MechanicsScalar  A quantity without direction. Length/Distance, Speed, Mass, Temperature, Time, Energy  Vector  A quantity with both direction and magnitude Displacement, Velocity, Force (inc. Weight), Acceleration, Momentum  Equilibrium  When all forces acting on an object are balanced and cancel each other out. There is no resultant force  Freebody Diagram  A diagram of all the forces acting on a body, but not the forces it exerts on other things. The arrows indicate magnitude and direction.  Principle of Moments  For a body to be in equilibrium, the sum of the clockwise moments equals the sum of the anticlockwise moments.  Moment  The product of the size of the force and the perpendicular distance between the turning point and the line of action of the force.  Couple  A pair of forces with equal size which act parallel to each other but in opposite direction. E.g. turning a car's steering wheel.  Centre of Mass  The single point from which the body's weight acts through. The object will always balance around this point. To calculate for uniform objects: Σmx = Mx̄  SUVAT (Constant Acceleration)  v = u + at s = 1/2 (u+v)t v^{2} = u^{2} + 2as s = ut + 1/2 at^{2} s = vt  1/2 at^{2}  DisplacementTime Graph  Displacement (y) against Time (x). Gradient = Velocity Acceleration = Δgradient  VelocityTime Graph  Velocity (y) against Time (x) Gradient = Acceleration ΔGradient = ΔAcceleration Area = Displacement  Variable Acceleration  Differentiate x v a Δa Integrate  AccelerationTime Graph  Acceleration (y) against Time (x). Gradient = ΔAcceleration 0 Gradient = No acceleration constant velocity. Constant Gradient = constant acceleration Area = Velocity NB: Remember to treat area below the time axis as negative!  Newtons 1st Law  The velocity of an object will not change unless a resultant force acts on it.  Newtons 2nd Law  F = ma The acceleration of an object is ∝ to the resultant force acting upon it. (for objects with a constant mass) Points to remember: • Resultant Force is vector sum of all the forces • Unit = N • Ensure mass is in kg • Acceleration is in the same direction as resultant force.  Newtons 3rd Law  If object A exerts a force on object B, then object B exerts an equal but opposite force on object A  Freefall  When there is only gravity acting upon an object. i.e. motion with an acceleration of g (9.81ms^{2}) The same SUVAT equations apply, however, u = 0 and a = g {{ng}} NB: 'direction' of motion, dictates the sign of g  Projectile Motion  An object given an initial velocity, then left to move freely under g. There is separate horizontal and vertical motion with time being the only common attribute. Both motion follows SUVAT equations but horizontal motion has no acceleration.  Friction  Force that opposes motion. When in a fluid (liquid or gas) it is 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  Terminal Speed  When frictional forces equal the driving force. For a falling object, 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 external forces are involved)  Inelastic Collision  Not all of the kinetic energy is conserved. Momentum however is conserved.  Elastic Collision  Kinetic energy is conserved i.e. no energy is dissipated as heat or other energy forms.  Impulse  An extension of N2L. Impulse is the product of force and time and is equal to the momentum of that body. FΔt = Δ(mv) Also equal to the area under a forcetime graph.  Work Done  The energy transferred 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  ForceDisplacement Graph  Area = Work Done  Conservation of Energy  Energy cannot be created nor destroyed, only converted from one form to another, but the total energy of a closed system will not change.  Efficiency  useful output/input in terms of energy or power. 
MaterialsDensity  ρ = m/V A property all materials have and is independent of both shape and size.  Limit of Proportionality  The point where Hooke's law no longer applies. On a forceextension graph, the limit of proportionality is where the line is no longer straight  Hooke's Law  F = kΔL The force is proportional to the extension of a stretched wire. k is the stiffness constant a measure of how hard it is to stretch  Elastic Limit  The point on a forceextension graph where the line begins to curve. Beyond this point, permanent deformation occurs where the wire will no longer return to its original shape.  ForceExtension Graph  Straight section Gradient = k Loading and unloading plot a loop, if a stretch is elastic, the curve starts and finishes in the same position (the origin). If plastic deformation occurs, the unloading line has the same gradient (k) but crosses the x axis at a different point
Area = Elastic Strain Energy
The area between the loading and unloading line (after plastic deformation) is equal to the work done in deforming the material  Tensile Stress  The ratio of forced applied and crosssectional area. stress = F/A  Tensile Strain  The ratio of extension to original length, it has no units and is just a ratio. strain = ΔL/L  Youngs Modulus  The ratio of tensile stress and tensile strain E = FL/AΔL The YM of a material is the constant value up to the limit of proportionality,  StressStrain Graph  Stress (y) against Strain (x). Gradient = Young's Modulus Area = strain energy per unit volume  Yield Point  The point on a stressstrain graph where the material stretches without any extra load.  Brittleness  When a material breaks after a certain about of force is applied. The line simply stops on a stressstrain graph. The same thing applies on a forceextension graph, the line just stops. 
Thermal PhysicsKelvin  A temperature scale that is in terms of an atoms movements. °C K + 273  Absolute Zero  The lowest theoretical temperature of anything 0 K = 273°C  Internal Energy  The internal energy of a body is the sum of the randomly distributed kinetic and potential energies of all its particles  Closed System  A system where no matter or energy is transferred in or out of the system  Heat Transfer  Heat is always transferred from a hot area/substance to a cold area/substance.  Specific Heat Capacity  The amount of energy required to heat up 1kg of the material by 1°C/1 K ΔQ = mcΔT Energy Change is equal to the product of the mass, specific heat capacity and the change in temperature.  Specific Latent Heat  The specific latent heat of fusion ( Solid) / vaporisation ( gas) is the quantity of thermal energy needed/will be lost to change the state of 1kg of the substance. Q = ml where m is the mass and l the latent heat.
When a substance changes state, there is a period where the temperature of the material is constant, as the internal energy rises, this is due to the latent heat.  Boyle's Law  At a constant temperature, pV is constant. i.e. p1 V1 = p2 V2 On a pV plot, the higher the line, the higher the temperature.  Charles' Law  At a constant pressure: V is directly proportional to its absolute temperature T V1 /T1 = V2 /T2  Pressure Law  At a constant volume: p is directly proportional to its absolute temperature. p1 /T1 = p2 /T2
 Molecular Mass  the sum of the masses of all the atoms that make up the molecule.  Relative Molecular Mass  The sum of the relative atomic masses of all the atoms.  Avogadro Constant  The number of atoms in exactly 12g of carbon isotope ^{12}6 C. NA = 6.02 x10^{23} mol^{1}  Molar Mass  The mass of a material containing NA molecules  Ideal Gas Equations  pV = nRT n = number of moles R = molar gas constant
pV = NkT N = number of molecules k = Boltzmann constant
A way of remembering which n is which. Moles will be small, therefore small n. Number of molecules will be large so, big N.  Kinetic Theory  The pressure exerted by an ideal gas can be derived by considering the gas as individual particles. pV = 1/3 x Nm(Crms )^{2} Crms is the root mean square speed.
Assumptions • All molecules in the gas are identical • Gas contains a large number of molecules • The volume of the molecules is negligible when compared to the volume of the container/gas as a whole.  Brownian Motion  Random motion of particles suspended in a fluid helped provide evidence that the movement of the particles was due to the collisions of the fast randomlymoving particles, which supported the model of kinetic theory.  Average Kinetic Energy  1/2 x m(Crms )^{2} = 3/2 x nRT/N 1/2 x m(Crms )^{2} = 3/2 x RT/NA 
Particles and RadiationProton & 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^{27} kg).  Electron  A fundamental lepton, with a charge of 1. Cannot be broken down into other subatomic particles. Relative mass of 1/2000 (9.11x10^{31} kg)  Nuclide Notation ^{A}Z X  The general notation of elements.  Proton Number (Z)  The number of protons in an atom. Defines the element. For a neutral atom, proton no. also == the electron number  Nucleon Number (A)  AKA Mass Number  number of total nucleons (protons + neutrons)  Specific Charge  The ratio of a particles charge to its mass. Specific meaning per kg. S.C. = Charge (Q) / Mass (kg)  Isotope  Atoms with the same number of protons but a different number of neutrons. Affects the stability of a atom  Strong Nuclear Force  A strong force that holds atoms together at small distances, strong enough to overcome the electrostatic repulsion of the protons. Distances Repulsive: <0.5 fm (0.5 x10^{15}m) Attractive: 0.5 to 3 fm Rapidly falls to ) after 3 fm.  Alpha Decay (α)  Occurs in big atoms (82+ protons). Atoms emits a helium nucleus (2 protons 2 neutrons). Particles is too big to be kept stable by the SNF.  BetaMinus Decay (β^{})  Emission of a electron and antielectronneutrino. Happens in neutron rich particles. In nucleus structure terms, a neutron turns into a proton by changing an d quark to a u quark, emitting an electron and antielectronneutrino.  BetaPlus Decay (β^{+})  Emission of a positron and an electron neutrino. One of the atoms protons, changes a u quark to a d quark, changing to a neutron emitting a positron and an electronneutrino.  Photon  A discrete packet of electromagnetic radiation with 0 mass. E = hf = hc/λ  Antiparticle  The corresponding antiparticle to any particle has the same mass and rest energy but opposite charge.  Pair Production  When 2 of the same particles collide at high speed and produce a particleantiparticle pair. The energy of the collisions is converted into the pair. Also occurs when a photon has enough energy to produce an electronpositron pair. Emin = 2E0 (in MeV)  Annihilation  When a particle and antiparticle collide producing 2 photons in opposite directions. Emin = E0 This collision is used in PET scanners to detect cancers.  Hadron  Particles that can feel the strong force. Either a baryon or a meson depending on its quark structure  Baryon  A hadron consisting of 3 quarks. All are unstable except a free proton  all eventually decay into a proton. Proton: uud Neutron: ddu  Baryon Number  A quantum number which is always conserved. Baryons have a B.N. of +1. Antibaryons have a B.N. of 1 and all other particles have a B.N of 0.  Mesons  A hadron consisting of 2 quarks  a quarkantiquark pair. There are 9 possible combinations, making either Kaons or Pions.  Lepton  A fundamental particle that doesnt feel the strong force. Interacts via the weak interaction.  Lepton Number  Another quantum number that is always conserved. Must be separate for leptonelectron number and electronmuon number.  Strange Particles  Particles that have a property of strangeness  contain a strange/antistrange quark. Created via the strong interaction Decay via the weak interaction Rules of conversation mean that strange particles are only produced in pairs.  Strangeness  Another quantum number  however it can change by ±1 or 0 in an interaction.  Quark  A fundamental particle that makes up hadrons. There are 6 types:up/down, top/bottom, strange/charm.  Quark Confinement  There is no where to get a quark on its own, when enough energy is provided, pairproduction occurs, with one quark remaining in the particle.  Weak Interaction  β^{+} and β^{} are both examples of weak interactions, which is interaction via the weak force, the force acting between leptons.  Feymann Diagram  A diagram of particle interactions, with: Wavy Lines : Exchange Particle Straight Lines : Particles in/out of the interaction (with arrows indicating direction) 
Magnetic FieldsMagnetic Field  A region where a force acts, force is exerted on magnetic/magnetically susceptible materials (e.g. iron).  Magnetic Field Lines  Lines that show a magnetic field. They run from north to the south pole of a magnet. The more dense the lines are, the stronger the field  Magnetic Flux Density  The force on one metre of wire carrying a current of 1 A at right angles to the magnetic field. AKA The strength of the magnetic field B = F/Il Magnetic flux density is the force by the current meter  Magnetic Field around a wire  When current flows, a magnetic field is induced. Right hand rule: • Curl Fingers around "wire". • Stick up thumb Thumb:Direction of current Fingers: Direction of magnetic field  Solenoid  A cylindrical coil of wire acting as a magnet when carrying electric current. Forms a field like a bar magnet.  Force on a CurrentCarrying Wire  A currentcarrying wire, running through a magnetic field generates a resultant field of the one induced by the current and the preexisting one. The direction of the force is perpendicular to the current direction and the mag. field.  LeFthand Rule  For finding the direction of the Force. • Thumb upwards • First finger forwards • Second finger to the right (perpendicular to f.f.)
Thumb:Force/Motion First Finger:Field Second Finger:Current  Charged Particles in a mag. field  F = BQv  Circular Path  For a charge travelling perpendicular to a field is always perpendicular to the direction of motion The condition for circular motion.
F = mv^{2}/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 the charge increases • f = v/2πr •Combined with r = mv/BQ f = BQ/2πm  Particle Accelerator  A cyclotron consists of 2 hollow semiconductors, with a uniform magnetic field applied perpendicular to the plane of the D magnets. An A.C. is applied. Charged particles are fired into the D's. They accelerate across the gap between magnets, taking the same amount of time for the increasing radius.  Magnetic Flux  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  Electromagnetic Induction  Relative motion between a conductor and a mag. field, causes an emf to generate at the ends of the conductor as the electrons accumulate at one end.  Flux Linkage  The amount of field lines being cut NΦ = BANCos(θ) where θ is the angle between the normal to the coil and the field. (if it is perpendicular, θ = 0°  Faraday's Law  Induced e.m.f. is proportional to the rate of change of flux linkage... ε = NΔΦ/Δt  Lenz's Law  The induced e.m.f. is always in such a direction that it opposes the change that caused it.  e.m.f in a rotating coil  NΦ = BANCos(ωt) ε = BANωSin(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 a electric current.  Righthand Rule  For Generators. • Thumb upwards • First finger forwards • Second finger to the left (perpendicular to f.f.)
Thumb:Force/Motion First Finger:Field Second Finger:Current  Alternating Current  Current that's direction changes over time. The voltage across the resistance goes up and down.  Root Mean Squared (rms) Power  Vrms = V0 /sqrt(2) Irms = I0 /sqrt(2) Prms = Irms x Vrms  Transformer  A device that uses electromagnetic induction to change the size of a voltage for an alternating current.
An alternating current flowing in the primary coil causes the core to magnetise/demagnetise continuously in opposite directions. This produces a rapidly changing magnetic flux in the core (made of magnetically soft material. The changing flux passes through the secondary coil induces a alternating e.m.f. if the same frequency but different voltage (if the no. of turns is different)  Transformer Equations  P.Coil: Vp = Np x ΔΦ/Δt S.Coil: Vs = Ns x ΔΦ/Δt
Combines to: Ns /Np = Vs /Vp  Inefficiencies in a Transformer  • Eddy Currents (looping currents induced by changing flux) create opposing magnetic fields reducing its strength reduced by laminating the core so that current cannot flow between the cores layers • Heat Generation due to the resistance in the coils reduced by using a wire with a low resistance • Magnetising/Demagnetising the core energy is wasted as the core is heated reduced by using a magnetically soft core, which has a small hysteresis loop, this the energy required to create/collapse the field is minimised
Efficiency Equations efficiency = Is Vs /Ip Vp powerout /powerin 
EngineeringMoment of Inertia  A measure of how difficult it is to rotate an object or change its rotational speed
I = Σmr^{2} This equation means that the moment of inertia is dependent in the masses, and their distribution, so a solid disk may have a lower moment of inertia than a hoop.  Rotational Kinetic Energy  The rotational kinetic energy of an object is dependant on its moment of inertia. Ek = 1/2 x Iω^{2}  Rotational SUVAT  The SUVAT equations can be applied directly to rotational motion, but with rotational's counterparts: s θ (rads) u ω0 v ω a α t t  Torque  When a force causes an object to turn, the turning effect is torque. T = Fr T = Iα  Work & Power  The work done is the product of the force and the angle turned 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 = Tapplied  Tfrictional  Flywheels  A flywheel is a heavy wheel that has a high moment of inertia, meaning once spinning it is hard to stop. They are charged as they are spun, turning T into rotational kinetic energy. It is used as a energy storage device if energy is needed, the wheel decelerates and provides some of its rotational energy to another part of the machine.
Flywheels maximused for energy storage are dubbed flywheel batteries.
Factors that effect storage: • Mass If the mass is increased, the moment of inertia and hence the r. Ek • Angular Speed if the angular speed is increasd, the energy stored increases with angular speed^{2}, so increasing the a.speed, greatly increases energy storage. • Spoked Wheel this again increases the moment of inertia as the mass is distributed further away from the center. • Material Carbon fibre is generally used as it is strong and allows for higher angular speeds • Friction Reduction lubrication is used to reduce friction as well as superconducting magnets to stop contact and therefore friction. Vacuums are also used so air resisitance is not a factor.
Uses • Smoothing Torque Flywheels are used to keep systems relying on torque running smoothly • Breaking especially in F1 cars, flywheels are used to harness some of the force when breaking to allow for faster acceleration afterwards • Wind Turbines to provide stable power for days without wind and/or peak times
 Angular Momentum  Angular Momentum = Iω
Iinitial x ωinitial = Ifinal x ωfinal Angular Momentum IS** conserved  Angular Impulse  Impulse = Δ(Iω) = TΔt  1st Law of Thermodynamics  Q = ΔU + W
If energy is transferred to the system: Q = +ve If work is done on the gas: W = ve If the internal energy increases:U = +ve
For closed systems, the first law can be applied, also known as nonflow processes as no gas flows in or out. To apply the law, it is assumed to be an Ideal Gas.  Isothermal (Constant temperature) Change  ΔU = 0 Therefore Q = W There is no change in internal energy... no change in temperature therefore: pV = Constant.
pV plot is a curve, with higher lines indicating a higher temperature. The work done is the area under the line.
Expansion is and is positive. Compression is and is negative.  Adiabatic (No heat transfer) Change  Q = 0 Therefore ΔU = W pV^{γ} = constant
Steeper gradient than a isotherm's plot. There is a greater amount of work done for an adiabatic change than a isotherm  Isobaric (Constant Pressure) Changes  W = pΔV Therefore V/T is constant
No work done.  Isometric (Constant Volume) Changes  W = 0 Therefore Q = ΔU and p/T is constant
Work done = area under straight line  Cyclic Process  A System that undergos a number of combinations of processes. They start at a certain pressure and volume and return to it at the end of a cycle.  4Stroke Petrol Engine  • Induction The piston starts at the top of the cylinder, and moves down increasing the volume of the gas above it. A airfuel mixture is drawn in through an open inlet valve. Pressure remains constant just above atmospheric. • Compression The inlet valve is closed, the piston moves up the cylinder. Work is done on the gas, and the pressure increases. Just before the end of the stoke, a spark ignites the airfuel mixture. Temperature and pressure increase. • Expansion The explosion expands and pushes the piston back down. Work is done as the gas expands, there is also a net output. Just before the bottom, the exhaust valve opens and the pressure reduces. • Exhaust The piston moves up the cylinder and the burnt gas leaves through the exhaust valve, the pressure remains constant just above atmospheric.  4Stroke Diesel Engine  Induction Stroke Only air is drawn. Compression The air is compressed enough to have a temperature to ignite diesel fuel just before the end of the stroke, diesel fuel is sprayed in and ignites. Expansion & Exhaust The same as petrol
 Indicated Power  Pindicated = Area of pV loop x cycles per second x no. of cylinders The net work done by the cylinder in one second.  Output Power  The useful power at the crankshaft P = Tω  Friction Power  The power lost due to friction between moving parts Pfriction = Pind  Pbrake  Engine Efficiency  Pinp = Calorific Value x Fuel Flow Rate Mechanical Efficiency = Pbrake /Pind Affected by energy lost due to moving parts Thermal Efficiency = Pind /Pinp Heat energy transferred into work Overall Efficiency = Pbrake /Pinp  2nd Law of Thermodynamics  Heat engines must operate between a heat source and a heat sink Engine Efficiency = W/QH = (QH  QC )/QH Max Theoretical Efficiency = (TH  TC )/TH  Heat Engine  A Source of heat (TH ) QH Heat Engine W QC Heat Sink (TC )
 Reverse Heat Engine  Hot (TH ) QH Heat Engine W QC Cold (TC )
 Refridgerator  A reverse heat engine where the cold space is the actual fridge. Whilst the hot space is the surroundings, the fridges aim is to extract as much heat from the cold space to the surroundings.  Coefficient of Preformance  COPref = Qc /W = Qc /(Qh Qc ) = Tc /(Th Tc ) COPhp = Qh /W = Qh /(Qh Qc ) = Th /(Th Tc ) 
  ElectricityCurrent (I/A)  The rate of flow of charge. Conventionally running from + to . Measured my an Ammeter (in series) I = ΔQ/Δt  Potential Difference (V/V)  The work done in moving a unit charge between 2 points. 1 V = 1JC^{1}. 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 the circuit. R = V/I  Ohmic Conductor  Under constant physical conditions, I is proportional to V. On a graph of I (y) against V (x), the gradient is equal to 1/R.  Filament Lamp  A filament lamp has an IV characteristic of a cubic (s shape) going through the origin. The heat in the filament causes the resistance to increase  the particles in the filament vibrate more, meaning its harder for the currentcarrying electrons to move through it, therefore resistance increases as the current increases.  Diode  A diode only allows current to flow in one direction. The IV characteristic is virtually no current until the threshold voltage, where the voltage increases exponentially. The threshold voltage is approx. 0.6V  Resistivity  How difficult it is for current to flow through a material. Depends on: • Length of the wire • Crosssectional area • Resistance. ρ = RA/L Unit: Ωm The lower the resistivity, the better it is at conducting electricity.
For Reference: Copper: 1.68x10^{8} Ωm  Semiconductor  A group of materials that arent as good as conducting as metals, however, if more energy is supplied, the resistance lowers more charge carriers are released.  Superconductor  A metal that can be cooled, and the resistivity is reduced. There is no resistivity below the critical. The main uses are for strong electromagnets, power cables with no energy loss and fast electronic circuits with minimal energy loss.  Power (P/W)  The rate of transfer of energy. 1W = 1JS^{1}
P= E/t = IV = V^{2}/R = I^{2}R  Energy (E/J)  E = ItV = V^{2}t/R = I^{2}Rt
kWh J kWh x 3.6x10^{6}  Electromotive Force (e.m.f.)  The amount of electrical energy the battery provides and transfers to each coulomb of charge. ε = E/Q  Internal Resistance  The resistance inside cells. ε = I(R + r)  Kirchhoff's First Law  The total current entering a junction is equal to the total current leaving it, i.e. current is split when it reaches a junction  Kirchhoff's Second Law  The total emf of a series circuit, equals the sum of the pd across each component, i.e. pd is split between components in series but not parallel. ε = ΣIR  Resistance across Circuits  Series: RT = R1 + R 2 + R3 + ... Parallel: 1/RT = 1/R1 + 1/R 2 + 1/R3 + ...  Potential Divider  A circuit with a voltage source and resistors in series. The voltage of one of the resisitors can vary and therefore be used to detect certain changes when thermistors and LDRs are used. 
Gravitational FieldsForce Field  A region in which a body experiences a noncontact force.  Newtons Law of Gravitation  The force a body experiences due to gravity is dependant on its weight, the weight of the object exerting the force and the distance between them An inverse square law. F = GmM/r^{2} NB The result of this is the magnitude of the force, the direction is always towards the centre of the mass causing the gravitational force.  Gravitational Field Strength  The force per unit mass, depending on the location of the body in a field. g = F/m Also a vector quantity, directed towards the centre of the mass causing the force.
g = ΔV/Δr  Earth's g  ≈ 9.81 Nkg^{1}  Radial Field  Point masses have a radial gravitational field (such as planets): g = GM/r^{2}  Gravitational Potential  The gravitational potential energy that a unit mass would have. It is negative on the surface of a mass and increases with the distance from the mass. It can also be considered as the energy required to fully escape the body's gravitational pull V = GM/r  Gravitational Potential Difference  The energy required to move a unit mass. When an object is moved, work is done against gravity ΔW = mΔV  Equipotentials  Lines/Planes that join points of equal gravitational potential similar to contour lines on maps. Along these lines both ΔV and ΔW are zero, the objects energy isn't changing.  Satellite  Are smaller objects orbiting a larger object, they are kept in orbit by the force due to the larger body's gravitational field.
In terms of planets Orbits are ≈ circular, therefore circular motion equations apply.  Orbital Period Proportionality  T^{2} ∝ r^{3} PROOF • Combine F=mv^{2}/r and F = GmM/r^{2} Solve for v • T = 2πr/v Sub in v  Escape Velocity  The minimum speed an powered object needs to leave the gravitational field of a planet  Synchronous Orbit  When an orbiting object has an orbital period equal to the rotational period of the object its orbiting  Geostationary Orbit  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 the equator to be a true geostationary orbit  Low Orbiting Satellite  Satellites that orbit between 180 and 2000 km above Earth. They are designed for communication and as they are loworbit, they're cheaper to launch and require less powerful transmitters. 
EM Radiation and QuantumPhotoelectric Effect  The emission of electrons from the surface of a metal in response to an incidence light, where the frequency of the incidence light is above that of the metals threshold frequency.  Threshold Frequency  The lowest frequency of light that can cause electrons to be emitted from the surface of a metal.  Work Function  The minimum quantity of energy which is required to remove an electron to infinity from the surface of a given solid, usually a metal. Φ = hf0  Maximum Kinetic Energy  The energy a photon is carrying minus any other energy loses. These energy loses explain the range of kinetic energies of the photons. The max is equal to hf, with no energy loss. hf = Φ + 1/2(m)(vmax )^{2}  Stopping Potential  The potential difference required to stop the fastest moving electrons travelling at Ek(max) eVs = Ek(max)  Electron Volt  The kinetic energy carried by an electron after it has been accelerated from rest to a pd of 1 V. 1eV = 1.6 x10^{19} J  Ground State  The lowest energy level of an atom/electron inside an atom.  Excitation  The movement of an electron to a higher level in an atom, requiring energy. ΔE = E1  E2 = hf  DeExcitation  An electron moving towards ground state releasing energy equal to the difference between the states in the form of a photon.  Fluorescent Tubes  The tubes contain mercury vapour, when a high voltage is passed across, producing free electrons, which collide with the mercury electrons exciting them. When they return to the ground state, they release a photon in the UV range. These then collide with the tubes phosphorus coating exciting it's electrons, and then when they return to the ground state they release photons in the visible light range  LineEmission Spectra  A series of bright lines against a black background, with each line corresponding to a wavelength of light.  LineAbsorption Spectra  When light with a continuous spectrum of energy (white light) pass through a cool gas. Most of the electrons will stay in their ground states but some will be absorbed and excite them to higher states, these photons are then missing from the spectrum causing black lines on the continuous spectrum.  Diffraction  When a beam of light passes through a narrow gap and spreads out.  WaveParticle Duality  An entity behaving with both particle and wavelike behaviour. Light has a relationship between wavelength and momentum: DeBroglie's Wavelength: λ = h/mv  Electron Diffraction  When electrons are accelerated and sent through a graphite crystal, they pass through the spaces between the atoms producing a diffraction pattern 
WavesReflection  When a wave is bounced back when hitting a boundary  Refraction  When a wave changes direction as it enters a different boundary medium. The change in direction is as a result of the wave changing speed in the new medium  Diffraction  When a wave spreads out as it passes through a gap or around a obstacle.  Displacement (x/m)  The distance a wave has moved from its undisturbed position/its starting point. It is a vector quantity  Amplitude (A/m)  The maximum magnitude of displacement.  Wavelength (λ/m)  The length of one whole oscillation of the wave.  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 given point. f = 1/T  Phase  A measurement of the position if a certain point along the wave cycle  Phase Difference  The amount by which one wave differs from another  Wave Speed  c = fλ  Transverse Wave  The displacement of the particles/field is at a right angle to the direction of energy transfer. e.g. a spring shaking up and down as displacement and energy transfer is  Longitudinal Wave  The displacement of the particles/fields is along the line of energy transfer  Polarisation  A wave passing through a filter resulting in a polarised wave that oscillates in one direction only. 2 polarising filters at right angles blocks all light as it blocks both directions. Polarising filters are common sunglasses  Glare Reduction  Polarising filters reduces the amount of reflected light therefore reducing the intensity of the light on your eyes  TV Signals  TV signals are polarised by the rod orientation on the transmitting aerial. If the rods are lined up, you receive a good signal.  Superpostion  When 2 waves pass through each, at the instance where the wave cross, the displacement is combined, then each wave continues.  Constructive Interference  When 2 waves meet and their displacements are in the same direction, the displacements combine to give a bigger one.  Destructive Interference  When 2 waves meet and their displacement is in opposite directions, they cancel out 'destroying' the displacement. The displacement of the combined wave is the sum of the individual displacements.  Exactly Out of Phase  When 2 points on a wave are a odd multiple of 180°/Ⲡ apart.  In phase  When the phase difference of 2 points is 0 or a multiple of 360°/2Ⲡ.  Stationary Wave  The superposition of 2 progressive waves with the same frequency/wavelength and amplitude moving in opposite directions  Node  A point on a stationary wave where no movement occurs  zero amplitude. There is total destructive interference.  Antinode  Points on a stationary wave with maximum amplitude  constructive interference  Resonant Frequency  When the stationary wave produced has an exact number of halfwavelengths  First Harmonic  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 1st harmonics freq. by n. f = 1/2l x sqrt(T/μ) where μ is the mass per unit length, T is the tension in the string and l is the length of the vibrating string.  Second Harmonic  Twice the frequency of the 1st harmonic. With 2 loops, 2 antinodes and 3 nodes (one in the center)  Amount of Diffraction  When a wave is passed through a narrow gap. Gap > Wavelength No diffraction Gap = n x Wavelength Minimal Diffraction Gap = Wavelength Maximum Diffraction  Monochromatic Light  Light of a signal wavelength/frequency and therefore a single colour. Best for producing clear diffraction patterns.  White Light Diffraction  When white light is diffracted, the different wavelengths of light diffract by different amounts. The result is a diffraction pattern of spectra instead of single coloured fringes  TwoSouce Interference  When waves from 2 sources interfere to produce a pattern. In order to get a clear pattern, the sources must be monochromatic and coherant  Coherancy  If the waves produce have the same wavelength/frequency and have a fixed phase difference.  DoubleSlit Formula  Young's doubleslit formula relate a waves fringe spacing (w/m), its wavelength(λ/m), the slit separation(s/m) and the distance from the screen(D/m) into a single formula w = λD/s  Diffraction Grating  Lots of equally spaced slits very close together, produces a sharp interference pattern, therefore allowing more accurate measurements. The formula relates the distance between slits (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 away from the central spot (which has order 0)  Refractive Index  A measure of how optically dense a material is  the more optically 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 Indexes Vacuum = 1 Glass ≈ 1.5 Water ≈ 1.33
At a boundary: 1 n2 = c1 /c2 = n2 / n1 The relative refractive index from material 1 to material 2. Note when using the refractive indexes of the materials its 2/1 rather than 1/2 with the speeds.  Snells Law  n1 Sin(θ1 ) = n2 Sin(θ2 ) When a ray of light travels from one refractive medium to another.  Critical Angle  The angle of incidence at which the angle of refraction = 90° i.e. Sin(θcrit ) = n2 /n1 where n1 >n2  Total Internal Reflection  When all light is completely reflected back into a medium at a boundary with another medium instead of being refracted. Occurs when θi > θcrit  Optical Fibre  A very thin flexible tube of glass/plastic fibre in which light signals are carried across long distances and around corners by applying TIR. The fibres are surrounded by a cladding with a high refractive index and a core of a lower refractive index. The light is refracted where the mediums meet and travels along the fibre.  Signal Absorbtion  When some of the signals energy is absorbed by the material of the fibre. The final amplitude is reduced.  Signal Dispersion  When the final pulse is broader than expected, which can cause information loss as it may overlap with another signal.  Modal Dispersion  Light entering at different angles and taking different paths, resulting in signals arriving in the wrong order Singlemode fibre is used to prevent this  light is only allowed to folllow a very narrow path.  Material Dispersion  Different amounts of dispersion depending on wavelength. Monochromatic light prevents this. 
NuclearRutherford Scattering  An experiment that proved the current model of the atom that it is mostly empty space.
Rutherford set up an experiment, with an alpha emitter pointed at gold foil. He observed the deflection of the particles and it showed that atoms have a concentrated mass at the centre and are mostly empty space, which disproved the plumpudding model which was accepted previously.
It showed that: • Atoms = mostly empty space • Nucleus has a large positive charge, as some of the +ve charged alpha particles are repelled and deflected • Nucleus must be tiny due to few particles being deflected by an angle > 90° • Mass must be concentrated in the nucleus  Distance of Closest Approach  Ek = Eelec = Qnucleus qalpha /4πε0 r where r is the distance of closest approach  Electron Diffraction  λ≈hc/E where the first minimum occurs at: sinθ ≈ 1.22λ/2R  Nuclear Radius  R = R0 A^{1/3}  Alpha Decay (α)  Charge(rel): +2 Mass(u): 4 Penetration: low Ionising: high Speed: slow Affected by mag. field: y Stopped by: paper/~10cm air
Used for: Smoke alarms if the particles cant reach the detector, the smoke must be stopping them  Beta Decay(β^±)  Charge(rel): ±1 Mass(u): n/a Penetration: mid Ionising: weak Speed: fast Affected by mag. field: y Stopped by: ~3mm of aluminium
Used for: PET Scanners, In production of metals the levels penetrating through the metal can be used to control the thickness.  Gamma Decay(γ)  Charge(rel): 0 Mass(u): 0 Penetration: low Ionising: very weak Speed: c (speed of light) Affected by mag. field: n Stopped by: several cm of lead.
Used for: PET Scanners produced through annihilation, cancer treatment.  Background Radiation  The low level of radiation that always exists. Must be taken into account when measuring radiation.  Sources of Background Rad.  • The Air Radioactive radon gas released from rocks • Ground/Buildings Nearly all rock contains radioactive materials • Cosmic Radiation nuclear radiation from particle collisions due to cosmic rays • Living things living things are made of carbon, some of which is radioactive carbon14 • ManMade Radiation from industrial/medical sources  Intensity  I = k/x^{2} Intensity (Wm^{2}) = constant of proportionality (W)/distance from source (m)  Radioactive Decay  It both spontaneous and random.
Spontaneous: Decay is not affected by external factors Random: It cannot be predicted when the next decay occurs  Decay Constant  The probability of a specific nucleus decaying per unit time. 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 of unstable nuclei in the sample
It can also be written as:
ΔN/Δt = λN (ΔN is always a decreasing number hence the neg sign)
A = A0 e^{λt} A0 is the activity at t=0  Number of unstable Nuclei (N)  N = N0 e^{λt} 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  HalfLife (T1/2 )  The average time the isotope takes for the number of nuclei to halve. T1/2 = ln2/λ (Derived from N = N0 e^{λt})  Uses of Radiation  • Carbon Dating Using the amount of C14 left in the organic material. Problems are that the material may have been contaminated, high background count, uncertainty in c14 in the past and sample size may be too small • Medical Diagnosis Tracers that emit radiation to track things in the body  Instability  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. If they lie above, they undergo β^{} decay, if they lie below, the undergo β^{+} decay. If they have a Z number of over ~82 (Protons) they undergo α decay.  Mass Defect  The mass of a nucleus is less than the mass of its constituents. This energy difference is the mass defect and is lost to energy as E = mc^{2}, energy and mass are equivalent.  Binding Energy  If you were to pull a nucleus apart, this binding energy would be the energy required to do so, equal to the energy released when the nucleus formed.  Average Binding Energy  Average Binding energy per nucleon = Binding Energy/Nucleon number  Nuclear Fission  When large unstable nuclei randomly split into smaller more stable nuclei. Energy is released as the smaller nuclei have a higher avg. binding energy per nucleon  Nuclear Fusion  When 2 smaller nuclei combine to form a larger nuclei. A lot of energy is released because the new heavier nucleus has a higher avg. binding energy (if the 2 original nuclei are light enough). This is the energy that keeps stars burning  Nuclear Fission Reactors  • Control Rods Usually made of carbon, they are lowered and raised to control the rate of fission. The amount of fuel required to produce one fission per fission is the critical mass. Any less (subcritical) then the reaction will eventually fizzle out. Any more, and the reactor could go into meltdown, which is why control rods are used. • Moderator Fuel rods are placed in the moderator, this slows down/absorbs neutrons to control the rate. The choice of moderator needs to slow down the neutrons enough to slow down neutrons enough to keep the rate of fission steady. It slows down neutrons through elastic collisions, a moderator with a similar nucleonmass to the neutrons. • Coolant is sent around the reactor to remove heat produced by the fissio. The material is either liquid or gas at room temp. Often it is the same water (heavywater) as the moderator and can be used to make steam and turn turbines. • Shielding Reactors are surrounded by thick concrete, which shields and protects from radiation escaping and anyone working there. • Emergency Shutdown All reactors have an emergency shutdown where the control rods are completely lowered into the reactor, thus absorbing all the neutrons produced and slowing the reaction down as quickly as possible. • Waste Unused uranium only produces α so can be easily contained. Spent uranium however emit β & γ radiation. Once removed from the reactor they are cooled and ten stored in sealed containers until the activity is at a low enough level. 
Further MechanicsRadian  Objects in circular motion travel through angles, mostly measured in radians. Rads to Deg: Angle in deg x π/180  Angular Speed  The angle an object rotates through per second. ω = θ/t = v/r = 2π/T = 2πf  Frequency  The number of revolutions per second. f = 1/T  Time Period  The time taken for a complete revolution.
 Centripetal Acceleration  Objects travelling in a circle are accelerating as their velocity is changing constantly. The acceleration is always acting towards the centre of the circle. a = v^{2}/r = ω^{2}r  Centripetal Force  Is the resolved force which is always directed towards the centre of the circle. F = mv^{2}/r = mω^{2}r  Simple Harmonic Motion  An object undergoing SHM is oscillating to and fro, either side of an equilibrium position.
It is defined as An oscillation in which the acceleration of an object is directly proportional to its displacement, which is always directed towards the equilibrium position  Displacement (x)  Displacement varies as a cosine/sine wave with a maximum value of A (Amplitude)
x = Acos(ωt)  Velocity (v)  Is the gradient of the displacement time graph. Its maximum value is ωA
v = ±ω x sqrt(A^{2} x^{2}) vmax = ωA
 Acceleration (a)  Is the gradient of the velocity time graph. Its maximum value is ω^{2}A
a = ω^{2}x  MassSpring System  A mass on a spring is a simple harmonic oscillator. When the mass is pulled/pushed from the equilibrium position, there is a force directed back towards the equilibrium position.
F = kΔL where k is the spring constant and ΔL is the displacement.
The Time period for a MS System is given by:
T = 2π x sqrt(m/k)  Pendulum  A pendulum is an example of a Simple Harmonic Oscillator. The time period for a pendulum is given by:
T = 2π x sqrt(l/g)  Free Vibration  Free vibrations involve no transfer of energy to/from the surroundings. If a massspring system is stretched, it will oscillate at its natural frequency fn .  Forced Vibration  Forced Vibration occurs when there is an external driving force. A system can be forced to vibrate by a periodic external 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.  Resonance  As fd → fn , the system gains more and more energy from the driving force, thus the amplitude rapidly increases. The system is now considered to be resonating. At resonance, the phase difference between the driver and the oscillator is 90°.  Damping  Any oscillating system loses energy to its surroundings damping. System are also deliberately damped to stop them oscillating or minimise resonance.
Light Damping Take a long time for oscillation to stop, the amplitude is decreased slowly. DisplacementTime Graph: sharp peak. Heavy Damping The amplitude decreases rapidly, and oscillation takes much less time to stop.DisplacementTime Graph: flat peak. Critical Damping Oscillation is stopped in the shortest amount of time possible. Over Damping Systems with even heavier damping, they take longer to reach equilibrium than a critically damped system. 

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