for a level physics that are a vast number of equations and formula that you need to know and also be able to apply to a vast number of questions now luckily each exam board will provide you with some kind of data booklet and that outlines probably 95 of the formulas that you're going to be using in any exam but there are some others that they do not tell you about now in this video I'm going to be showing you some of the key formula you just need to remember off by heart you can of course skip forward there are chapters beneath where I go through things by topic but before we begin can I just show you what I feel is probably the most important and underrated equations basically if you want to look at the area of something which is circular you can of course use area equals pi r squared however in physics you tend to measure the diameter of a wire or a piece of metal and therefore we can say that area is equal to Pi D Squared over four and that means you don't need to tell your diameter divided by 2 to get the radius you can just put your diameter straight into the equation Square it divide it by four and I think that this is probably one of the most underrated but also probably most commonly used equations that I use in physics we tend to look at bits of y when we think about resistivity when we think about stress and strain and things like that so that equation there number one is one that I think you should just remember so let's begin looking at forces and motion and mechanics now even before you did your gcses you'll be familiar with the equation that says speed is equal to distance divided by time but we can say that the displacement is equal to the velocity multiplied by time now that is something they don't give to you um it's pretty much a cvat equation where we have a constant velocity and I think that's really important because we if we ever think about projectile motion we might think about how in the vertical Direction the component of velocity is maybe going to be increasing however in the horizontal Direction the component of velocity Remains the Same and effectively this is the suvat equation where a is equal to zero and U is equal to V now that's the first one the other suvat equation which I think is a bit maybe underrated is the fifth through that equation that they don't tell you and this basically says s is equal to VT minus a half a t squared normally we have u t plus a half a t squared this one though is the Zubat equation which doesn't have a u in it so if you don't know the initial velocity of something you can still work out its displacement or any of these others provided you know the other three terms now there are another couple of equations that OCR in particular don't actually give to students in their formula booklet and to be honest you should know these by now the first one is that the kinetic energy of something is equal to a half MV squared but of course you know that from GCSE and the other one is that the gravitational potential energy is equal to MGH now of course I'm sure that you should remember them but those aren't given to you if you are an OCR student however what can be useful to remember is if we have something maybe where we uh project it up into the air and we want to know how high it goes or maybe something is dropped and we want to know how quickly it's impacting the ground we can equate the two things together providing it's 100 efficient and therefore we can say that a half MV squared is equal to MGH the M's cancel on the on each side and therefore we can say that that final velocity is going to be equal to the square root of 2 G8 and I think that comes up quite a lot again sometimes you might see this when you're looking at the motion of a projectile and you can do it in terms of looking at energy conservation or you can still maybe look at it in terms of suvat and here if we think about how this relates to a super equation uh the final speed would be equal to 2 a s so these two things you might have seen that they will give you the same answer and it doesn't matter if you're using mechanics or you're using like kind of energy conservation you will still get to that same answer I hope that makes sense now there is another equation that we can use to work out the velocity and here we can say that V is equal to the square root of 2 GM over R and this is the escape velocity of an object maybe if it's escaping a planet which has a mass m and radius R and Big G is our gravitational constant so this one over here that tells you the escape velocity of an object it's not always given to you in the data sheets but I think that's a really valuable thing also related to gravitational fields is this basic one that all of you remember or you should remember about the relationship between weight which is the force on an object due to gravity and the mass of an object and here G is our gravitational constant so gravitational field strength Big G is a gravitational constant little G is a gravitational field strength at that point of course it's 9.81 for a level but it can change especially if you look at radial Fields as you go into the second year of study now the next couple of equations are to do with momentum now if you've got a closed system we know that the total momentum before an event and that could be a collision or an explosion is equal to the total momentum afterwards and something that I quite like is to say that m1u1 plus n2u2 is equal to M1 V1 plus M2 V2 just got about enough space there and this is basically if you have two objects which are colliding then we've got Mass 1 and Mass two traveling initially at U1 and U2 and find it V1 and V2 now sometimes we have an event where the two things stick together and then we know that their combined velocity is going to be the same so you can also write this as M1 U1 plus M2 U2 is equal to M1 plus M2 multiplied by their combined final velocity V now that looks like a lot but often you find that maybe one object is initially stationary so maybe U2 might be zero and that makes everything a lot quicker but if you just write that down and also you draw a diagram maybe you've got Mass 1 and Mass two that's maybe beforehand afterwards the two objects maybe move off together you can just add a quick diagram you can start putting in your numbers and that allows you to work out how quickly something is moving off and also in which direction now these equations are to do with material properties the first one is about maybe the elastic strain energy or elastic potential energy stored inside an object maybe a spring which has been stretched now sometimes this is given us a half F Delta l now that's the way that AQA give it in their former sheet AQA tend to use Delta L other examples might use an e like you did at GCSE or maybe an X or even a Delta X there are loads of different ways of representing the change in length of that spring now the other one that they don't always give you is that this is equal to a half K Delta L squared okay now you might be familiar with that from GCSE the energy stored is equal to half times the spring constant times the change in length for the extension squared okay that one there is not actually given to you though if you're doing aq8 they'll give you that and of course if you know that f equals KX or f equals K Delta L you can get to this equation but that one there is worth remembering now related to that are these equations to do with material properties and AQA give you like a long word equation OCR kind of shorted down and they say that the stress is equal to the force divided by the area and the strain is equal to the change in length over the original lead now again different examples have different notations for example if you're doing OCR they say that this is equal to X over L and if you're doing Edexcel they call it Delta X over X I'm going to keep it like this for the moment now the other thing is we have the young modulus of the material or the Young's modulus and that's equal to the stress divided by the string so if it's equal to the stress divided by The Strain that's equal to the force divided by the area divided by the change in length over the original lead obviously that's a bit messy so we can neaten up a little bit so this one's quite nice we've got the young modulus equal to the force times the length divided by the extension times area sometimes we often want to look at maybe the extension of an object and here we can say that the extension is equal to FL over EA I quite like that one okay let's go on to the next topic so the next topic gets dangerously close to chemistry and is to do with thermal physics and ideal gases now lots of students still struggle between the conversion between degrees Celsius into Kelvin or back the other way all you've got to do is remember that you add either 273 or you take 273 awake very often as well have our temperature in Kelvin represented with the symbol capital T that's the absolute temperature and if you're doing equations maybe we are using p v and T you must always convert to Kelvin I sometimes get to do that I get caught out it's an easy mistake to make often as well when we give our temperatures in degrees celsius we often use the symbol Theta so this is my might be what you're used to if you're looking at equation for specific heat capacity um whereas T is often used for ideal gas equations it doesn't really matter which one you're using just make sure that you're using an appropriate unit either degree Celsius or kelvin when it comes to doing any questions the next equation is one that you're going to be really familiar with if you are doing a level chemistry and it basically says that the number of moles is equal to the mass divided by the molar mass now again we've got to be careful here in chemistry they tend to use grams a lot of the time when it comes to the molar mass of things in physics though we tend to use the s i unit of the kilogram so just make sure you've got the appropriate mass and molar mass now the number of moles we give the letter little n to that's a number of moles of the substance now that's going to be related to Big N which is actually the number of molecules of the number of particles in that sample and here the number of particles is equal to the number of moles multiplied by Avogadro's constant and again the value for that is going to be given to you in the data sheet so just make sure you don't get confused between little n big n and n a and equally sometimes we might talk about the mass of an individual molecule or the total mass of all of the particles within that system again sometimes we use little m's or big M's but again your exam board will be quite clear and ultimately as long as it's very clear and you're working out and you get the right answer that's all that's important now the next set of equations are I think the most important set because they are not given to you in your formula book but you will definitely be asked an exam question about these and these are to do with uncertainty by the way a lot of people ask how I do this video I'm actually writing on this kind of light board at the moment which has been provided to me by learning glass and actually I'm this way round so what I do is I write on the board like this and then I flip the image up afterwards that does of course mean that my t-set is printed out back to front and this document here is actually printed out the opposite array around to how it should be so when I flip the image over everything looks normal again so this is actually the mirror image of me talking to you at the moment so yeah uncertainty now there's not a standard notation but I'm going to say percentage U it's just going to represent my percentage uncertainty in a measured value now this is going to be equal if you have a single reading to the absolute uncertainty divided by the measured value so say for example you had a meter ruler and you were measuring something which was a hundred millimeters long then your absolute uncertainty would be related to the measuring device in this case would be one millimeter the measured value would be a hundred and then you do one divided by a hundred you multiply it by 100 again and that would then maybe in that case give you an uncertainty of one percent now of course we can improve this by taking repeated readings and if you have repeated readings you're absolute uncertainty now is going to be equal to half the range and we divide that by the mean value so that is when you have multiple readings of course we can also look at the percentage uncertainty in plotted data on a graph and there are two things that we can look at we can look at the percentage uncertainty in the gradient and here we can draw our line of best fit and our worst acceptable line of best fit and therefore our percentage uncertainty in the gradient is going to be equal to the gradient of the line the best fit take away the gradient of the line of worst fit divided by the gradient of your liner best fit and what we then do is we take the modulus of that so it's just a positive number and then again we multiply that by a hundred uh just like we should have done up there to get it as a percentage uncertainty and of course you can do exactly the same with the intercept but here rather than having M we have our values of c so these equations here are to do with calculating the percentage uncertainty in your data of course we can also calculate the total uncertainty maybe if we have an equation so imagine we had the equation a equals B times C the percentage uncertainty in B added to the percentage uncertainty in C is going to be equal to our total or combined percentage uncertainty in a so we can say here that the percentage of uncertainty of a is equal to the percentage uncertainty and B plus the percentage uncertainty in C and we can do the same thing for loads of slight variations of this so for example if we had three thieves multiplied together we just add up that individual percentage of certainties if something is squared then we double the percentage uncertainty in that value if it's cubed we multiply that percentage uncertainty by three so these ones over here again it's just a way that we can estimate the uncertainties in our measured data and of course if you go want to do physics or Engineering University they do these in slightly different ways but make sure that you're with the Practical handbook that goes with your course and therefore you can be confident that you can deal with any questions to do with uncertainties so let's start by looking at an equation for electricity which says Q is equal to n e this means if you know the total charge transferred and maybe the charge on each individual electron or whatever kind of charge carrier it might be you can maybe look at then the total number of charge carriers often this is in the form of how many electrons have passed a point in a circuit when maybe a charge of two coulombs has been transferred so yeah Q equals any that's a nice one the next one is to do with a resistors which is set up in parallel now there is of course the equation that says 1 over RT is equal to 1 over R1 plus 1 over R2 and also you can continue that for as many resistors as you might have but if you only have two resistors we can rearrange this to say that RT is equal to R1 R2 divided by R1 plus R2 and this can also then be seen as a product of these two things divided by their sum so if you have just two resistors in parallel you don't need to use that equation instead you can just multiply their values together and divide by the sum of their values now an area that many students do find difficult are potential divider circuits and you might be familiar with this equation looking at V out where it says V out is equal to V in times R2 over R1 plus R2 now that only really made sense if you know in that circuit which one you consider as R1 and which you consider as R2 now the circuit looks like this where we are looking at V out across R2 so that's the circuit that you need to remember in order to apply that equation there is something else that also relates the relationship between their resistances to the potential difference across each of them and this says that basically V1 over V2 is equal to R1 over R2 effectively the ratio of their resistances is going to be the same as the ratio of the potential differences across them why is that well if we think about it we know that the current is equal to V divided by R and in this circuit here because we have one Loop the current is going to be the same everywhere so we could say that V1 over R1 is equal to V2 divided by R2 and therefore all you need to do is rearrange this by bringing that down there and bringing this up here and therefore we get to this equation up here so potential divider circuits if you're not sure just apply this equation I equals V over r or V equals IR to any point and that allows you to work out the current and therefore the potential differences with resistances of each part of that circuit thank you the next equation is still related to electricity but now we might think about individual electrons or other charged particles which are accelerated through a potential difference and as they go through that PD they're going to increase their store of kinetic energy so you could say that EV is equal to a half m v squared and here you've got to be careful the way that's a large V to be the potential difference that something has been accelerated through now e the elementary charge is only going to be true if we have maybe an electron a positron or a proton but indeed there could be any charged particle of charge Q maybe an ion for example that we should maybe get a charge of two plus that could be accelerated now that's good but again a better variation of it is to maybe look at the final velocity of that thing and that's that equal to the square root of 2qb over M okay so that's how quickly something is moving when you know the charge on it the PDX accelerated by and its rest Mass the final equations to do electricity are to do with capacitors now when they are discharging there's going to be this exponential decrease and therefore the charge Q is going to be equal to Q naught times e to the minus t over RC okay RC by the way is the time constant of that capacitor and often we use the letter Tau the Greek letter Tau to represent RC so that's our time constant now of course we can say the same for charge as well as current and potential difference so those equations are for when something is discharging with this exponential decrease now if you charge something up we don't get an exponential increase the graph doesn't look like that instead the graph looks a bit more like this but if you wanted to maybe look at the charge on something which is a capacitor which is being charged up we can use a variation of this and say that Q is equal to Q naught times 1 minus E to the minus t over RC hopefully you can just about see that okay so it's not this exponential increase but it's effectively Q naught minus this graph here to get that shape in there hopefully that makes sense now of course exponential things are really important when it comes to radioactive decay as well and therefore there's a lovely segue into the final set of calculations and equations of the formula and this is to do with log laws now of course if you are doing a-level maths and a lot of this will be stuff that you've done many many times but it's still something that students find tricky especially in year 13 when you're applying this to practical experiments and looking at plotting real data to work out real constants so first of all let's say you had Y is equal to e to the minus X if you were to take logs of both sides we're going to take the natural log because it's to the base C and therefore you could say Ln Y is equal to minus X If instead you have the form that said Y is equal to e to the minus b x and you have to take the natural log of both sides we can say that the natural log of Y is equal to minus 3x and of course if we had maybe something where Y is equal to a times e to the minus b x for again we're to take logs of both sides we can say the natural log of Y is equal to the natural log of a minus b x once I got to do with anything with a level physics well this is often how we see equations and what we can do is maybe if we have some data and on the y-axis we plotted the natural log lung Y and on the x-axis we plotted X we then find that we have a negative gradient on the line and that's because here if we write this in the form of low natural log Y is equal to minus B X Plus natural log of a then effectively on the y-axis we plotted Lin y on the x-axis we've plotted X and that means minus B is equal to our gradient and plus C the y-intercept is equal to the natural log of 8. hopefully that makes sense so what this means is if you have some real data by calculating the gradient you can work out the value of B and by looking at the intercept we can then use that to find our value of a and that's because often we have an equation like this which can be fitted to such as some practical data in an experiment so that's what you need to know about log to the base e and if you have log to the base 10 then you should remember that log a b is the same as log a plus log B if you've got log A over B this is equal to log a minus log B and I think the one which is uh seen quite a lot again especially if this is related to practical experiments is if x is equal to Y to the Z if you take logs of both sides we can say that log X is equal to Z log Y and that means it allows you especially if you have some kind of practical experiment allows you to kind of plot data and maybe find the power that this other thing has actually been rated to now of course uh I think the one thing I did forget actually was some equations to do with wave so let's just quickly finish off with those so when it comes to waves the one I really want to talk about is this equation here that says N1 sine Theta one is equal to N2 sine Theta 2. I think that's really useful I think if you do OCR they just say the N sine Theta is a constant this is a much more useful way of thinking about it now probably about 90 of the time we have things going from air or a vacuum into glass or a liquid and therefore a lot of the time N1 is just equal to one and therefore what we could say was that N2 is equal to sine Theta 1 over sine Theta 2. now this is going to be very familiar to an equation you might have seen have been more familiar with at GCSE where n the refractive index is just equal to sine I divided by sine R so Theta 1 in this case would be the angle of instance Theta 2 would be the angle of refraction reflect refraction and that means n is just going to be the refractive index of that material relative to air or a vacuum so um yeah I think that's it I think these are some of the most important equations and formulas that you should memorize to help you prepare for any exams and the best way to learn these is to make sure you do as many questions as possible and if there's an equation or a formula which you find useful but it isn't on your data sheet add it onto the data suits that means you've always got it to refer to as you do more questions so yeah there we go those were some of the most important equations for a level physics that they don't give to you