let's see how quickly we can go through everything you need to know for AQA AS level physics all particles are put into the group's hadrons and leptons leptons are fundamental particles and they include the electron muon that's just a heavy electron basically and neutrino that has no charge these all have Aon number of one whereas their antiparticle equivalents have Aon number of minus one neutrinos can also be specifically electron neutrinos or muon neutrinos so you have to treat their lepton numbers separately if an interaction involves both electrons and muons hadrons are split into Barons made of three quarks and misons made of two quarks a quark antiquark pair so hadrons aren't fundamental particles the three flavors of Quark we deal with are up down and strange up has a charge of plus 2/3 down and strange minus a thir of course that's in terms of e only strange quarks have strangeness minus one for a strange Quark plus one for an antistrange after all they are strange aren't they they all have a baron number of plus a thir so Barons have a baron number that isn't zero it can be one or minus one if you have antiquarks in there too neutrons are up down down protons are up up down so you can say the nud and the Pud to help you remember them anti- up anti- down and anti- strange have the opposite charge and baron number P are misons that don't have strangeness whereas kons are misons that do have it we can call them pi+ Pi 0 Pi minus and K plus K minus K 0 Etc to distinguish between them the electromagnetic force can affect any ch charged particle The Exchange particle is the photon we might say the virtual Photon gravity's exchange particle is called the graviton but you know about those two already let's go with the two that are new to a level the weak force or weak nuclear force can affect any particle its exchange particle is the w+ W minus or z0 boson the strong nuclear force only affects hadrons its exchange particle is the pon or gluon if Pon isn't an option in a question this is what holds nuclei together the electrostatic repulsion between protons pushes outwards while the strong force pulls inwards okay A bit of gravity too but that's not much when these forces are balanced a nucleus is stable the range of the strong force is 3 to 4 FM but it switches from attractive to repulsive at 0.5 FM to stop the nucleus from imploding in any interaction charge barion number and lepton numbers must be conserved which is why there must be an anti-electron neutrino added in a beta minus decay equation to balance lepton number we can draw fan diagrams to represent interactions this will always be a weak interaction involving a w minus B on say for beta minus Decay or w+ for beta plus Decay or electron capture for normal beta minus Decay we can also just say that one of the down quarks in the neutron is decaying to an up quark and that turns the whole thing into a proton it goes from nut to PUD finally strangeness rules any interaction involving leptons must be a weak interaction regardless of strangeness if an an interaction only involves hadrons and strangeness is conserved it must be a strong interaction these can create strange particles though so say zero strangeness going to+ one and minus one for two different particles if strangeness isn't conserved in an interaction it must be weak not strong this happens when strange particles Decay for example a k0 meon decaying into pi plus and Pi minus misons in essence the weak interaction can destroy strangeness but the total Stranges can only change by one specific charge is merely the charge to mass ratio for a particle charge in kums divided by mass in kilogram so the unit is kums per kilogram so you'll always end up with a huge number for example for an electron we have the charge of 1.6 * 10 -9 K divided by its mass of 9.1 * 10 - 31 kg yes okay technically minus for the negative charge but it's really only the magnitude that we're concerned with a nucleus say helium 4 that's 2 * 1.6 * 10-9 for the two protons divided by 4 * 1.67 * 10us 27 for the mass of the four nucleons in the nucleus a singly Charged ion well it's overall charges just 1.6 * 10 -9 we divide that by the total mass of the nucleus we don't really need to add the negligible mass of the electrons in this case the term radiation means any particle or wave that's emitted by something the electromagnetic spectrum is radiation but they're all emitted by electrons all apart from gamma radiation that is gamma radiation is actually emitted by the nucleus of an atom if it has excess energy it's getting rid of gamma rays are high energy em WS they can be dangerous as they can ionize atoms if absorbed by them knocking electrons off this can cause damage to the cells in your body and also cause cancer but there are two other types of radiation nuclei can emit too but these are actual particles and they're emitted when nuclei Decay ch isotopes with more neutrons are generally more unstable and likely to Decay heavier nuclei like amorium 241 Decay by what we call alpha decay to become more stable the nucleus will emit a bundle of two protons and two neutrons what we can just call an alpha particle this is Alpha radiation this is what the nuclear decay equation would look like for this to show that the nucleus has decayed into two parts the alpha particle which must have an atomic number of Two and a mass of four and the daughter nucleus that's just the nucleus left over which of course is no longer going to be amorium as it's lost protons to go from an atomic number of 95 to 93 turns out that's neptunium but you'll never have to remember these you just need to worry about the numbers it's just maths 95 goes to 93 + 2 and the mass is similar 241 goes to 237 and4 there is actually a nucleus that has the numbers two and four it's a helium nucleus lighter Isotopes lighter nuclei like carbon 14 Decay by Beta Decay or beta Decay instead what happens is that a neutron in the nucleus turns into a proton and an electron but the fast moving electron that's ejected by the nucleus escapes and we now call this beta radiation the mass of an electron is basically zero so we put that on top it has the opposite charge to a proton so we say it has an atomic number of minus one now be careful here six goes to what + - one no it's not five It's s 6 is equal to 7 plus us one like we said a neutron has turned into a proton so the nucleus has gained a proton it's gone from 6 to 7 the mass however is unchanged so it's still 14 and don't forget to add the anti-electron neutrino on the end to balance the lepton number if a particle and its corresponding antiparticle meet say an electron and positron they can annihilate and all of their mass is converted into energy in the form of two photons of em radiation it's two photons by the way as momentum must be conserved and even though photons don't have mass they still have momentum weirdly enough if we're asked what the minimum energy or frequency of the photons made is we infer that they had no kinetic energy so we just say that energy equals two lots of mc² we call this either rest energy or mass energy where C is the speed of light we can then say this is equal to two lots of HF which is the energy of a photon Plank's constant times the frequency the shortcut of course is just to split the whole problem in half we can just say that MC squ for one of the particles equals HF for one of the photons the opposite can happen when a photon spontaneously converts into two particles if it has enough energy this is called pair production this time HF is equal to 2 MC s because it's just one Photon making two particles if the photon has more energy than the minimum energy needed the extra energy is supplied to the particles as kinetic energy it's the opposite for annihilation if they have lots of kinetic energy before that goes into the energy of the photons too electron in an atom orbit the nucleus at specific or discrete energy levels N1 being the lowest energy level or ground state we can call it then N2 N3 Etc an electron can be excited or raised to a higher energy level either by another free electron colliding with it giving it some of its energy or by it absorbing a photon however in this case the energy of the photon must match the difference in energy levels exactly otherwise it will just pass through either way after it's been excited the electron will pretty much immediately fall back down to the ground state emitting photons in the process we call this de exitation but it can take different Roots down from N3 for example it can either go straight down to N1 or it can go to two first then down to one this means that there are three possible wavelengths or frequencies of photons that could be emitted when it de exites from N4 there are six different possible wavelengths the energy of each photon is equal to HF so the bigger the drop the higher the frequency of photon emitted and the shorter the wavelength is as of course c equal F Lambda if the incoming free electron or Photon has enough energy however the electron can reach the ionization level which then means it is able to leave the atom leaving behind a positively charged ion the energy levels can be given in Jewels or electron volts one electron volt is equal to 1.6 * 10us 19 Jew which should look familiar as the number is the same as the charge of an electron to convert jewels to electron volts and vice versa just think do I want a smaller number or bigger number you always want a very small number of jewels and a normalist number of electron volts after all that's why the unit is so handy sometimes Mega electron volts are even better you can convert to electron volts and then use the conversion factor of a million 10 the^ of 6 but I guarantee it's more helpful to remember that to go from Jews to Mega electron volts the conversion factor is 1.6 * 10 -13 instead of -19 an emission spectrum is just a diagram showing the various wavelengths of photons that are being emitted by an object for example a star that's different atoms or molecules have specific energy levels we can tell what particles are found in that star and we can also see how red shifted these wavelengths are to which we then use to determine the recessional speed of galaxies an absorption spectrum is obtained when we emit all wavelengths through a gas or plasma that's just an ionized gas and detect what wavelengths are not transmitted they don't pass through because they've been absorbed represented by black lines on the Spectrum fluorescent tube lights strip lights consist of a cathode and anode that cause electrons to be accelerated through the Mercury gas inside an electron will collide with a Mercury atom's electron exciting it to a higher energy level when it de excites it emits a UV Photon that's not useful for our eyes so it needs to be absorbed by the fluorescent coating on the inside surface of the tube it raises one of the electrons to a higher energy level in the coating and then that de exites via multiple levels emitting lower frequency visible photons instead we say photons have wave particle duality the photoelectric effect is the main piece of evidence that light acts like a particle shine light on certain metals and electrons will be liberated from the surface they pop off as they have absorbed the energy as kinetic energy how can we tell well if we have the metal in an evacuated tube in a circuit with an amiter a tiny current will start to flow as the electrons are crossing the Gap add a variable PD into the circuit and we can oppose this current until it reaches zero we call this potential needed the stopping potential vs we therefore say that at this point the kinetic energy an electron would have is equal to Q * V or E * V bear in mind that this technically gives the maximum kinetic energy an electron has after Liberation as most electrons will have less energy due to them not being right on the top of the surface of the metal we vary the frequency of this incident light and plot the EK Max against this and we end up with a straight line the gradient is where Plank's constant comes from it doesn't go through the origin though which means that the electron is not gaining as much K as the photon's energy going in it's lost some in the process of being liberated extrapolate this line back and we get this energy which we call the work function this is the minimum energy required for an electron to be liberated from the surface of a metal think of it as an energy toll the electron must pay to escape the minimum frequency needed to liberate an electron we call the threshold frequency F0 that means the minimum energy of a photon needed to liberate an electron is H * F0 and this is equal to the work function so here's the full equation EK Max equal HF minus 5 the kinetic energy the electron has left over equals the photon energy going in minus the work function the energy toll this proves the particle theory of light because if the frequency of light isn't high enough electrons won't be liberated no matter how Intense or bright the light this shows that one photon is absorbed by one electron we say it's a onetoone interaction and that requires photons to be discrete packets of energy so light acts like a particle but any particle can also act like a wave if we fire electrons at a graphite Target in an evacuated tube we see Rings forming on the phosphorescent screen behind the only way that this would be possible is if the electrons are defraculator bright rings and Minima dark Rings electron defraction is the evidence that particles also have wave nature moreon defraction in waves of course the wavelength of a particle is given by the deogi or de wavelength equation Lambda equals H PL constant over MV or P the momentum of the particle faster speed means smaller wavelength which means less defraction according to n Lambda equal D sin Theta from waves here's the standard graph showing how intensity varies with distance from the center note that it doesn't decrease to zero unlike defraction patterns for light at this point it's worth bringing up the fact that you might have to convert kinetic energy into momentum or vice versa the trick is this we know kinetic energy is equal to half mv^2 multiply both Sid by m which gives me equal half P that's momentum squared and then we just rearrange for p this comes in handy especially in multiple choice questions electricity is a flow of charge or charges like electrons they carry energy from a source of energy to a component by the way you're going to see me mix up cells and batteries in this video because they're just the same thing really and they do the same job leave an angry comment below if you're really that mad about it the battery has a store of chemical potential energy when connected in a complete circuit this energy is transferred to the electrons which movees through the wires this movement of charge is called a current and we say it always goes from the positive terminal of the battery to the negative don't think about it too much as the electrons pass through the bulb their energy is converted into light but the electrons don't just disappear once they transfer all the energy to the bulb as this is one big loop these electrons are pushed back round to the battery by the ones behind them where they're refilled with energy ready for another trip around the circuit this constant flow of electrons transferring energy is what keeps the light bulb on because electrons are so small and there are so darn many of them we don't deal with individual electrons but instead deal in kums of electrons or kums of charge potential difference PD for short also known as voltage tells us how much energy is transferred per Kum of electrons so if a cell or battery says it's one volt that means that one Jewel of energy is given to every Kum of electrons that pass through it if a battery is 6 volts that means six Jews is supplied per Kum instead we measure PD with a voltmeter they're always connected in parallel to the components you want to measure the voltage of in the real world that means the leads or cables from the voltmeter always piggyback into other leads if we put the voltmeter across the battery it should measure 6 volts right because 6 Vols is supplied to the electrons in the circuit that's just 6 Jews per Kum but put it across the bulb and it should still say 6 Vols why because the electrons have to lose all of that 6 volts worth of energy as they pass through here's the equation for PD PD in volts is equal to energy in Jews divided by charging kums in simple form V is equal to e over or div divided by q q is the symbol for charge but it's measured in C in kums you'll see the rearranged version E equals QV on your formula sheet current on the other hand tells us what the rate of flow of charges like any equation for a rate ASP usual it's something divided by time so here it's current in amps equals charge in kums divided by time in seconds or i = q / T yes we use capital i as the symbol for current not C blame the French for that as they called current intensit cant it does mean though that we don't get confused between current and kums though so we stick with it you're going to see the rearranged version of this equation on your formula sheet Q equal i t that's I * T we measure current with an ameter note that it's not amp meter unlike a voltmeter it must go in series that means in line with the component we want to measure the current for components in a circuit have resistance that is they resist the flow of charge or current through them but that's not a bad thing this has to happen in order for them to work a bulb has resistance which causes energy to be transferred and light to be emitted a resistor of course has resistance too but it just produces heat when current flows through it if we make a circuit with a resistor and change the PD available to it what we find is that an increasing PD results in a greater current flowing in fact doubling one doubles the other so we can say that PD and current or V and I are directly proportional drawing a graph of these two makes a straight line and if we turn the battery round we can get Negative values for both two but still a straight line through the origin this straight line a constant gradient shows that a resistor has constant resistance we say it's omic the steeper the gradient of this line the lower the resistance of the resistor as more current is Flowing per volt the equation for resistance is ohms law V equals I we can get the resistance of a component from an IV graph like this by just picking a point on the line and rearranging ohms law so R is equal to v/ I for a resistor you'll end up with the same answer no matter what point you pick if you repeat the same experiment for a bulb in place of the resistor however you'll end up with a curved graph like this this shows that the resistance is changing the resistance of the metal filament in the bulb in fact you'll find that any metal has a changing resistance if you increase the PD and current they're non OMC at higher PDS the current increases less and less so that means they can't be proportional this shows that the resistance of the metal is increasing with a higher PD and higher current the change in gradient shows us that this is true but we still just take a point on the line and use 's law if we want to find the resistance it's just that it does matter where you pick that point in this case so why does resistance change for a metal well it's because Metals consist of a lattice or grid of ions surrounded by a sea of delocalized electrons that just means they're free and free to move move or rather they're fairly free to move because they do collide with the ions as they flow that's why the metal heats up when you pass a current through it the higher the current the more frequent these collisions are this makes the ions vibrate more and more which in turn makes it harder for the electrons to flow the resistance has increased now there is another component called a diode it will give you this graph the circus symbol might give you a clue as to why this is a diode only lets current flow through in One Direction we say that in One Direction the resistance is very high and it's very low in the other which is why the current increases Suddenly at around 1 volt an LED is a light emitting diode similar symbol just with a couple of extra bits these are what most lights in electronics are these days rather than filament lamps they act in the same way as a diode so they give you the same graph but they just happen to emit light as well a superconductor is a material that has a resistance of zero not nearly zero zero generally these materials need to be cooled before they reach that point so you might see a graph like this the temperature is going down and so the resistance goes down until boom we hit what we call the critical temperature at the critical temperature and Below resistance Falls to zero every material has a different resistivity or resistivity some people say the definition is this it's the resistance of a cube of unit length sides of that material so in SI units that's the resistance in ohms of a 1 M Cube note that that is not resistance per M cubed the definition must involve an actual Cube the unit we use is OHM meters again be careful that's not ohms per meter to find resistivity we measure the diameter of a wire with a micrometer and calculate area from that using pi d^2 over 4 we then measure V and I to calculate R for varying lengths L of the wire measured with a meter rule plotting R against L gives a proportional relationship the equation for resistivity therefore is this r equal row L over a where row is resistivity in ohm meters rearranging this we have row equal ra over L the gradient of the graph is R over l so multiplying by the area gives us the resistivity series and parallel circuits this is where things get a bit tricky remembering what happens to current PD and resistance when we have components in series or in parallel here's the simplest series circuit we can make really just two resistors in line with the battery what you need to remember is that for components in series total PD is shared between them current is the same for all of them and the total resistance is just the sum of all resistances that just means added up let's deal with that first point if these resistors are the same let's say 10 ohms each then that 6 Vols total PD from the battery must be shared between them so if we put a voltmeter across each of these they'd both read 3 volts it wouldn't matter what resistance these resistors are they could be a million ohms each if they're the same then that total PD is shared equally by the time the electrons leave the second resistor they have to have lost all six volt Vol worth of energy ready to go back to the battery to be refilled this idea is actually just kof or kof's second law the sum of emfs must equal the sum of PD drops in a closed loop just remember that if batteries are pointing in opposite directions one of them must be a minus by the way we can also call this setup a potential divider circuit as the total potential total PD is being shared if the resistors don't have the same resistance then we can use the second point to help us that is the current is the same for both let's say the first resistor is 20 ohms using four volts of the total six volts available we know two things out of v i and r so let's use ohms law to find out the third for it current in this case I rearranging Ohm's law we get I is equal to V / R so that's 4 ID 20 0.2 amps same for the second resistor too is there also a second thing we know about the other resistor why yes there is remembering the first rule up here we know that if the first resistor is using 4 volts of the total 6 volts available well then the other resistor must be using up 2 volts we could then use ohms lore again to find its resistance 10 ohms the rule of thumb is this the greater the resistance the greater the share of the total PD it gets we can also use Ohm's law for a whole circuit we just need to make sure that we're dealing with the total PD total current and total resistance the rules for parallel circuits are the opposite the PD is the same for every Branch again this is true because of kov Second Law the battery is actually involved in two loops so therefore the PD drops in both Loops must be the same current is shared between each branch and the more resistors you add in parallel the lower the total resistance this by the way is because you're giving the current more roots to move through the circuit which means more current can flow so if these two resistors are connected to the 6vt battery in parallel you know straight away that the PD for both has to be 6 volts voltage isn't shared in parallel circuits if however we say 0.5 amps total current is flowing through the battery and 0.2 amps of that is flowing through the top resistor that must mean that there's 0.3 amps flowing through the bottom resistor this is actually kof's first law current and therefore charge must be conserved at any Junction if you're not in a rush why not pause the video and see if you can calculate these two resistances by the way if you want a little bit more help on this then have a look at my video how to answer any electricity question it's not only metals that can change resistance we can have a and you have a circuit that responds to changes in temperature a therm's resistance decreases if the temperature increases so in essence it does the opposite to a metal by the way you might see a thermos golden NTC negative temperature coefficient that just means that higher temperature lower resistance in this case if the temperature increased the resistance of the thermister would go down as does its share of the total PD that means the PD measured by this voltmeter will increase this could be the basis of a temperature sensor for your central heating for example an ldr is a light dependent resistor very similar to a thermister but resistance goes down with increased light intensity not temperature so this circuit could be on the top of a street lamp light intensity goes down resistance of the ldr goes up as does its share with voltage this could then be connected in some way to the light bulb so it turns on as it gets dark turns out batteries or cells have a resistance of their own so if you attach a bulb to a 6vt battery the bulb will get less than that a voltmeter across it might measure 5.5 volts say this would also be the same if we attached the voltmeter across the battery terminals instead so we can call this the terminal PD be careful that means the voltage available to the rest of the circuit that means 0.5 volts is being lost inside the battery due to its internal resistance little r the EMF electromotive Force Epsilon is the symbol we use is the total PD provided that's the 6 volts here so the equ equ is this EMF equals terminal PD V plus I little r where little r is internal resistance so I * little L is the voltage lost due to internal resistance if we increase the load resistance that's the resistance of the circuit the current flowing through the battery decreases of course but this results in less PD being lost in the battery so the terminal PD increases drawing a graph of terminal PD against current gives us a straight line the magnitude of this gradient is equal to to the internal resistance if we extrapolate the line back to the Y AIS the Y intercept is equal to the EMF which makes sense as if there's no current flowing then in theory the circuit should get the whole of the EMF there's no volts lost in the battery you can of course also get the EMF by just attaching a voltmeter across the battery by itself with nothing else connected this works as voltmeters generally have very high resistance all waves transfer energy without transferring matter longitudinal waves are those in which the direction of the oscillations is parallel to the direction of energy transfer that is the direction the wave is going in these ways particles Bunch up we call those compressions and when they're spread out we call those rare refractions transverse waves are those in which the direction of oscillations is perpendicular to the direction of energy transfer we can represent any wave including longitudinal waves like this we call this a waveform displacement is up the y- Axis basically just how far the particles have oscillated from their original position and it can be either distance or time on the x-axis the peak of a wave is called the amplitude it's the maximum displacement from equilibrium if it's distance on the x-axis one complete wave here gives you the wavelength we give this the symbol Lambda for short but it's measured in meters if it's time on the x-axis instead one complete wave gives you the time period this is the time it takes for one complete wave to pass frequency on the other hand is how many waves pass a point every second and the unit is hertz frequency is equal to 1 over time period f = 1/ t you can often be asked to find frequency from a wave form like this measure the time period Then do one divided by that easy the wave equation is this V equal F Lambda that's wavp speed equals frequency time wavelength it's worth remembering that visible light wavelengths vary from around 400 to 750 nanm or 4 to 7.5 * 10- 7 m with red light having the longest wavelength and blue the shortest the intensity of a wave is proportional to the amplitude squared that means that if the amplitude doubles the intensity quad Rupal when light waves move from one medium to another say from Air to Glass they change speed in this case the wave slows down and the wavelength also decreases a change in medium also results in a change in Direction This is called refraction that is if it's at an angle to the normal the line we draw perpendicular to the surface if light slows down it moves closer to the normal so that means that the angle of refraction is smaller than the angle of incidence now all of these angles are measured from the normal how much a medium refracts light is determined by its refractive index symbol n it's just a ratio that's equal to the speed of light in a vacuum basically the same for air divided by the speed of light in the medium so it will be a number that's always greater than one if you calculate s i over s r for a light Ray entering a medium from Air this happens to also give us the refractive index the full equation for refraction is Snell's law N1 sin Theta 1 equal N2 sin Theta 2 you can see that we've just replaced i and r with thetas bear in mind that in reality the refractive index of material varies with wavelength blue light's refractive index will always be higher than red lights for the same medium that means that it refracts more than red that's why white light undergoes dispersion when it passes through a prism let's say the light rate is coming out of the glass block and into air now if we keep increasing this angle of incidence eventually we'll end up with an angle of refraction of 90° that light Ray will be going along that boundary along the surface the angle of incidence is now equal to what we call the critical angle and that's going to be different for every medium if we make the angle of incidence even bigger than the critical angle that means that no light is going to be refracted out of the block instead all light is reflected back inside by the way we always get some reflection but now we have total internal reflection want to calculate the critical angle well you can start with Snow's law you call Theta 1 Theta C instead make N2 90° and we end up with sin Theta C = N2 over N1 this incidentally is how optic fibers or fiber optics work basic optic fiber is a glass core surrounded by a protective sheath the issue is that this will have a higher refractive index than the core so TI would not happen if it were not for the extra layer called the cladding that is in between them it has a lower refractive index than the core so TI can occur one of the issues with optic fibers is the fact that light will diverge spread out as it travels down a fiber this means Rays can take different paths and therefore different times to reach the other end this is called modal or multi-path dispersion and it results in pulse broadening if pulses are stretched too much they start to overlap as the next one has started to arrive before the first one has completed its Journey your data are goner to mitigate this we can do a few things number one make the fiber really thin the thinner it is the less light will diverge number two put repeaters in every so often to retransmit the slightly Broad pulses as brand new ones the final clever idea is to use graded index fibers light emitted from the Sun oscillates in all orientations however if you have a polarizing filter made of very small lines it only lets half of the light through only half is transmitted the other half is absorbed this is because it only lets waves of certain orientations through we say that if the lines are vertical waves oscillating vertically are absorbed while horizontally orientated waves are trans transmitted pass through and vice versa waves between vertical and horizontal are transmitted or absorbed according to their angle it's very complicated in reality but put simply the light is now polarized and the intensity of the light is halfed put another polarizing filter at 90° behind the first and all of the light is absorbed a normal wave is what we call a progressive wave the wave moves while the medium or particles just oscillate around a point say up and down two points one wave apart are said to be in Phase they're doing the same thing at any time we say their phase difference is zero or 360° as we can represent wave Cycles as circles we can also split circles and therefore Cycles into radians instead of degrees there are two Pi radians in a circle so again the phase difference of these two points is 2 pi radians like we said that's the same thing as zero points on opposite sides of a wave are completely out of phase or we might say in antifas they're half a wave out of phase so their phase difference is 180° or Pi radians these two points are a quarter of a wave out of phase so that's a phase difference of 90° or Pi / 2 radians we generally don't give phase differences above 180° Pi radius as we can just give the opposite phase difference so 270° is just given as 90° Etc any phase difference can be calculated as a fraction times the total in a cycle so we can do distance between two points divided by the wavelength or time difference between two points divided by the time period depending on what graph we're given then we just multiply by 360 or 2 pi depending on whether we want the phase difference in degrees or radians when two Progressive waves traveling in opposite directions meet they undergo superpositioning they are superposed when these waves have identical frequency in wavelength a stationary wave is formed the points at which the resulting wave doesn't move is called a node that's because the displacements are all always summing to zero at these points we call this destructive interference so the amplitude is zero at a node no energy is transferred at all other points the resulting wave will oscillate due to constructive interference where the amplitude is a maximum these are called antinodes we can see this if we attach a string under tension to a vibration generator the wave is sent down the string and it reflects at the pulley in these two waves interfere the simplest stationary wave looks like this we call this the first harmonic or the fund mental one Loop one antinode and a node at both ends we have half a wave on the string so that means L equals Lambda over 2 the frequency of this is given by the equation 1/ 2L link of the string time < TK T over mu T being the tension in Newtons which is usually the weight of the masses hanging on the end and mu being the mass per unit length of the string so that's in kilog per meter incidentally root T over mu actually gives you the weight speed double this fundamental frequency and we get the second harmonic L equal Lambda in this case third harmonic L equal 1 and A2 Lambda and so on stationary waves can also be formed in tubes of air at a closed end a node must be formed at an open end an anti-node we can represent the stationary wave much like we do for a string just bear in mind that the first harmonic is likely to be different than that of the string because one or two of the ends are probably going to be open unlike Progressive waves points on stationary waves can only ever be completely in Phase or completely out of phase it just depends on if they're the same side of equilibrium or not that's because two points above equilibrium will reach their own different amplitude at the same time and they'll both reach equilibrium at the same time too even if waves aren't traveling in opposite directions they still interfere when they meet Thomas Young put a thin slit next to a candle to First ensure that the light used for the experiment was coherent all of the light was in Phase but the definition of coherent is this actually all waves have a constant phase difference this light then passed through a double slit the result was bright and dark fringes appearing on the screen called these Maxima and Minima we have a central maximum because those two rays meeting have traveled the same distance so therefore they interfere constructively the dark fringes or Minima are due to the light from the two slits traveling slightly different distances to each other we say their path difference is half Lambda that means that they arrived 180° completely out of phase and interfered destructively canceling each other out the first bright Fringe from the central Fringe is a result of the path difference being the same as the wavelength Lander that means that these arrive in phase two interfering constructively resulting in a bright Fringe the next dark Fringe was the result of the path difference between one and a half Lambda and so on youngest double slit equation is this W equal Lambda d/ s where W is The Fringe spacing that's the distance between the center of two bright fringes or two dark fringes for example D is the slit to screen distance and s is the slit separation note that isn't slit width changing the actual width of the slits doesn't change the Fringe width at all however this equation is an approximation and it can only be used when the screen distance is much much larger than the slit separation that's why the equation is likely to break down when we use sound instead if you have two speakers producing the same waves in Phase if you walk at right angles to them you'll hear the volume fluctuate as you go through Maxima and Minima we can represent the pattern by drawing a graph of intensity against distance from the central Max the intensity Falls away gradually and they all have the same spacing but light can also defract when you just use a single slit as defraction occurs at both edges of the slit it gives this defraction pattern instead the two differences being that the intensity Falls away quicker and the central Maxes double the width of the subsequent fringes don't forget that if you do this in reality it's always more accurate to measure 10 fringes than divide by 10 to get W when we do the experiment we're probably going to use a laser as it provides coherent light that's also monochromatic just one wavelength is emitted resulting in clearly defined fringes however using a candle that emits a spectrum of wavelengths young saw the white light splitting into the different colors as red light has the longest wavelength it defract the most so it could be seen on the outside edge of the fringes blue light has the shortest wavelength so it diffracts the least so it can be seen on the Inside Edge of the fringes if you replace Young's Double slit with a grating of very small lines separated by line spacing Little D you only get constructive interference at a few points very far away from the central Max we call these orders instead of fringes the central Max is the zeroth order as we're dealing with large angles we can't use Young's double slit equations so we use the more accurate equation n Lambda equal D sin Theta often you'll be given the line or grating spacing in lines per millimeter which you need to turn into meters essentially meters per line is the reciprocal before it can go into the equation you can also be asked to find the maximum visible order in this case we want to find out what order is made at 90° sin 90 = 1 so n = d over Lambda let's say this ends up being 3.8 there's no such order so only orders up to three are visible also they might try to catch you out by asking hey how many orders will be visible rather than what is the highest order in this case you have to count the orders on both sides including the zeroth order so that will be seven in this case very cheeky just be careful with some multiple choice questions involved in this equation you might get asked what will happen to the orders if the wavelength is half say in this case you don't look at Theta at all as it's not proportional to anything in the equation instead we say n is inversely proportional to Lambda if Lambda halves n doubles that means that what was the first order is now the second order and a new first order is created between it and the zeroth order if D is changed we say n is proportional to D we can represent forces with vectors that is an arrow that shows the direction and magnitude of the force if two forces act on an object there's a resultant Force we find this by technically adding the vectors however if they're going in opposite directions one must be negative so in this case the resultant force would be 3 Newtons to the right and that's positive if we decided that positive is in the right direction if vectors are at right angles to each other you use pythag is to find the resultant this works because you can make a triangle by moving one of the forces you could also be expected to use trig that's socker to to find either one of these angles if a measurement or quantity just has magnitude but no direction it's not a vector but it's called a scalar instead here are some examples of both note that displacement is distance traveled with a direction similarly velocity is the vector form of speed weight is another name for the force due to gravity that acts on an object it's calculated by multiplying the mass in kilograms by gravitational field strength or G which here on Earth is 9.8 Newtons per kg now if you hold an object up with your hand you must be pushing up with a force that is equal to its weight in order for the forces to be balanced and so it doesn't accelerate however that means that if you lift it upwards at a constant speed that's also true we can therefore then calculate the energy that is used to lift this object using the equation for work done that's work done equals force time distance moved this equation is true for any situation but in this case the force is the weight and the distance is the height so we could say the gain in energy is equal to mass * G * H does that look familiar it should because that's the exact same equation for calculating gravitational potential energy that's GP gained to be precise to calculate work done the force and distance moved must be parallel if the force is at an angle however we must resolve it to find the component that is parallel to the distance that's why sometimes you'll see a COS Theta on the end of the work done equation in your formula sheet if we divide both sides of the equation by time we end up with power equals force time velocity we sometimes call this power developed just tells you how much work is done per second by or against the force Newton's first law is this when there's no resultant Force an object's motion is constant in other words no change in velocity that could be because there's no forces acting or the forces are balanced Newton's Second Law involves unbalanced forces that is there is a resultant Force this is equal to ma masstimes acceleration only one of these can be true in any situation there's either no resultant force or there is Newton's third law however is always true and this is the one that people get confused about understandably for every action of force there is an equal and opposite reaction force but this is not referring to balanced forces it's all about perspective when we think about the first two laws we only really consider the object itself for example the force pulling downwards on the ball is its weight we know that the Earth is pulling down the ball but Newton's third law says the complete opposite is true as well the ball is also pulling the Earth up now the Earth is so massive that it doesn't really have an effect but it's still true nevertheless another example if you have two ice skaters if the guy Gator pushes on the girl skater there's an equal and opposite reaction force pushing back on him too that's why they both move away from where they were if an object is on a slope its weight mg will try to pull it downwards however the reaction force of the slope pushes perpendicular to the slope this is equal to mg cos Theta where Theta is the angle of the ramp for an explanation of where the angles come from check out my mass on a slope video the combination of these two forces result in a force pulling down parallel to the slope this is equal to mg sin Theta that's always going to be true no matter what the object is doing if it's stationary or traveling at a constant speed that must mean another force is pushing or pulling up the slope that has to be equal to this component mg sin Theta quite often that's friction no matter what forces are involved you find the resultant like you do for any other situation the sum of all forces in One Direction minus the sum of all forces in the opposite direction then you can use this resultant force in FAL ma if you given the height of the ramp chances are you're going to have to use energy too maybe the mass is sliding down the ramp for example if there's no frictional forces we can say MGH at the top equals half MV S at the bottom as per usual if you're told the speed at the bottom chances are some energy is being lost instead so we just use the work done equation with the work done being that energy lost and that can give us the average frictional force just remember that the distance has to be the distance traveled not the height in that case if an object is accelerating we use one of Newton's equations of motion and their suat variables if an object is only moving in One Direction s u and v can all be positive even if it's downwards you do have to be careful with a though as that could be negative for example if the object is decelerating in any question you write down your variables and the unknown you need to find cross out the unused fifth variable choose the right equation and rearrange if necessary to deal with an object being thrown upwards and returning to its original position s is technically zero and things get a bit messy then in this situation it's always a good idea to split the problem in half from start to the Apex where V ends up being zero and then just double the time if the question requires it for objects being fired horizontally off the edge of something say a cliff you split the into vertical and horizontal U Su that for vertical where U is zero as the initial speed is only horizontal a is equal to G 9.81 and S is the height it falls chances are you're going to use S = UT + half a^2 UT disappears because U is zero you don't use suvat for the horizontal motion though as its horizontal velocity stays at that initial speed so horizontally you just use speed equals distance over time for objects fire in an angle just use my easy vectors trick to resolve the the initial speed into vertical and horizontal components Link in description if you haven't watched that yet again use suat for vertical speed equals distance over time for horizontal like the ball being thrown upwards and coming back down you might need to split the trajectory in half and just go from the start to the Apex momentum is equal to mass times velocity the unit therefore is kilogram m/s momentum is a vector which means you have negative momentum if your velocity is negative in a collision kinetic energy isn't always conserved but total momentum all always is calculations on this can be tricky but you just have to be careful with your pluses and minuses you write down M1 U1 if there's just one object moving to begin with remember U from suat we can use it here too and on M2 U2 if there's a second object moving too this then is the total momentum before the Collision before the event this could also be zero if nothing's moving to begin with say a cannon about to fire then all we have to say is that this is equal to the total momentum afterwards M1 V1 for one object Plus M2 V2 if there's a second object moving too if theyve coupled together we just say m * V where m is the total mass of the two then all you have to do is pop your numbers in making sure that everything traveling to the left say has a negative velocity and you'll be left with one unknown rearrange to find it you get your answer incidentally in the case of the Cannon as there's zero total momentum before the same must be true after too even though the cannon ball is moving that must mean the cannon has the same momentum but in the opposite direction so they still add up to zero this is an example of recoil one last and very important example rebound when an object or particle collides with an object that essentially doesn't move say a wall it will Rebound with the same speed but in the opposite direction that's not a zero change in momentum though as momentum is a vector if its initial momentum is Mu where U is the initial velocity then the change in momentum also known as impulse will be minus 2 muu of course total energy is always conserved to but some of that will likely be lost to the surroundings as heat sound Etc total kinetic energy is very rarely conserved as a result we call such collisions inelastic like two plasticine balls smooshing together there's no kinetic energy afterwards so that's as inelastic as you can get if the conditions and the objects are just right though you can get collisions where the total kinetic energy is conserved in theory anyway these are elastic collisions an example of this would be snooker balls hitting each other or a newton cradle these collisions are very close to being elastic so we can treat them as such total kinetic energy is conserved force and momentum are closely linked Newton's second law says that f equals ma but we also know that a is equal to Delta V / T so actually it's also true that force is equal to change in momentum over time or we can say the rate of change of momentum that's why the alternative unit for momentum is Newton seconds impulse is the alternative name for change in momentum so it has the same unit if we draw a graph of how the force acting on an object changes over time the area under the graph gives us the impulse so if the object was stationary initially it will now have that momentum due to the impulse provided to it if a fluid like air or water pushes on something at a constant rate say a hose pipe spraying a wall or air through a wind turbine we can find the momentum carried per second by it in reality this is the same as Force as you know from our equation units are your friends here as you won't be given an equation for the this so let's take FAL delta mv/ T but instead of swapping v/ t for acceleration we split it into M overt * V M/T is the mass in kilogram moving per second you might be given that but you'll more likely be given the density of the fluid instead and the cross-sectional area that it's moving through so mass is equal to density time volume and volume is equal to area time length length over time gives you speed so the most useful equation for this is f Row a^ 2 a moment or Torque is a turning Force around a pivot it's calculated by force time distance to the pivot so its unit is Newton meters however it's not the same as work done as force and distance must be perpendicular instead of parallel if they're not perpendicular you must resolve one of them usually the force by multiplying by S or cos Theta depending on what angle you're given again you can use my easy vectors trick in short we multiply by cos Theta if the angle is between the resultant and the component s if not the principle of moments is this for an object to be in equilibrium the sum of clockwise moments must equal the sum of anticlockwise moments bear in mind that an object can already be spinning and this still be the case in reality there is another condition needed for an object to be in equilibrium which you already know there also can be no resultant force acting on the object it turns out that the principle of moments can be applied to any scenario even if there appears to be no pivot as such in fact you can make any point your imaginary pivot and it still works for example this guy standing on a plank resting on two supports you first take moments about one of the supports to eliminate it from the equation taking moments about the left support the moments due to the weight of the plank this is easy to forget by the way and the dude going clockwise must be balanced by the moment due to the reaction force from the support on the right you can find the reaction force this way and then you can use this with just balanced forces to calculate the reaction force on the left you don't need to use moments if you just have one unknown force a couple is defined as two forces pushing in opposite directions on an object such that they produce a resultant moment but no resultant Force meaning that the object will start to spin if it wasn't already but it will not accelerate it's not in equilibrium as it's only satisfied one of our two conditions an object will topple over if its center of gravity is moved past the pivot vertically so the moment due to its weight has changed direction from clockwise to anticlockwise or or vice versa forces can also deform an object if you pull on a spring that is fixed at one end it will stretch or extend hooks law states that f equals K that's Force equals spring constant sometimes called stiffness times extension the unit for spring constant is Newtons per meter this works for any object that stretches elastically that is returns to its original shape once the force is removed it can also be true if an object is compressed instead the area under the graph gives you the work done on the spring spring and therefore the elastic potential energy stored in the spring if you attach two Springs in series we might say end to end they stretch twice as far with the same Force meaning the spring constant must be half what it is for one of the Springs side by side in parallel and the opposite is true even if not a spring materials can still be stretched or compressed they can be deformed with a force stress is basically pressure it's Force per unit area so Newtons per met squar also called pascals strain is just a ratio of extension to original length drawing a graph of stress against strain will likely give you a proportional relationship at least to begin with the gradient of this graph gives us the young modulus every material has its own unique number as strain doesn't have a unit the young modulus is also measured in pascals replacing stress and strain with their own equations the full version of the equation is eal FL over a Delta l or X or E depending on what you use for extension area is proportional to d^2 as area is equal 2 pi D ^2 over 4 that means if you double the diameter the extension quarters add more Force again and the graph starts to curve though we've gone past the limit of proportionality we can't use Young's modulus past this point however even after it curves if we remove the force it can still return to its original position it can still behave elastically we say the unloading Curve will look different to the Loading curve if you make a graph of force against extension the area under the loading curve is still the energy needed to stretch the material just like with springs the area under the unloading curve is the energy that you get out as it's returned to its original length that means that the area enclosed between the two is the energy lost usually as heat increase the force even more and it won't return to its original length we've gone past the elastic limit it's now undergoing plastic deformation instead of elastic the maximum stress the curve goes to is called the ultimate tensile stress the line can go down after this point as the wire starts to neck it carries on extending even if you remove some of the force a ductile material like copper will have a large plastic region whereas a brittle material generally has a high young modulus and suddenly snaps before being able to deform plastically you always want to make accurate measurements reducing any errors and uncertainties to a reasonable degree when measuring any length the ruler should be as close to the object as possible to avoid Parallax error you want your eye to be in line with the point on the ruler too for the same reason parallax error is a random error by the way it won't be the same every time if it's not possible to have them close together say when measuring the extension of a spring you can use set squares just a right angle triangle even made out of a piece of card to accurately show where it lines up on the ruler it's also a good idea to use one between the ruler and a flat surface say the table to ensure that the ruler is indeed vertical the resolution of a ruler or a meter rule is usually 1 mm that's the smallest difference it can measure there can be large random error when using a stopwatch due to reaction time to mitigate this you should always do rep and calculate a mean this is also true when taking measurements say with a venue caliper and micrometer too for example when you're finding the thickness of the wire in the young modulus and resistivity experiments digital instruments will give you a value on the screen all you have to do is record the reading say a digital voltmeter however sometimes it's more useful to use an analog instrument in this case your eye must be in line with the needle to avoid Parallax error sometimes they have a mirror behind it to help you you might have to choose one that has an appropriate full scale deflection for your measurements that is the max Maxum measurement it can make this is usually 1 2 5 10 50 100 Etc let's say that we figure out that the maximum voltage we're going to have to measure is 6 volts the appropriate full scale deflection would be 10 volts in this case one volt would be too small of course and 100 volts would result in inaccurate readings because the resolution would be too large and the uncertainty would be massive a micrometer has a much higher or I prefer saying smaller resolution usually 0.01 mm that's 1/ 100th of a millimet first is a good idea to calibrate it close the jaws with nothing between using the ratchet on the end this ensures you don't overtighten them which would result in the Jaws being compressed giving the wrong measurement if it says 0. millim at this point it's all good if not there is a zero error a systematic error with any measurements you make after that systematic meaning it will be the same error every time to mitigate this just subtract the error from every measurement when measuring the thickness of an object with it say a wire we use a ratchet again until it stops see how many half mm the barrel has moved past so in this case it's 1.5 mm then add on the hundreds using the scale on the barrel itself which is 24 here so 1.5 + 0.24 mm gives you 1.74 mm if it read 0.01 mm when we were calibrating this measurement would actually be 1.73 mm in reality if it read minus 0.01 mm on the other hand this would be 1.75 mm instead we've taken away a minus number which makes the measurements bigger ven calipers is work in a similar way the zero on the slide tells you how many millimeters then the Veria scale gives you the 10th or sometimes 20th that's 0.05 millimeters you have on top AIA scale works because its lines are spaced such that they don't line up with the main scale however one of them will line up with the main scale that's what you take as your T so this would be 8.7 mm they can also measure the depth of a hollow object say a tube using the rod that comes out of the other end that goes in the tube and the edge of the caliper rests on the top up then you just read it as normal uncertainty is the idea that even if you avoid parallx error zero error Etc no measurement will ever be completely accurate because there's always a bit of rounding involved in every one you make for example using a thermometer with a 1° c resolution will require you to decide if the liquid is closer to say 27 or 28° in chemistry you'll likely say that this temperature therefore is 27 plus orus 0.5° they say the uncertainty in any measurement is half the resolution now you will likely get the Mark if you put that in a phys exam as well but many argue including myself that there's every possibility that you might think the liquid is closer to 27 when it's actually closer to 28 that means that the true value is not within your uncertainty that's why most questions expect you to State the uncertainty as being equal to the resolution itself so this would be 27 plus orus 1° C it's being a bit more honest and ering on the side of caution the uncertainty of a digital instrument can be inferred to be just one of the last digit so if you're given a voltage of 5.32 Vols you can assume that the resolution used was 0.01 volts which will also be the uncertainty finding the uncertainty in a mean value just find the range of the values you added up that's the maximum takeway the minimum by the way not the first takeaway the last which people often do and then you Harve it this gives you an absolute uncertainty which you can then turn into a percentage uncertainty if needed drawing a line of best fit on a graph allows you to find a gradient however sometimes the points will have error bars to reflect the uncertainty if so you can draw a line of worst fit too this is a line that has the maximum or minimum possible gradient as your call that still crosses every bar note that that might mean that it doesn't hit the ends of the first and last error bar then find the difference between the gradients of it and the line of best fit to get the uncertainty alternatively you can just draw the two lines of worst fit and find the mean of the two to get the gradient and the uncertainty will be half their range if you add or subtract two values that have an uncertainty then the total uncertainty is the sum of the two uncertainties if you're using a ruler that you can move so the zero can be lined up with the edge of whatever you're measuring the uncertainty will be equal to the resolution however if the ruler can't move and you have to find the measurement by finding the difference between two points then the uncertainty will be double at resolution this is because we've essentially just combined two uncertainties or rather two absolute uncertainties absolute uncertainty is a normal uncertainty it has a unit just like the measurement but what if you're multiplying or dividing values that have uncertainties instead in this case you convert the absolute uncertainties into percentage uncertainties and you then add them all up regardless of what's being multiplied or divided so let's say we have these measurements which we've put into an equation to calculate an answer here are the uncertainties in percentage form as well and I've added them up to give the total percentage uncertainty uncertainties always increase by the way regardless of whether you're adding subtracting multiplying or dividing the only exception to this is when you're rooting a value so if you wanted the percentage uncertainty in the square root of V we just half the percentage uncert certainty in V you get the idea once you have the total percentage uncertainty you need to turn this back into an absolute uncertainty for the final calculated value just multiply it by the percentage and certainty as a decimal and boom you're done we usually try to obtain a StraightLine graph in physics experiments which allows us to find a gradient and therefore the relationship between the two variables on the axis variables aren't always directly proportional though of course but if we know their relationship we can plot the right thing on the axis so we still get a StraightLine graph for example with the stationary wave on a string experiment we know that the frequency is proportional to the square root of the tension or f^ S is proportional to T so if we plot f^2 on the Y AIS t on the x-axis we'll get a straight line if we have some sort of inverse proportional relationship then one over something must go on one of the axes log graphs are powerful because they can allow us to find the relationship between two variables if we don't know it prime example of this is what Kepler did to coin his third law he saw that the further away planets were from the Sun the longer their time period but he needed to find out exactly how they were related as T clearly wasn't proportional to R but R to the power of something instead if we take the planets in our solar system and plot log T against log R we get a straight line doesn't matter what log base we use by the way it works even for natural log Ln a graph with log values always gives a straight line the gradient is the important thing here usually this is what gives us the relationship in this case the gradient is 1.5 or 3 over2 the general straight line formula is y = mx plus C or in this case log T = 3 log R plus some constant which is our y intercept let's call it log K from there we have two log identities we need to use first we can take the three halves and make it the power on the r then we can also say that the sum of two logs is equal to the log of the two things multiplied so on the right we have log KR to the^ 3es D logging both sides we see that t is proportional to r ^ 3 or t^2 is proportional to R cubed even if logs aren't involved you still need to be able to interpret a graph in terms of y mx plus C to produce an equation bear in mind that sometimes it's only one of the axes that will be a log just remember that if you dlog one side in this case it's 10 to the power of the other side or e to the power of the other side if it's natural log finally it's possible you'll be given a graph that has an actual log scale it's nonlinear in this case the first line is one of that order and the lines then get smaller approaching nine and then it goes into the next power up so 10 20 30 up to 90 then 100 200 Etc reading off these graphs often requires you to make a judgment call with values between the lines so just remember that going halfway to the next line isn't actually half the difference it's not five but it's more like three leave a like and a comment if you found this helpful all the best for your exam and I'll see you next time