accele ration constant velocity. Constant Gradient = constant accele ration Area = Velocity NB: Remember to treat area below the time axis asnegative!

Newtons 1stLaw

The velocity of an object will not change unless aresultant force acts on it.

Newtons 2ndLaw

F = ma The accele ration of an object is ∝ to the resultant forceacting upon it. (for objects with a constant mass) Points to rememb er: • Resultant Force is vector sum of all the forces • Unit = N • Ensure mass is in kg • Accele ration is in the same direction as resultant force.

Newtons 3rdLaw

If object A exerts a force on object B, then object Bexerts an equal but opposite force on object A

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Published 3rd June, 2017.Last updated 3rd June, 2017. of 21.

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Mechanics (cont)

Freefall When there is only gravity acting upon an object. i.e. motionwith an accele ration of g (9.81m s ) The same SUVAT equations apply, however, u = 0 and a =g {{ng}} NB: 'direc tion' of motion, dictates the sign of g

ProjectileMotion

An object given an initial velocity, then left to move freelyunder g. There is separate horizontal and vertical motionwith time being the only common attribute. Both motionfollows SUVAT equations but horizontal motion has noaccele ration.

Friction Force that opposes motion. When in a fluid (liquid or gas) itis drag, drag depends on: • Viscosity of the fluid • Speed of object • Shape of the object

For all frictional forces • Force is in the opposite direction to motion • Can never increase speed or induce motion• They convert kinetic energy heat.

Lift Upwards force on a object in a fluid

TerminalSpeed

When frictional forces equal the driving force. For a fallingobject, when drag equals the force due to their mass.

Momentum The product of the mass and velocity of an object.Momentum in any collision is conserved (when no externalforces are involved)

InelasticCollision

Not all of the kinetic energy is conserved. Momentumhowever is conserved.

Mechanics (cont)

ElasticCollision

Kinetic energy is conserved i.e. no energy is dissipated asheat or other energy forms.

Impulse An extension of N2L. Impulse is the product of force andtime and is equal to the momentum of that body. FΔt = Δ(mv) Also equal to the area under a force-time graph.

WorkDone

The energy transf erred from one form to another. W = Fd Work Done = The force causing motion x distance moved

Power The rate of work done over time P = ΔW/Δt P = Fv derived from combining P and W = Fs

Force- Dis ‐pla cement‐Graph

Area = Work Done

Conser vation ofEnergy

Energy cannot be created nor destroyed, only convertedfrom one form to another, but the total energy of a closedsystem will not change.

Efficiency useful output /input in terms of energy or power.

Materials

Density ρ = m/V A property all materials have and is indepe ndent of bothshape and size.

Limit ofPropor tio nality

The point where Hooke's law no longer applies. On aforce- ext ension graph, the limit of propor tio nality is where theline is no longer straight




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Materials (cont)

Hooke'sLaw

F = kΔL The force is propor tional to the extension of a stretched wire. k is the stiffness constant a measure of how hard it is tostretch

ElasticLimit

The point on a force- ext ension graph where the line begins tocurve. Beyond this point, permanent deform ation occurs wherethe wire will no longer return to its original shape.

Force- Ext ensionGraph

Straight section Gradient = k Loading and unloading plot a loop, if a stretch is elastic, thecurve starts and finishes in the same position (the origin). Ifplastic deform ation occurs, the unloading line has the samegradient (k) but crosses the x axis at a different point

Area = Elastic Strain Energy

The area between the loading and unloading line (after plasticdeform ation) is equal to the work done in deforming thematerial

TensileStress

The ratio of forced applied and cross- sec tional area. stress = F/A

TensileStrain

The ratio of extension to original length, it has no units and isjust a ratio. strain = ΔL/L

YoungsModulus

The ratio of tensile stress and tensile strain E = FL/AΔL The YM of a material is the constant value up to the limit ofpropor tio nality,

Stress -StrainGraph

Stress (y) against Strain (x). Gradient = Young's Modulus Area = strain energy per unit volume

Materials (cont)

YieldPoint

The point on a stress -strain graph where the material stretcheswithout any extra load.

Brittl eness

When a material breaks after a certain about of force is applied.The line simply stops on a stress -strain graph. The same thingapplies on a force- ext ension graph, the line just stops.

Thermal Physics

Kelvin A temper ature scale that is in terms of an atomsmovements. °C K + 273

AbsoluteZero

The lowest theore tical temper ature of anything 0 K = -273°C

InternalEnergy

The internal energy of a body is the sum of the randomlydistri buted kinetic and potential energies of all its particles

ClosedSystem

A system where no matter or energy is transf erred in or outof the system

HeatTransfer

Heat is always transf erred from a hot area/s ubs tance to acold area/s ubs tance.

SpecificHeatCapacity

The amount of energy required to heat up 1kg of thematerial by 1°C/1 K ΔQ = mcΔT Energy Change is equal to the product of the mass, specificheat capacity and the change in temper ature.










Thermal Physics (cont)

SpecificLatentHeat

The specific latent heat of fusion ( Solid) / vapori sation (gas) is the quantity of thermal energy needed /will be lost tochange the state of 1kg of the substance. Q = mlwhere m is the mass and l the latent heat.

When a substance changes state, there is a period where thetemper ature of the material is constant, as the internal energyrises, this is due to the latent heat.

Boyle'sLaw

At a constant temper ature, pV is constant. i.e.p1V1 = p2V2

On a p-V plot, the higher the line, the higher the temper ature.

Charles'Law

At a constant pressure: V is directly propor tional to itsabsolute temper ature TV1/T1 = V2/T 2

PressureLaw

At a constant volume: p is directly propor tional to its absolutetemper ature. p1/T1 = p2/T2

MolecularMass

the sum of the masses of all the atoms that make up themolecule.

RelativeMolecularMass

The sum of the relative atomic masses of all the atoms.

AvogadroConstant

The number of atoms in exactly 12g of carbon isotope 6C.

NA = 6.02 x10 mol

MolarMass

The mass of a material containing NA molecules

Thermal Physics (cont)

Ideal GasEquations

pV = nRT n = number of moles R = molar gas constant

pV = NkTN = number of moleculesk = Boltzmann constant

A way of rememb ering which n is which. Moles will be small,therefore small n. Number of molecules will be large so, bigN.

KineticTheory

The pressure exerted by an ideal gas can be derived byconsid ering the gas as individual particles. pV = 1/3 x Nm(Cr ms)

Crms is the root mean square speed.

Assu mpt ions • All molecules in the gas are identical • Gas contains a large number of molecules• The volume of the molecules is negligible when comparedto the volume of the contai ner/gas as a whole.

BrownianMotion

Random motion of particles suspended in a fluid helpedprovide evidence that the movement of the particles was dueto the collisions of the fast random ly- moving particles, whichsupported the model of kinetic theory.

AverageKineticEnergy

1/2 x m(Crm s) = 3/2 x nRT/N

1/2 x m(Crm s) = 3/2 x RT/NA

Particles and Radiation

Proton &Neutrons

The 2 Baryons that make up the nucleus of an atom.Comprised of 3 quarks. Protons have a relative charge: +1,neutrons: 0. Both have a relative mass of 1 (1.67 x10 kg).




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Particles and Radiation (cont)

Electron A fundam ental lepton, with a charge of -1. Cannot be brokendown into other subatomic particles. Relative mass of 1/2000(9.11x 10 kg)

NuclideNotationZX

The general notation of elements.

ProtonNumber(Z)

The number of protons in an atom. Defines the element. For aneutral atom, proton no. also == the electron number

NucleonNumber(A)

AKA Mass Number - number of total nucleons (protons +neutrons)

SpecificCharge

The ratio of a particles charge to its mass. Specific meaningper kg. S.C. = Charge (Q) / Mass (kg)

Isotope Atoms with the same number of protons but a different numberof neutrons. Affects the stability of a atom

StrongNuclearForce

A strong force that holds atoms together at small distances,strong enough to overcome the electr ostatic repulsion of theprotons. Dist ances Repulsive: <0.5 fm (0.5 x10 m) Attrac tive: 0.5 to 3 fm Rapidly falls to ) after 3 fm.

AlphaDecay(α)

Occurs in big atoms (82+ protons). Atoms emits a heliumnucleus (2 protons 2 neutrons). Particles is too big to be keptstable by the SNF.

Beta-MinusDecay(β )

Emission of a electron and anti-e lec tro n-n eut rino. Happens inneutron rich particles. In nucleus structure terms, a neutronturns into a proton by changing an d quark to a u quark,emitting an electron and anti-e lec tro n-n eut rino.

Beta-PlusDecay(β )

Emission of a positron and an electron neutrino. One of theatoms protons, changes a u quark to a d quark, changing to aneutron emitting a positron and an electr on- neu trino.


Photon A discrete packet of electr oma gnetic radiation with 0 mass. E = hf = hc/λ

Antipa rticle The corres ponding antipa rticle to any particle has the samemass and rest energy but opposite charge.

PairProduction

When 2 of the same particles collide at high speed andproduce a partic le- ant ipa rticle pair. The energy of thecollisions is converted into the pair. Also occurs when aphoton has enough energy to produce an electr on- pos itronpair. Emin = 2E0 (in MeV)

Annihi lation

When a particle and antipa rticle collide producing 2 photonsin opposite direct ions. Emin = E0

This collision is used in PET scanners to detect cancers.

Hadron Particles that can feel the strong force. Either a baryon or ameson depending on its quark structure

Baryon A hadron consisting of 3 quarks. All are unstable except afree proton - all eventually decay into a proton. Proton: uud Neutron: ddu

BaryonNumber

A quantum number which is always conserved. Baryonshave a B.N. of +1. Antiba ryons have a B.N. of -1 and allother particles have a B.N of 0.

Mesons A hadron consisting of 2 quarks - a quark- ant iquark pair.There are 9 possible combin ations, making either Kaons orPions.

Lepton A fundam ental particle that doesnt feel the strong force.Interacts via the weak intera ction.

LeptonNumber

Another quantum number that is always conserved. Must beseparate for lepton -el ectron number and electr on-muonnumber.




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StrangeParticles

Particles that have a property of strang eness - contain astrang e/a nti -st range quark. Crea ted via the strong intera ction Decay via the weak intera ction Rules of conver sation mean that strange particles are onlyproduced in pairs.

Strang eness

Another quantum number - however it can change by ±1 or 0in an intera ction.

Quark A fundam ental particle that makes up hadrons. There are 6types: u p/d own, top/bo ttom, stra nge / charm.

QuarkConfin ement

There is no where to get a quark on its own, when enoughenergy is provided, pair-p rod uction occurs, with one quarkremaining in the particle.

WeakIntera ction

β and β are both examples of weak intera ctions, which isintera ction via the weak force, the force acting betweenleptons.

FeymannDiagram

A diagram of particle intera ctions, with: Wavy Lines : Exchange Particle Straight Lines : Particles in/out of the intera ction (with arrowsindicating direction)

Magnetic Fields

MagneticField

A region where a force acts, force is exerted onmagnet ic/ mag net ically suscep tible materials (e.g. iron).

MagneticFieldLines

Lines that show a magnetic field. They run from north to thesouth pole of a magnet. The more dense the lines are, thestronger the field

Magnetic Fields (cont)

MagneticFluxDensity

The force on one metre of wire carrying a current of 1 A atright angles to the magnetic field. AKA The strength of themagnetic field B = F/Il Magnetic flux density is the force by the current meter

MagneticFieldaround awire

When current flows, a magnetic field is induced. Right hand rule: • Curl Fingers around " wir e". • Stick up thumb Thum b :Di rection of current Fingers: Direction of magnetic field

Solenoid A cylind rical coil of wire acting as a magnet when carryingelectric current. Forms a field like a bar magnet.

Force onaCurren t-C arryingWire

A curren t-c arrying wire, running through a magnetic fieldgenerates a resultant field of the one induced by the currentand the pre-ex isting one. The direction of the force isperpen dicular to the current direction and the mag. field.

LeF t-handRule

For finding the direction of the Force. • Thumb upwards• First finger forwards• Second finger to the right (perpe ndi cular to f.f.)

Thumb:Force/MotionFirst Finger:FieldSecond Finger : Current

ChargedParticlesin amag.field

F = BQv




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CircularPath

For a charge travelling perpen dicular to a field is alwaysperpen dicular to the direction of motion The condition forcircular motion.

F = mv /r can be combined with F = BQv. Rearranged for r, this shows that: • r increases if mass or velocity increases• r decreases if the mag. field strength is increased or thecharge increases• f = v/2πr•Combined with r = mv/BQ f = BQ/2πm

ParticleAccele rator

A cyclotron consists of 2 hollow semico ndu ctors, with auniform magnetic field applied perpen dicular to the plane ofthe D magnets. An A.C. is applied. Charged particles are firedinto the D's. They accelerate across the gap betweenmagnets, taking the same amount of time for the increasingradius.

MagneticFlux

The number of flux lines through a certain area hence{{n}}Φ =BA In other words its the amount of flux passing through an area

Electr oma gneticInduction

Relative motion between a conductor and a mag. field, causesan emf to generate at the ends of the conductor as theelectrons accumulate at one end.


Flux Linkage The amount of field lines being cutNΦ = BANCos(θ) where θ is the angle between the normal to the coil andthe field. (if it is perpen dic ular, θ = 0°

Faraday'sLaw

Induced e.m.f. is propor tional to the rate of change of fluxlinkage... ε = NΔΦ/Δt

Lenz's Law The induced e.m.f. is always in such a direction that itopposes the change that caused it.

e.m.f in arotating coil

NΦ = BANCos(ωt) ε = BANωSi n(ωt)

Flux Linkage and Induced e.m.f. are 90° out of phase.

Generator Ek is converted into electrical energy, the kinetic energy

turns a coil in a magnetic field so that they induce aelectric current.

Ri ght -handRule

For Ge ner ators. • Thumb upwards• First finger forwards• Second finger to the left (perpe ndi cular to f.f.)

Thumb:Force/MotionFirst Finger:FieldSecond Finger : Current

Altern atingCurrent

Current that's direction changes over time. The voltageacross the resistance goes up and down.

Root MeanSquared(rms) Power

Vrms = V0/s qrt(2)

Irms = I0/s qrt(2)

Prms = Irms x Vrms




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Transf ormer

A device that uses electr oma gnetic induction to change thesize of a voltage for an altern ating current.

An altern ating current flowing in the primary coil causes thecore to magnet ise /de mag netise contin uously in oppositedirect ions. This produces a rapidly changing magnetic fluxin the core (made of magn eti cally soft materi al. Thechanging flux passes through the seco ndary coil induces aaltern ating e.m.f. if the same frequency but diff erent voltage(if the no. of turns is different)

Transf ormerEquations

P.Co il: Vp = Np x ΔΦ/Δt

S.Co il: Vs = Ns x ΔΦ/Δt

Combines to: Ns/Np = Vs/V p

Ineffi cie ncies in aTransf ormer

• Eddy Currents (looping currents induced by changing flux) create opposing magnetic fields reducing its strength reduced by laminating the core so that current cannotflow between the cores layers• Heat Generation due to the resistance in the coils reduced by using a wire with a low resistance• Magnet is ing /De ma g n etising the core energy is wastedas the core is heated reduced by using a magnet icallysoft core, which has a small hysteresis loop, this theenergy required to create /co llapse the field is minimised

Efficiency Equationsefficiency = IsVs/ Ip Vp power out /p owe rin

Engine ering

Momentof Inertia

A measure of how difficult it is to rotate an object or changeits rotational speed

I = Σmr This equation means that the moment of inertia is dependentin the masses, and their distri bution, so a solid disk mayhave a lower moment of inertia than a hoop.

RotationalKineticEnergy

The rotational kinetic energy of an object is dependant on itsmoment of inertia. Ek = 1/2 x Iω

RotationalSUVAT

The SUVAT equations can be applied directly to rotationalmotion, but with rotati onal's counterparts:s θ (rads)u ω0

v ωa αt t

Torque When a force causes an object to turn, the turning effect istorque. T = Fr T = Iα

Work &Power

The work done is the product of the force and the angleturned by:W = Tθ

Power is the amount of work done in a given time:P = Tω as Δθ/Δt = ω

Frictionalk Torque occurs in real world systems therefore:Tnet = Tap pli ed - Tfr ict ional




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Engine ering (cont)

Flywheels A flywheel is a heavy wheel that has a high moment ofinertia, meaning once spinning it is hard to stop. They arecharged as they are spun, turning T into rotational kineticenergy. It is used as a energy storage device if energy isneeded, the wheel decele rates and provides some of itsrotational energy to another part of the machine.

Flywheels maximused for energy storage are dubbedflywheel batteries.

Factors that effect storage:• Mass If the mass is increased, the moment of inertia andhence the r. Ek

• Angular Speed if the angular speed is increasd, theenergy stored increases with angular speed , so increasingthe a.speed, greatly increases energy storage.• Spoked Wheel this again increases the moment ofinertia as the mass is distri buted further away from the center.• Material Carbon fibre is generally used as it is strongand allows for higher angular speeds• Friction Reduction lubric ation is used to reduce frictionas well as superc ond ucting magnets to stop contact andtherefore friction. Vacuums are also used so air resisi tance isnot a factor.

Uses• Smoothing Torque Flywheels are used to keep systemsrelying on torque running smoothly• Breaking especially in F1 cars, flywheels are used toharness some of the force when breaking to allow for fasteraccele ration afterwards• Wind Turbines to provide stable power for days withoutwind and/or peak times

Engine ering (cont)

AngularMomentum

Angular Momentum = Iω

Iinitial x ωinitial = Ifinal x ωfinal

Angular Momentum IS** conserved

AngularImpulse

Impulse = Δ(Iω) = TΔt

1st Law ofThermo dyn amics

Q = ΔU + W

If energy is transf erred to the system: Q = +veIf work is done on the gas: W = -veIf the internal energy incr eas es:U = +ve

For closed systems, the first law can be applied, alsoknown as non-flow processes as no gas flows in or out.To apply the law, it is assumed to be an Ideal Gas.

Isothermal(Constanttemper ature)Change

ΔU = 0 Therefore Q = W There is no change in internal energy... no change intemper ature therefore: pV = Constant.

pV plot is a curve, with higher lines indicating a highertemper ature. The work done is the area under the line.

Expansion is and is positive. Compression is and is negative.

Adiabatic (Noheat transfer)Change

Q = 0 Therefore ΔU = -W pV = constant

Steeper gradient than a isotherm's plot. There is agreater amount of work done for an adiabatic changethan a isotherm




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Engine ering (cont)

Isobaric(ConstantPressure)Changes

W = pΔV Therefore V/T is constant

No work done.

Isometric(ConstantVolume)Changes

W = 0 Therefore Q = ΔU and p/T is constant

Work done = area under straight line

CyclicProcess

A System that undergos a number of combin ations ofprocesses. They start at a certain pressure and volumeand return to it at the end of a cycle.

Engine ering (cont)

4-StrokePetrolEngine

• Induction The piston starts at the top of the cylinder, andmoves down increasing the volume of the gas above it. A air-fuel mixture is drawn in through an open inlet valve. Pressureremains constant just above atmospheric.• Compre ssion The inlet valve is closed, the piston moves upthe cylinder. Work is done on the gas, and the pressureincreases. Just before the end of the stoke, a spark ignites theair-fuel mixture. Temper ature and pressure increase.• Expansion The explosion expands and pushes the pistonback down. Work is done as the gas expands, there is also anet output. Just before the bottom, the exhaust valve opens andthe pressure reduces.• Exhaust The piston moves up the cylinder and the burntgas leaves through the exhaust valve, the pressure remainsconstant just above atmosp heric.

4-StrokeDieselEngine

Induction Stroke Only air is drawn.Compression The air is compressed enough to have atemper ature to ignite diesel fuel just before the end of thestroke, diesel fuel is sprayed in and ignites.Expansion & Exhaust The same as petrol










Engine ering (cont)

IndicatedPower

Pind icated = Area of p-V loop x cycles per second x no. of

cylinders The net work done by the cylinder in one second.

OutputPower

The useful power at the crankshaft P = Tω

FrictionPower

The power lost due to friction between moving parts Pfri ction = Pind - Pbrake

EngineEfficiency

Pinp = Calorific Value x Fuel Flow Rate Mech anical

Efficiency = Pbrak e/ Pind Affected by energy lost due to

moving parts Thermal Efficiency = Pind/P inp Heat

energy transf erred into work Overall Efficiency =Pbrak e/ Pi np

2nd LawofThermo dyn amics

Heat engines must operate between a heat source and aheat sink Engine Efficiency = W/QH = (QH - QC)/QH Max

Theore tical Efficiency = (TH - TC)/TH

HeatEngine

A Source of heat (TH)

QH

Heat Engine W

QC

Heat Sink (TC)

ReverseHeatEngine

Hot (TH)

QH

Heat Engine W

QC

Cold (TC)

Engine ering (cont)

Refrid gerator

A reverse heat engine where the cold space is the actual fridge.Whilst the hot space is the surrou ndings, the fridges aim is toextract as much heat from the cold space to the surrou ndings.

Coeffi cient ofPrefor ‐mance

COPref = Qc/W = Qc/( Qh -Qc) = Tc/(Th-Tc)

COPhp = Qh/W = Qh/( Qh -Qc) = Th/( Th -Tc)

Electr icity

Current(I/A)

The rate of flow of charge. Conven tio nally running from + to-. Measured my an Ammeter (in series) I = ΔQ/Δt

PotentialDifference(V/V)

The work done in moving a unit charge between 2 points. 1V = 1JC . Measured by a voltmeter (in parallel) V = IR / V = W/Q

Resistance(R/Ω)

A measure of how difficult it is to move current around thecircuit. R = V/I

OhmicConductor

Under constant physical condit ions, I is propor tional to V. Ona graph of I (y) against V (x), the gradient is equal to 1/R.

FilamentLamp

A filament lamp has an IV charac ter istic of a cubic (s shape)going through the origin. The heat in the filament causes theresistance to increase - the particles in the filament vibratemore, meaning its harder for the curren t-c arrying electronsto move through it, therefore resistance increases as thecurrent increases.




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Electr icity (cont)

Diode A diode only allows current to flow in one direction. The IVcharac ter istic is virtually no current until the threshold voltage,where the voltage increases expone nti ally. The thresholdvoltage is approx. 0.6V

Resist ivity

How difficult it is for current to flow through a material. Dependson:• Length of the wire • Cross- sec tional area • Resist ance. ρ = RA/L Unit: Ωm The lower the resist ivity, the better it is at conducting electricity.

For Reference: Copper: 1.68x1 0 Ωm

Semico nductor

A group of materials that arent as good as conducting asmetals, however, if more energy is supplied, the resistancelowers more charge carriers are released.

Superc ond ucto‐r

A metal that can be cooled, and the resist ivity is reduced. Thereis no resist ivity below the critical. The main uses are for strong electr oma gnets, power cableswith no energy loss and fast electronic circuits with minimalenergy loss.

Power(P/W)

The rate of transfer of energy. 1W = 1JS

P= E/t = IV = V /R = I R

Energy(E/J)

E = ItV = V t/R = I Rt

kWh J kWh x 3.6x10

Electr icity (cont)

Electr omotive Force(e.m.f.)

The amount of electrical energy the battery provides andtransfers to each coulomb of charge. ε = E/Q

InternalResistance

The resistance inside cells. ε = I(R + r)

Kirchh off'sFirst Law

The total current entering a junction is equal to the totalcurrent leaving it, i.e. current is split when it reaches ajunction

Kirchh off'sSecondLaw

The total emf of a series circuit, equals the sum of the pdacross each component, i.e. pd is split between componentsin series but not parallel. ε = ΣIR

ResistanceacrossCircuits

Series: RT = R1 + R 2 + R3 + ...

Parallel: 1/RT = 1/R1 + 1/R 2 + 1/R3 + ...

PotentialDivider

A circuit with a voltage source and resistors in series. Thevoltage of one of the resisitors can vary and therefore beused to detect certain changes when thermi stors and LDRsare used.

Gravit ational Fields

ForceField

A region in which a body experi ences a non-co ntact force.

NewtonsLaw ofGravit ation

The force a body experi ences due to gravity is dependant onits weight, the weight of the object exerting the force and thedistance between them An inverse square law. F = GmM/r NB The result of this is the magnitude of the force, thedirection is always towards the centre of the mass causing thegravit ational force.




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Gravit ational Fields (cont)

Gravit ational FieldStrength

The force per unit mass, depending on the location of thebody in a field. g = F/m Also a vector quantity, directed towards the centre of themass causing the force.

g = -ΔV/Δr

Earth's g ≈ 9.81 Nkg

RadialField

Point masses have a radial gravit ational field (such asplanets): g = GM/r

Gravit ationalPotential

The gravit ational potential energy that a unit mass wouldhave. It is negative on the surface of a mass and increaseswith the distance from the mass. It can also be considered asthe energy required to fully escape the body's gravit ationalpull V = -GM/r

Gravit ationalPotentialDifference

The energy required to move a unit mass. When an object ismoved, work is done against gravity ΔW = mΔV

Equipo ten tials

Lines/ Planes that join points of equal gravit ational potential similar to contour lines on maps. Along these lines both ΔV and ΔW are zero, the objectsenergy isn't changing.

Satellite Are smaller objects orbiting a larger object, they are kept inorbit by the force due to the larger body's gravit ational field.

In terms of planets Orbits are ≈ circular, therefore circularmotion equations apply.

Gravit ational Fields (cont)

OrbitalPeriodPropor tio nality

T ∝ rPROOF• Combine F=mv /r and F = GmM/r Solve for v • T = 2πr/v Sub in v

EscapeVelocity

The minimum speed an powered object needs to leave thegravit ational field of a planet

Synchr onousOrbit

When an orbiting object has an orbital period equal to therotational period of the object its orbiting

Geosta tionaryOrbit

An satellite in orbit of a body that remains in the same place it has the same time period. It would have to be over theequator to be a true geosta tionary orbit

LowOrbitingSatellite

Satellites that orbit between 180 and 2000 km above Earth.They are designed for commun ication and as they are low-orbit, they're cheaper to launch and require less powerfultransm itters.

EM Radiation and Quantum

Photoe lectric Effect

The emission of electrons from the surface of a metal inresponse to an incidence light, where the frequency of theincidence light is above that of the metals thresholdfrequency.

ThresholdFrequency

The lowest frequency of light that can cause electrons to beemitted from the surface of a metal.

WorkFunction

The minimum quantity of energy which is required toremove an electron to infinity from the surface of a givensolid, usually a metal. Φ = hf0




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EM Radiation and Quantum (cont)

MaximumKineticEnergy

The energy a photon is carrying minus any other energyloses. These energy loses explain the range of kineticenergies of the photons. The max is equal to hf, with noenergy loss. hf = Φ + 1/2(m) (v max )

StoppingPotential

The potential difference required to stop the fastest movingelectrons travelling at Ek(max)

eVs = Ek(max)

ElectronVolt

The kinetic energy carried by an electron after it has beenaccele rated from rest to a pd of 1 V. 1eV = 1.6 x10 J

GroundState

The lowest energy level of an atom/e lectron inside an atom.

Excitation The movement of an electron to a higher level in an atom,requiring energy. ΔE = E1 - E2 = hf

De-Exc itation

An electron moving towards ground state releasing energyequal to the difference between the states in the form of aphoton.

Fluore scent Tubes

The tubes contain mercury vapour, when a high voltage ispassed across, producing free electrons, which collide withthe mercury electrons exciting them. When they return to theground state, they release a photon in the UV range. Thesethen collide with the tubes phosphorus coating exciting it'selectrons, and then when they return to the ground state theyrelease photons in the visible light range

Line-E missionSpectra

A series of bright lines against a black backgr ound, with eachline corres ponding to a wavelength of light.

EM Radiation and Quantum (cont)

Line-A bso rptionSpectra

When light with a continuous spectrum of energy (white light)pass through a cool gas. Most of the electrons will stay in theirground states but some will be absorbed and excite them tohigher states, these photons are then missing from thespectrum causing black lines on the continuous spectrum.

Diffra ction

When a beam of light passes through a narrow gap andspreads out.

Wave-P articleDuality

An entity behaving with both particle and wave-like behaviour.Light has a relati onship between wavelength and momentum:DeBrog lie's Wavele ngth: λ = h/mv

ElectronDiffra ction

When electrons are accele rated and sent through a graphitecrystal, they pass through the spaces between the atomsproducing a diffra ction pattern

Waves

Reflection When a wave is bounced back when hitting a boundary

Refraction When a wave changes direction as it enters a differentboundary medium. The change in direction is as a result ofthe wave changing speed in the new medium

Diffra ction When a wave spreads out as it passes through a gap oraround a obstacle.

Displa cement (x/m)

The distance a wave has moved from its undist urbedpositi on/its starting point. It is a vector quantity

Amplitude(A/m)

The maximum magnitude of displa cement.

Wavelength(λ/m)

The length of one whole oscill ation of the wave.




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Waves (cont)

Period(T/s)

The time taken for a whole wave cycle. T = 1/f

Frequency(f/Hz)

The number of whole waves per second, passing a givenpoint.f = 1/T

Phase A measur ement of the position if a certain point along thewave cycle

PhaseDifference

The amount by which one wave differs from another

WaveSpeed

c = fλ

TransverseWave

The displa cement of the partic les /field is at a right angle tothe direction of energy transfer. e.g. a spring shaking upand down as displa cement and energy transfer is

Longit udinalWave

The displa cement of the partic les /fields is along the line ofenergy transfer

Polari sation A wave passing through a filter resulting in a polarised wavethat oscillates in one direction only. 2 polarising filters atright angles blocks all light as it blocks both direct ions.Polarising filters are common sunglasses

GlareReduction

Polarising filters reduces the amount of reflected lighttherefore reducing the intensity of the light on your eyes

TV Signals TV signals are polarised by the rod orient ation on thetransm itting aerial. If the rods are lined up, you receive agood signal.

Superp ostion

When 2 waves pass through each, at the instance wherethe wave cross, the displa cement is combined, then eachwave continues.

Waves (cont)

Constr uctiveInterf erence

When 2 waves meet and their displa cements are in thesame direction, the displa cements combine to give a biggerone.

Destru ctiveInterf erence

When 2 waves meet and their displa cement is in oppositedirect ions, they cancel out 'destr oying' the displa cement. Thedispla cement of the combined wave is the sum of theindividual displa cem ents.

ExactlyOut ofPhase

When 2 points on a wave are a odd multiple of 180°/� apart.

In phase When the phase difference of 2 points is 0 or a multiple of360°/2�.

StationaryWave

The superp osition of 2 progre ssive waves with the samefreque ncy /wa vel ength and amplitude moving in oppo sitedirections

Node A point on a stationary wave where no movement occurs -zero amplitude. There is total destru ctive interf erence.

Antinode Points on a stationary wave with maximum amplitude -constr uctive interf erence

ResonantFrequency

When the stationary wave produced has an exact number ofhalf-w ave lengths

FirstHarmonic

When the stationary wave is at its lowest possible frequency- a single loop with one antinode and a node at each end.To find the freq of the nth harmonic, multiply the 1stharmonics freq. by n. f = 1/2l x sqrt(T /μ) where μ is the mass per unit length, T is the tension in thestring and l is the length of the vibrating string.

SecondHarmonic

Twice the frequency of the 1st harmonic. With 2 loops, 2antinodes and 3 nodes (one in the center)










Waves (cont)

Amount ofDiffra ction

When a wave is passed through a narrow gap. Gap > Wavelength No diffra ction Gap = n x Wavelength Minimal Diffra ction Gap = Wavelength Maximum Diffra ction

Monoch romatic Light

Light of a signal wavele ngt h/f req uency and therefore asingle colour. Best for producing clear diffra ction patterns.

WhiteLightDiffra ction

When white light is diffra cted, the different wavele ngths oflight diffract by different amounts. The result is a diffra ctionpattern of spectra instead of single coloured fringes

Two-SouceInterf erence

When waves from 2 sources interfere to produce a pattern.In order to get a clear pattern, the sources must bemonoch romatic and coherant

Coherancy If the waves produce have the same wavele ngt h/f req uencyand have a fixed phase differ ence.

Double -SlitFormula

Young's double -slit formula relate a waves fringe spacing(w/m), its wavele ngt h(λ/m), the slit separa tio n(s/m) and thedistance from the screen (D/m) into a single formula w = λD/s

Waves (cont)

Diffra ctionGrating

Lots of equally spaced slits very close together, produces asharp interf erence pattern, therefore allowing more accuratemeasur ements. The formula relates the distance betweenslits (d/m), the angle to the normal (θ/°), the wavelength(λ/m) and the order of maximum(n) dSin(θ) = nλ The order of maximum is the number of bright spots awayfrom the central spot (which has order 0)

RefractiveIndex

A measure of how optically dense a material is - the moreoptically dense, the higher refractive index. n = c/cs

where c is the speed of light and cs is the speed of light in

the material.

Common Refractive IndexesVacuum = 1 Glass ≈ 1.5 Water ≈ 1.33

At a boundary: 1n2 = c1/c2 = n2 / n1

The relative refractive index from material 1 to material 2.Note when using the refractive indexes of the materials its2/1 rather than 1/2 with the speeds.

SnellsLaw

n1Si n(θ1) = n2Si n(θ2)

When a ray of light travels from one refractive medium toanother.

CriticalAngle

The angle of incidence at which the angle of refraction = 90°i.e. Sin(θ crit) = n2/n1 where n1>n2

TotalInternalReflection

When all light is completely reflected back into a medium ata boundary with another medium instead of being refracted.Occurs when θi > θcrit










Waves (cont)

OpticalFibre

A very thin flexible tube of glass/ plastic fibre in which lightsignals are carried across long distances and aroundcorners by applying TIR. The fibres are surrounded by acladding with a high refractive index and a core of a lowerrefractive index. The light is refracted where the mediumsmeet and travels along the fibre.

SignalAbsorbtion

When some of the signals energy is absorbed by thematerial of the fibre. The final amplitude is reduced.

SignalDispersion

When the final pulse is broader than expected, which cancause inform ation loss as it may overlap with another signal.

ModalDispersion

Light entering at different angles and taking different paths,resulting in signals arriving in the wrong order Single -mode fibre is used to prevent this - light is only allowed tofolllow a very narrow path.

MaterialDispersion

Different amounts of dispersion depending on wavele ngth. Monoch romatic light prevents this.

Nuclear

RutherfordScattering

An experiment that proved the current model of the atom that it is mostly empty space.

Rutherford set up an experi ment, with an alpha emitterpointed at gold foil. He observed the deflection of theparticles and it showed that atoms have a concen tratedmass at the centre and are mostly empty space, whichdisproved the plum-p udding model which was acceptedpreviously.

It showed that: • Atoms = mostly empty space• Nucleus has a large positive charge, as some of the +vecharged alpha particles are repelled and deflected• Nucleus must be tiny due to few particles being deflectedby an angle > 90°• Mass must be concen trated in the nucleus

Nuclear (cont)

Distance ofClosestApproach

Ek = Eelec = Qnucl eus qalp ha /4π ε0r

where r is the distance of closest approach

ElectronDiffra ction

λ≈hc/E where the first minimum occurs at: sinθ ≈ 1.22λ/2R

NuclearRadius

R = R0A

AlphaDecay (α)

Charge (rel): +2Mass(u): 4Penetration: lowIonising: highSpeed: slowAffected by mag. field: yStopped by: paper/ ~10cm air

Used for: Smoke alarms if the particles cant reach thedetector, the smoke must be stopping them

BetaDecay(β^±)

Charge (rel): ±1Mass(u): n/aPenetration: midIonising: weakSpeed: fastAffected by mag. field: yStopped by: ~3mm of aluminium

Used for: PET Scanners, In production of metals thelevels penetr ating through the metal can be used to controlthe thickness.

GammaDecay(γ)

Charge (rel): 0Mass(u): 0Penetration: lowIonising: very weakSpeed: c (speed of light)Affected by mag. field: nStopped by: several cm of lead.

Used for: PET Scanners produced throughannihi lation, cancer treatment.




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Nuclear (cont)

BackgroundRadiation

The low level of radiation that always exists. Must betaken into account when measuring radiation.

Sources ofBackgroundRad.

• The Air Radioa ctive radon gas released from rocks• Ground /Bu ildings Nearly all rock containsradioa ctive materials• Cosmic Radiation nuclear radiation from particlecollisions due to cosmic rays• Living things living things are made of carbon, someof which is radioa ctive carbon-14• Man-Made Radiation from indust ria l/m edical sources

Intensity I = k/x Intensity (Wm ) = constant of propor tio nality(W)/di stance from source (m)

Radioa ctiveDecay

It both sponta neous and random.

Spontaneous: Decay is not affected by external factorsRandom: It cannot be predicted when the next decayoccurs

DecayConstant

The probab ility of a specific nucleus decaying per unittime. It is a measure of how quickly a isotope will decay.

Activity (Bq) The number of nuclei that will decay each second.

A = λN where λ is the decay constant, and N is the number ofunstable nuclei in the sample

It can also be written as:

ΔN/Δt = -λN (ΔN is always a decreasing number hence the neg sign)

A = A0e

A0 is the activity at t=0

Nuclear (cont)

NumberofunstableNuclei(N)

N = N0e

where N0 is the original number of the unstable nuclei

N = nNA

where n is the number of moles and NA is Avogadro's

constant

Half-Life(T1/2)

The average time the isotope takes for the number of nucleito halve.T1/2 = ln2/λ

(Derived from N = N0e )

Uses ofRadiation

• Carbon Dating Using the amount of C-14 left in theorganic material. Problems are that the material may havebeen contam inated, high background count, uncert ainty in c-14 in the past and sample size may be too small• Medical Diagnosis Tracers that emit radiation to trackthings in the body

Instab ility Nuclei are unstable when:• Too many/not enough neutrons• Too many nucleons• Too much energy

If they nuclei lies on the N=Z line they are generally stable. Ifthey lie above, they undergo β decay, if they lie below, theundergo β decay. If they have a Z number of over ~82(Protons) they undergo α decay.

MassDefect

The mass of a nucleus is less than the mass of itsconsti tuents. This energy difference is the mass defect and islost to energy as E = mc , energy and mass are equiva lent.

BindingEnergy

If you were to pull a nucleus apart, this binding energy wouldbe the energy required to do so, equal to the energy releasedwhen the nucleus formed.




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Nuclear (cont)

AverageBindingEnergy

Average Binding energy per nucleon = BindingEnergy /Nu cleon number

NuclearFission

When large unst able nuclei randomly split into smaller morestable nuclei. Energy is released as the smaller nuclei have ahigher avg. binding energy per nucleon

NuclearFusion

When 2 smaller nuclei combine to form a larger nuclei. A lot ofenergy is released because the new heavier nucleus has ahigher avg. binding energy (if the 2 original nuclei are lightenough). This is the energy that keeps stars burning

Nuclear (cont)

NuclearFissionReactors

• Control Rods Usually made of carbon, they are loweredand raised to control the rate of fission. The amount of fuelrequired to produce one fission per fission is the critical mass.Any less (sub-c rit ical) then the reaction will eventually fizzleout. Any more, and the reactor could go into meltdown, whichis why control rods are used.• Mode rator Fuel rods are placed in the moderator, thisslows down/a bsorbs neutrons to control the rate. The choiceof moderator needs to slow down the neutrons enough to slowdown neutrons enough to keep the rate of fission steady. Itslows down neutrons through elastic collis ions, a moderatorwith a similar nucleo n-mass to the neutrons. • Cool ant is sent around the reactor to remove heatproduced by the fissio. The material is either liquid or gas atroom temp. Often it is the same water (heavy -water) as themoderator and can be used to make steam and turn turbines. • Shie lding Reactors are surrounded by thick concrete,which shields and protects from radiation escaping andanyone working there.• Emer gency Shut-d own All reactors have anemergency shutdown where the control rods are completelylowered into the reactor, thus absorbing all the neutronsproduced and slowing the reaction down as quickly aspossible. • Waste Unused uranium only produces α so can beeasily contained. Spent uranium however emit β & γ radiation.Once removed from the reactor they are cooled and ten storedin sealed containers until the activity is at a low enough level.










Further Mechanics

Radian Objects in circular motion travel through angles, mostlymeasured in radians. Rads to Deg:Angle in deg x π/180

AngularSpeed

The angle an object rotates through per second. ω = θ/t = v/r = 2π/T = 2πf

Frequency The number of revolu tions per second. f = 1/T

TimePeriod

The time taken for a complete revolu tion.

Centri petalAccele ration

Objects travelling in a circle are accele rating as their velocityis changing consta ntly. The accele ration is always actingtowards the centre of the circle. a = v /r = ω r

Centri petalForce

Is the resolved force which is always directed towards thecentre of the circle. F = mv /r = mω r

SimpleHarmonicMotion

An object undergoing SHM is oscill ating to and fro, eitherside of an equili brium position.

It is defined as An oscill ation in which the accele ration ofan object is directly propor tional to its displa cement,which is always directed towards the equili briumposition

Displa cement (x)

Displa cement varies as a cosine /sine wave with a maximumvalue of A (Amplitude)

x = Acos(ωt)

Velocity(v)

Is the gradient of the displa cement time graph. Its maximumvalue is ωA

v = ±ω x sqrt(A x )vmax = ωA

Further Mechanics (cont)

Accele ration (a)

Is the gradient of the velocity time graph. Its maximum valueis ω A

a = ω x

Mass-S pringSystem

A mass on a spring is a simple harmonic oscill ator. Whenthe mass is pulled /pushed from the equili brium position, thereis a force directed back towards the equili brium position.

F = kΔL where k is the spring constant and ΔL is thedispla cement.

The Time period for a M-S System is given by:

T = 2π x sqrt(m/k)

Pendulum A pendulum is an example of a Simple Harmonic Oscill ator.The time period for a pendulum is given by:

T = 2π x sqrt(l/g)

FreeVibration

Free vibrations involve no transfer of energy to/from thesurrou ndings. If a mass-s pring system is stretched, it willoscillate at its natural frequency fn.

ForcedVibration

Forced Vibration occurs when there is an external drivingforce. A system can be forced to vibrate by a periodicexternal force. This is called the driving frequency, fd.

fd << fn Both are in phase

fd >> fn The oscillator will not be able to keep up and will

end up out of control. i.e. completely out of phase.




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Further Mechanics (cont)

Resonance As fd → fn, the system gains more and more energy from

the driving force, thus the amplitude rapidly increases. Thesystem is now considered to be resona ting. At resonance,the phase difference between the driver and the oscillator is90°.

Damping Any oscill ating system loses energy to its surrou ndings damping. System are also delibe rately damped to stop themoscill ating or minimise resonance.

Light Damping Take a long time for oscill ation to stop,the amplitude is decreased slowly. Displa cem ent -TimeGraph: sharp peak.Heavy Damping The amplitude decreases rapidly, andoscill ation takes much less time to stop.D isp lac eme nt-TimeGraph: flat peak.Critical Damping Oscill ation is stopped in the shortestamount of time possible.Over Damping Systems with even heavier damping,they take longer to reach equili brium than a criticallydamped system.









a level physics key terms - cheatography.com

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