so the first thing you need to know is that waves transfer energy without transferring matter and there are two types transverse and longitudinal longitudinal is when the particles involved in the wave are oscillating parallel to the direction of energy transfer and of course they're made up of compressions and rare fractions EG sound waves transverse is the opposite particles oscillate perpendicular EG light or any em for that matter electromagnetic waves waves on a string waves in water so on and so forth so this is your standard wave this could be time it could also be distance as well usually it's time this axis here is displacement from the midpoint which is equilibrium so the particles are when they're not oscillating this here is Lambda that's wavelength this here is amplitude now it would be wavelength if this is distance if it's time on the x-axis then distance between one Peak and the next we don't have wavelength but we have time period time period is the time taken for one complete wave to pass a point I'll measure that in seconds frequency number of complete waves passing a point every second so therefore if you want to find the frequency then we just do one divided by the time period so our other equation is V equals F Lambda that's wave speed equals frequency times wavelength polarization transverse waves can be polarized by a filter that's just made up of very small lines this only lets off of lights be transmitted we say it's a password for just let through and absorbs the rest what we say is that it selects waves oscillating in the particular direction interference also known as superpositioning when the displacements of the individual waves sum at each point they add up a piece of string this is what we call the first harmonic and this is when the wavelength is equal to two lots of the length of the string draw the second harmonic as well when the wavelength is equal to the length of the string so at a node always destructive interference no energy transferred at these points and an anti-node we have both constructive and destructive interference but energy is transferred because the string is actually moving the fraction so Young's Double slits in a candle and he had a single slit and then a double slit which then made the diffraction pattern he needed a single slit to produce coherent sources at the double slit coherent what does that mean well it means basically in sync in Phase but the proper definition is waves that have a constant phase difference we use a laser nowadays because that is coherent it's also monochromatic whereas the candle wasn't I mean it's just one wavelength so if we draw a graph of what's going on here's our intensity here's our distance from the center Fringe width or Fringe spacing is given the letter W and a young double State equation is W equals Lambda D over s or S is the slit separation that's the double slit the spacing between the two slits there in reality what does this look like well it looks like bright spots with dark spots in between we also call these Maxima that's where we get constructive interference in other words two waves arriving in Phase they reinforce each other as it were so making a Super Wave so that's why we see a bright spot Minima is where we get destructive interference dark and for a maximum the path difference that's how much further one Ray is traveling than the other it's equal to a multiple of the wavelength for a minimum path difference is equal to a whole number take away a half times the wavelength so one and a half two and a half Etc speaking of parts difference in Phase difference phase difference is just how out of sync two bits on one wave or two waves are so all we do is that we take the difference in the time divided by the time period or difference in distance divided by the whole wavelength so it's just the bit divided by the lot Times by two pi and that turns it into a radians single slits it looks like this have a big Central Max Falls away very quickly Central Max is twice as big than the other fringes diffraction grating the equation is n Lambda equals D sine Theta where n is the order and D is the line spacing and we calculate that by doing one divided by lines per meter so you might get lines per millimeter change it into lines per meter and then do one divided by that to get D find the maximum order theta equals 90 degrees EG you'll end up with something like n is equal to 3.7 Max is three you can't have a 3.7 order 90 degrees and last but not least we have a fraction and the only equation you need to be concerned about is N1 sine Theta 1 equals N2 sine Theta 2. here's our normal so it's 90 degrees here's our N2 here's our N1 So This Could Be Water and Air don't know worth remembering that air n is one for TIR to occur angle of incidence must be greater than critical angle and also the fractive index of this medium must be greater than the second medium otherwise it doesn't work to find the critical angle all we do is make Theta 290 degrees therefore N1 sine Theta C because that's what we're talking about is the angle of incidence just equal to N2 TIR is when all light is reflected because we always get a partial reflection but not with TIR first thing we need to talk about is average speed it's distance over time we say average speed because we don't know what's happening to the speed over the course of that distance here our graphs we have a distance time graph we could say displacement time graph gradient is equal to speed or velocity if it's displacement time velocity time graph the gradient gives you acceleration the area under the graph gives you distance traveled or displacement but what about suvat we use the suvat equations or Newton's equations of motion if the object is accelerating if we're chucking something up or dropping something doesn't matter acceleration is always 9.8 meters per second Square towards the ground so it might be minus if something's moving upwards don't forget that for projectile motion if something's chucked horizontally and we use suvat vertically but then we just use speed equal systems over time horizontally because we assume there's no frictional forces the path that an object takes in this case is a parabola or it's parabolic let's have a look at forces Newton's first law is that an object's motion is constant if there's no external force acting on it in other words velocity is constant don't forget that that could mean that the direction is changing while speed is staying the same circular motion we're not going into that here though Second Law is f equals m a force equals mass times acceleration don't forget that f is the resultant Force doing the accelerating and mass is the total mass being accelerated third law to each action or Force there is an equal and opposite reaction weight is equal to mg that's mass times gravitational field strength 9.8 or 9.81 for an object to be in equilibrium that means constant motion we're talking about Newton's first all there we need no resultant force that means that forces are balanced and also we have to have no results at the moment or talk we'll talk about that a little bit later on as well hair resistance and frictionless frictional forces increase with speed if you've got a mass on a slope then the force pulling parallel to the slope down the slope is equal to mg sine Theta that's the component of the white all right energy here we go kinetic energy is half MV squared gpe is MGH if we're given H we pretty much know that we're going to use gpe if there's no energy lost when something Falls then we know MGH equals half MB squared and the M's cancel but if the GP at the top does not equal the kinetic energy at the bottom then energy is lost in the form of thermal energy or heat and we can say that that's actually work done against frictional forces that leads us nicely onto work done work done is equal to force times distance E equals FD I prefer e some people use W but it is energy is measured in joules remember that the force and distance need to be parallel so if they're not then you need to Times by cos Theta Theta be in the angle between them the power version of this power developed is p equals FV we just avoided the whole equation by time okay materials let's look at hooke's law force is equal to spring constant times extension f equals ke or f equals KX or f equals K Delta L doesn't matter which one you use here's the graph of force against extension the gradient gives you the spring constant and that's measured in Newtons per meter the area under the graph is equal to the energy stored it's a triangle so therefore it's going to be half times fours times extension if we substitute in ke instead of f then we get half k e squared stress or tensile stress measured in pascals is equal to force divided by area strain is the ratio of extension to original length the young modulus is equal to stress of a strain so therefore the whole version is FL over a e and if you draw a graph of stress against strain then obviously our gradient is going to be equal to the young modulus let's look at that graph again we've got three main points that we look at we have the limit of proportionality that's when it starts to curve downwards we have the elastic limit beyond that it's not going to return to its original length it deforms plastically and then the top of the curve is the ultimate tensile stress don't forget that things can take a different route when they unload compared to loading and the area of the graph in between is equal to the energy lost between loading loading and loading don't forget that if forces are balanced then no matter how many forces there are they will always make a closed loop if you add them up that is top and tailor if something's being accelerated upwards then the force needed is not only M A but it's mg plus ma because you need the force of mg just to keep it there floating as it were and then we need the extra Force ma to make it accelerate upwards okay moments we know that moment is equal to force times distance don't forget that our definition is force times distance perpendicular from pivot to Force's line of action so we might have to Times by cos Theta if there are two unknown forces in a diagram then you take moments about one or in other words make it a pivot to remove it from the equation as it were and then you can find out the other the principle of moments is that for assistant to be in equilibrium the sum of the clockwise moments must equal the sum of the anti-clockwise moments and we know there has to be no resultant Force for complete equilibrium for an object to topple the center of mass must be pi us to Pivot so that the moment of the weight does pull it the wrong way as it were scalars and vectors scalars just have magnitude like area distance energy and power whereas vectors have magnitude and Direction like force acceleration velocity and displacement momentum is equal to m v so that means the unit is kilogram meters per second or Newton seconds how does it link to force while force is equal to Delta MV that's change in momentum divided by time in word form force is equal to the rate of change of momentum this is the equation that shows that the longer a collision takes the less the force felt and that's how crumple zones and airbags work they increase the Collision time in other words increase the time that it takes for you to lose your momentum so you feel less Force if you have a force time graph there's really only one thing you can do with it and that is find the area under the graph that gives you the impulse that's the change in momentum principle of conservation of momentum is total momentum is concerned third absent that means so long as there are no external forces a couple of examples if we have two objects colliding then we know that the momentum of a plus a momentum of B must equal the momentum of both of them if they couple together then if we have a recoil situation like a bullet being fired from a gun then we know that there's no momentum before and no momentum afterwards so that must mean that the momentum of the gun going backwards must be equal to the momentum of the bullet going forwards okay technically we should stick a minus in front of one of them because one of them is going to have a negative velocity but when it comes to recoil we don't care about that too much let's think about breaking distance breaking distance quadruples if you double your speed because kinetic energy is half MV squared so if you double your V then you have four times the kinetic energy other things that can affect breaking distance are the road condition weather and tire condition what about thinking distance speed again drugs distractions and tiredness and we have a couple to equal forces that means that there's no acceleration but it does turn or start a turn if you have something that's traveling under constant velocity but mass is being tuned out as it were like a fluid like water in a hose then we re-jig the rate of change in momentum equation so that we have f equals Delta M over T times V and so that's kilograms per second times meters per second units are really helpful for these kind of questions but if you have density area and speed then the force is going to be equal to rho a v squared note that you might see that called momentum carried per second but that's effectively false and if we have a force or any Vector then we can find the components of the resultant vector by times in by cos Theta or sine Theta 10 through the angle Times by cos turn away from the angle Times by sine and we have two types of collision we have elastic collisions and inelastic collisions for elastic collisions total kinetic energy is conserved and it's not in in our religions but don't forget that total energy is conserved in both total energy is always conserved so let's first look at the types of particles that we have that is things that make up matter we split particles into two main groups hadrons and leptons leptons are fundamental particles examples are electron positron and neutrinos however we can split hadrons in two again into baryons and mesons Barons and mesons are made of quarks and quarks are fundamental particles as far as we know burials have three quarks and mesons have two quarks always a quark and an antiquark and the quarks are held together by the strong nuclear force samples are the neutron and proton and the main Meson we deal with is the Pion but there are others conservation rules we know that baryons have a barium number and leptons have a lepton number so let's talk about the four forces that we're concerned with in physics specifically in the area of quantum electrodynamics the electromagnetic force the gauge boson or the exchange particle for that is the virtual Photon strong nuclear force the gauge boson is the Pion sometimes you'll see the glue on weak it's w Plus or W minus we don't really deal with the Z zero and the cousin that we all ignore is gravity because we don't really understand it as well and even though we haven't found it we call the exchange particle the graviton okay let's talk about the strong nuclear force it keeps a nucleus together of course the electrostatic repulsion of the protons in the nucleus means that the EM force is always trying to explode a nucleus so that means that we must have another Force keeping it together and that's the strong nuclear force and that affects neutrons and protons what's stopping the strong nuclear force from imploding a nucleus then well what we say is when the nucleons get too close together to 0.5 centimeters the strong nuclear force flips from being attractive to repulsive and the range of Attraction for the strong nuclear force is about three to four centimeters okay so we know that mass and energy are interchangeable the equation that links to 2 is the equation for rest energy of a particle and that's E equals m c squared mass is converted into energy in Annihilation that's when a particle and its corresponding antiparticle Collide and they're destroyed and the rest energy is converted into photons so we can say that E equals Mt squared plus half MV squared that's the kinetic energy of the particles going in and we have two lots of HF coming out the opposite is pair production that's when a photon turns into two particles again the particle and its corresponding antibarticle of course the photon must have at least the same amount of energy as the rest energy of the particles so again E equals m c squared but if the photon has more than the minimum amount of energy then the leftover energy is turned into kinetic energy of the particles afterwards okay let's talk about ionizing radiation Alpha Beta gamut column ionizing radiation because all of these can give electrons enough energy to escape an atom or molecule therefore ionizing them an alpha particle is a helium nucleus two protons and two Neutron it's highly ionizing mostly because it's very heavy but it's weakly penetrating it's stopped by a piece of paper or a few centimeters of uh beta particle it's a fast moving electron the more you'll fix my mistake in a second then it has medium ionizing and penetrating ability stop by a few millimeters of aluminum gamma is just a high energy em Ray or Photon and that's emitted from an energetic nucleus photons don't have charge so they can't change the nucleus in any way when they're emitted it's weakly ionizing but it's highly penetrative it can't be stopped really but the intensity can be reduced by concrete and Lead okay here are the Decay equations for Alpha and beta we know that Alpha is four and two beta is zero and minus one because it's got the opposite chart of a proton and so therefore it's just mass then isn't it don't forget that for beta Decay we must have an anti-electron neutrino produced as well to make sure that lepton number is conserved here's a Feynman diagram for beta minus Decay we have a neutron turning into a proton and the W minus boson takes the negative charge away as it were to produce an electron and an anti-electron neutrino a neutron is up down down proton is up up down so therefore we can say that actually it's a down Quark turning into an up Quark you can see either one on a Feynman diagram for this okay conservation rules what has to be conserved charge laptop number and barium number Q L and P they're always conserved strangeness however is only conserved in strong interactions instantly any interaction that involves leptons has to be a weak interaction it's good to be reminded about what a mu one is it's effectively a heavy electron and a reminder that lepton number wise electrons and neutrinos have a lepton number of plus one because the electron is the OG lepton as it were positron has a left or number of minus one okay let's go back a little bit Isotopes what are they well they're the same element that means the same number of protons or same atomic number but with a different number of neutrons so that means they have a different relative atomic mass like carbon 12 and carbon 4 14 here specific charge is the charge to mass ratio so we calculate it by doing charge developer Mass so the unit is coulombs per kilogram generally a very big number because the masses of these particles are tiny with remembering that one electron volt is the same number as the charge of electron because one electron volt is the energy in joules that an electron has when accelerated through a PD of one volt so that means that one electron volt is 1.6 times 10 to the minus 19 joules quite often we deal with mega electron volts and so if we have to convert that into jules's 1.6 times 10 to the minus 13. yes you can figure that out but it's useful as a shortcut okay so let's go on to some Quantum then what is the photoelectric effect it's when photons of sufficient energy are absorbed by electrons on the surface of a metal therefore liberating them they escape the equation is EK Max is equal to HF minus Phi HF being the energy of the photon that goes in by being the work function that's the minimum energy needed to liberate electrons and so taking one away open here that gives you the kinetic energy left when an electron has escaped here's the graph the y-intercept is minus Phi the x-intercept is the threshold frequency that's the minimum frequency needed for electrons to be liberated if the frequency is less than that you won't see any electrons liberated and in that case EK Max is equal to zero so hf0 equals Phi okay so what did the photoelectric effect prove well it proved that light has a particle nature not just wave nature due to the one-to-one interactions between photons and electrons and it's one to one because if it were only a wave then increasing the intensity of light would have increased the EK of the electrons liberated but it doesn't all it does is increase the number of electrons that are emitted per second because there are more photons okay so here's a circuit that we can use to measure the kinetic energy of these electrons we have a variable PD applied across these two plates we shine light on one of them specifically the anode and then we'll make electrons across the Gap and then they will flow around the circuit producing a current what we do is increase the PD in the opposite direction as it were until the current goes to zero that means that the electrons are no longer crossing the Gap so we know that their kinetic energy has been counteracted as it were by the energy supplied by the battery we call this PD the stopping potential and we know that any voltage is energy divided by charge and it's the same here so we can say that EK Max is equal to e charge of an electron times the stopping potential for vs a deployee wavelength is the wavelength that a particle can have and the wave natural particles was proven with electrons being fired at a graphite film and we see circular fringes on a phosphorescent screen behind that's because the electrons are diffracting around the carbon atoms and producing Maxima and Minima on the screen so like light here's the pattern for it note that the intensity doesn't really go to zero debris wavelength is equal to place constant over momentum or h of P or H over MV quite often we'll be given the energy of electrons but we'll have to find out the momentum in order to put it into the equation so we find that by doing equals half MV squared times in the whole thing by m and that gives you m e equals half P Squared rearranging we get momentum P equals root 2 m times the energy okay fluorescent tube what we have is a tube with a cathode on one end and an anode on the other end the cathode is heated with a current electrons are emitted by thermionic emission they're attracted to the anode on the other side and they bash into low pressure Mercury gas atoms on the way raising the electrons to higher energy levels we'll talk about energy levels in a bit as these electrons de-excite they emit UV photons not visible light and then these UV Photon are absorbed by the electrons in the coating and then when these deoxite they emit visible light and then finally energy levels running out of space here so I apologize for the crampness of this bit electrons can be promoted or excited to higher energy levels through two ways either they can absorb Photon of energy exactly equal to the difference in energy levels or a free electron can come along and collide with it and impart some of its energy to the electron making it go up to a higher energy level we have the ionization level if enough energy is given to an electron then it will escape an atom or molecule completely we have absorption and emission Spectra emission spectrum we can get from the sun because light is just being emitted from it or any other light absorption spectrum is when we have a gas and Shine full wavelengths through it and see what's transmitted what's absorbed and then we can tell what kind of elements are present so let's draw the simplest circuit that we can we have a battery or a cell or power supply don't get your knickers in a Twist if some somebody uses battery instead of cell okay so what does one of these do well it provides an EMF that's short for electromotive Force it's more of an a level term a GCSE all you need to know is that a battery gives electrons or charge energy and the battery says that it's six volts so that means that it's giving six joules of energy to every coulomb of electrons or charge that passes through it and don't forget we deal with coulombs instead of individual electrons of charge because well coulombs are much easier numbers to deal with much like models we have a resistor and we have an ammeter that's in series with the rest of the circuit we put it in series because it measures rate of flow of charge the symbol for current is I and unit is amps a so any rate is something divided by time and so current is charge divided by time or Q over T Some people prefer Q equals i t but if you remember that it's the rate of flow of charge then you know it's going going to be that divided by T so we know that the battery is supplying 6 volts six joules of energy to each coulomb of electrons but where is that energy going well it's going to the resistor and the resistor converts electrical energy into thermal energy no I can't be bothered to think in terms of energy stores and Pathways because that's just confusing symbol is r and the unit is Omega for ohms the voltmeters always go across a component that is in parallel to it because it measures potential difference also known as voltage we know the volts the potential before the resistor is plus six volts the potential afterwards is zero volts so therefore the PD must be six volts that's what the voltmeter should say and we know the PD has to be six volts because all of that six volts from the battery has to be used up in the circuit somewhere and there's nothing else in the circuit apart from the resistor using it so the equations for PD voltage or potential in general V is equal to energy divided by charge joules per coulomb if you will and of course Ohm's law you'll be using that far more ve equals IR all of electricity boils down to that equation really okay so let's have a look at IV characteristics we know for a resistor it's going to be a straight line positive and negative and that's because it's ohmic it means it has a constant resistance if we change the PD double the PD the current through it doubles two for a filament like a lamp that's a piece of metal we have this curve at the ends that's because it's non-o-make it doesn't have a constant resistance and you need to know word for word why this is the case so when current is increased the frequency of collisions of electrons with the ions in the metallic lattice in the filament increases the bat into the ions more this makes the ions vibrate more they're always vibrating but we say they're now vibrating more this ends up where it blocks the electrons even more so it increases the frequency of the collisions even more therefore increasing the resistance of the filament that's why it curves at the end the current can't get through as well okay we have an ldr light dependent resistor and we have a thermostat the or NTC thermistor which stands for negative temperature coefficient that just means that the hotter it gets the lower the resistance and is the case for an ldr but in terms of light we can draw straight lines for both of these we have a higher resistance when it's dark for the ldr or cold for the thermistor and we get a lower resistance when it's light for the ldr and hotter for the thermistor notice that we've got straight lines for both but a different straight line depending on the conditions so we can say they are omic provided that the temperature or the light intensity stays the same for the respective component so why do we get a lower resistance well it's because the energy that goes in shakes electrons Loose as it were so that means that there are more electrons available to conduct proper explanation it's going to be technical it's because the electrons are moved into the conduction band and if you need a nice easy way to remember it both these things do the opposite to a piece of metal as it were so we have a diode and we know that diodes only let current through in One Direction so this is what the graph looks like the resistance breaks down to the positive direction at about 0.5 to 1 volt something like that but the proper explanation is that it has a very high resistance in One Direction and a very low resistance in the other okay so let's move on to looking at circuits here we have a simple series circuit one loop with two resistors in and a battery and because they're in one Loop we know the total voltage is going to be shared between the two but they're going to have the same current if they're in parallel well they have branches they're going to have the same PD and that's the same as the battery but the current is going to be shared between them two resistors in series can also be called a potential divider here's how you might see a diagram of this we don't have a full circuit but the power supply is implied with that plus 12 volts at the top we have the two resistors I'm going to make one of them a thermistor thermistor has a resistance of 20 ohms and the fixed resistor has 10 ohms so that means the 12 volts is going to be split between them as 8 volts and four volts respectively that's because the bigger resistor will have the bigger share of the total voltage available and that's because the ratio of the resistances is equal to the ratio of the voltages and that goes for the individual resistors but that also goes for one of the resistors and the total resistance as well so we can say V1 over V2 equals R1 over R2 or V1 over V total equals R1 over R total excuse my mistakes don't worry it's going to be fixed for the Mind map and something I'll add to the PDF as well these kind of circuits are used for sensing when it gets colder the resistance of a thermist it goes up so that means that its share of the voltage also goes up so you'd want your heater wired up in parallel with that okay in reality it's probably just going to be a sensor that's attached to it so the increase in voltage is detected and then that will switch on a heater instead and you can use an ldr in a similar situation to make a circuit that detects when it gets dark and so it turns on a street lamp for example this is a bit that a lot of people hate internal resistance this is just for a level batteries aren't perfect conductors far from it they have a resistance of their own so we can model a battery as a perfect battery with a little resistor inside little r so this is the circuit the voltmeter it doesn't matter where it goes you can go across the battery or across the whole circuit or across just a load resistance it's the same thing it's going to give you the same value every time terminal PD is the voltage available to the Circuit or the load resistance after some of the voltage or energy has been lost in the battery due to the internal resistance so just remember it is not the EMF of the battery unless there's no circuit in that case it is so here's our graph what we do is that we increase current by decreasing the load resistance and we see that the terminal PD goes down I seem to have forgotten to write that on the y-axis but the y-intercept is the EMF of the battery and the gradient gives you the magnitude of the internal resistance is the equation Epsilon equals I bigger Plus I littler all this equation is really is voltage equals voltage plus voltage but specifically Epsilon is the EMF that's the total voltage supplied by the battery I bigger is the terminal PD and I little r is the voltage lost inside the battery and we can change it as well we can say epsilon equals V plus ir and we can factorize it as well to give Epsilon equals I times R plus r okay very quickly power electrical power is equal to IV and if you replace V with ir from Ohm's law we end up with P equals I squared r do the same with current and we get p equals V squared over R resistivity the symbol is rho it's a constant that is just dependent on the type of material the technical definition is it's the resistance of a cube of unit length sides so that means a one meter times one meter times one meter cube it's not a one meter cube volume it has to be a cube specifically that's because of the way it's calculated it's not ohms per meter it's ohm meters so the equation is R equals rho L over a here's a circuit that we can use to get the resistance for a varying length of wire this goes for GCSE as well and we can see that we have that flying lead on the wire and that's changing the length the PD is just across the whole circuit hopefully we'll get the same or similar PD a is the cross-sectional area like I said the unit is OHM meters here's our graph if we do that experiment resistance on y-axis L on the x-axis the gradient gives you R over L rearranging the resistivity equation gives us rho equals R A over l so that means that resistivity is equal to the gradient of this graph times a the cross-sectional area because if we double the diameter of the wire then the area goes up by a factor of four so that means that the resistance goes down by a factor of four and that's because the area being great so there's more electrons able to flow a thinner wire has a greater resistance kick off or kirchhoff's laws first law is that charge is conserved at a junction so that means that whatever current goes into a junction it must equal the total coming out of a junction as well EG i1 equals I2 plus I3 if we draw a little Junction like this second law is that the sum of emfs must equal the sum of PD drops in any closed loop in a circuit and that links into what we were talking about right at the start the fact that that six volts from the battery has to get used up by the whole of the circuit so we have a 6 volt EMF and a six volt PD drop don't forget that emfs can be minus as well if we have three batteries like this or three volts but one of them is facing in the wrong direction then two of them cancel each other out as it were so therefore the total EMF of this setup is only three volts and one thing that I probably should have put in earlier if we want to find the resistance of resistors in parallel we do one over R total equals one over r one plus one over R2 and then we can do that as many times for as many resistors that we have in parallel and don't forget that if they are the same resistance then the shortcut is that the total resistance is is half one of them so I hope that's helpful if it is then please leave a like if you want to test your knowledge on this then click on the card and it'll take you to my flash card questions see you there