A-Level Physics: Quantities and Units PDF

A-Level - Physics Quantities and Units https://vizi.education What are we trying to learn? Physical quantities SI units Symbols SI base units Derived units Expressing units as base units Prefixes Key skills: Learning units and symbols for physical quantitie...

A-Level - Physics Quantities and Units https://vizi.education What are we trying to learn? Physical quantities SI units Symbols SI base units Derived units Expressing units as base units Prefixes Key skills: Learning units and symbols for physical quantities Understanding how to express units as base units Understanding, using and converting prefixes Physical quantities In day to day language, we use quantities and units without thinking as a way to convey information about the World around us. In order to speak scientifically, we have to be accurate and specific about the physical quantities and units that we use to describe the World. For example, you might look at a field of cows and think ‘Wow, that’s a big field and a lot of cows!’ In order to be more accurate, rather than ‘a lot’ of cows we want to know….how many? If someone asked us ‘How many cows?’ they are asking for a physical quantity - a property that can be measured. In this case, the number of cows is just a number. If we replied with ‘7’, that would make sense and the person would know exactly how many cows there are. It tells us nothing about the size, breed or affability of the cows….but it answers the question. Examples of quantities: Length Mass Time Speed Pressure Force Energy Magnetic flux Units Now that we have established the number of cows, we move on to the size of the field. ‘How big was the field?’ this friend asks, overly invested in the details of our story. ‘12’ you reply, happy that we have established that numbers can express physical quantities. This time however your friend looks at you blankly (assuming they are actually interested in the answer to their question and not just politely making conversation). The problem here is that a number by itself is not a suitable measure for this physical quantity. Admittedly, ‘how big’ is a vague expression scientifically and not one we would generally use in Physics but any possible interpretation; length, area, volume, width…..would require UNITS as well as the number. If we don’t quote units clearly, misunderstandings can happen. You may mean the field is 12 metres long, your friend might think you mean 12 feet (about 3.7m), or 12cm. Leading them to assume that the cows are either being horribly mistreated, or are very small. This cow is small Symbols Vs. units Before we continue, we need to make an important distinction between SYMBOLS and UNITS. In Physics, we abbreviate a lot and both physical quantities and units often end up being expressed as individual letters rather than full words. It might be perfectly clear to you what it means for ‘The length of a field to be twelve metres’ but reading ‘l=12m’ might seem somewhat less obvious. SYMBOLS are the letters we use to represent the name of a quantity. This seems partly necessary due to laziness (no-one wants to be constantly writing magnetic flux density) and partly to make reading equations easier, At KS3 and GCSE, we often get away with learning full word equations and can recite that speed equals distance over time without worrying about the letters, but at A level it matters. It matters a lot. The added complication with this is that wikipedia lists 100 physical SI quantities AND includes a warning that the list is incomplete. The English alphabet has 26 letters. Even if we double them all up and make uppercase and lowercase letters distinct...this still leaves us a lot of abbreviations short. The second issue is that even if we did have a long enough alphabet (there are 49 slavic cyrillic letters which gets you closer…), 12 of the physical quantities begin with E and none with G, so just simple abbreviating doesn’t work. Here it gets complicated for the humble Physics student. What could have been a simple case of taking the first letter of a known physical quantity and shoving it into an equation, instead becomes a complex web of inconsistency, memorising random letters and paddling around in the shallows of the Greek alphabet. Depending on your A-level course, mood of the examiners, philosophical views of the textbook author, blood sugar level of your teacher and wind direction on a particular day, some symbols can vary massively. Distance is d, except for sometimes when we meant displacement but said distance and so now it’s s. Speed was s, but velocity is v and so s=d/t and v=s/t look oddly similar but mean completely different things. Energy is E except for when it’s work in which case it’s W and some people use KE or EK for kinetic energy and oh yes E is also Young’s modulus. Power, pressure and momentum are all P (varying upper and lower cases) and density looks like a p but that’s actually a rho and I can hear your brain pouring out your ears so you get the picture. Simple as symbols may seem at first glance, pay attention to them, take care when you use them, test yourself on them and ask someone if you are unsure,They underpin a lot of the equations, formulae and maths and making a mistake with them can be critical. Some examples of quantities and their symbols Energy E Speed s Force F Velocity v Distance d Volume V Displacement s Mass m UNITS are simultaneously more and less complicated than symbols. They are seemingly arbitrary in their words and notation, irritating to use, frequently littered with pesky prefixes and a constant source of nagging red pen annotations from teachers reminding you to use them at the end of exhausting calculations. However, since we expect this going in, we are less adverse to just sitting and learning them which reduces overall psychological stress. Units can be split into 2 main categories that define how we learn them: Base units and derived units. Keep reading….it gets more fun. Quantity Symbol Unit Quantity Symbol Unit Energy E J Speed s ms-1 Force F N Velocity v ms-1 DIstance d m Volume V m3 Displacement s m Mass m kg Time t s Acceleration a ms-2 Power P W Current I A Pressure P Pa Potential V V difference Momentum p kgms-1 Charge Q C Capacitance C F Resistance R Ω SI Base units The system selects 7 ‘base’ units that all other units can be derived from and we need to be able to list these. As mentioned previously, both the physical quantity AND the unit are going to be important here so we need to learn and remember both of When you’re learning these for each. base units, remember the difference we 1. Length, l - Metre (m) covered between 2. Mass, m - Kilogram (kg) QUANTITIES and 3. Time, t - Second (s) UNITS. 4. Temperature, T - Kelvin (K) If a question asks you 5. Current, I - Amps (A) to identify a base unit, 6. Luminous intensity, Iv - Candela (cd) time cannot be the 7. Amount of substance, n - Mole (mol) correct answer, neither can current. It’s a sneaky trick but That’s the list we’re aiming to learn. We’ll they might just use it! break it down and look at each in a bit more depth but remind yourself throughout that the information coming up is to provide context and understanding, not to be memorised. The rainbow wheel of base units Length - The metre (m) As a concept, this includes any substitute dimension measured as a length, for example a width, distance, height, breadth etc. In 1983, a metre was officially defined as the length of the path travelled by light in a vacuum during a time interval of 1/299792458 of a second. - Wikipedia. This definition seems confusingly arbitrary but the official measure of the metre has been redefined many times with increasing accuracy as Science has developed. Go ahead and read about the original history of the metre! There is also a brilliant three part documentary by Marcus De Sautoy called ‘Precision, a measure of all things’ that explores the history of the metre and the second. If you’re paying close attention you might have also noticed the part of the definition that referred to the time interval of a fraction of...a second! A second is another SI base unit…. So we’re assuming in our measurement of the metre that we calculated the second correctly? There are people in life who will get really into the history and research surrounding units of measurements. I’m one of those people. If you’re not, now would be an ok time to skip ahead, or keep reading and you might fall in love with the whole thing. Mass - The kilogram (kg) We’ll circle back to the second later. The kilogram used to stand alone, unreliant on the definition of any other base unit. It was originally defined as the mass of a litre of water (I’ll leave you to guess the difficulties with this one, but hey it was 1795! Also it was known as a grave, not a kilogram at the time.) By 1889 there was a physical cylindrical ‘International prototype of the kilogram’ that existed. Following a redefinition in 2019, it is now defined based on the Planck Constant, not a physical object. Interestingly it’s also the only base unit with a prefix! The history has far more fun facts and twists and turns but I’ll leave you to read that on your own. I’ll leave you with the fact that the definition of the kilogram now depends on the measurements of the metre and the second. Time - The second (s) About time! The second has a lot of weight on its young shoulders. The second is defined by the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom. Historically it was based on a division of the Earth’s rotation cycle and occasionally a leap second has to be added to clocks to keep atomic time in line with the Earth’s gradually slowing rotation. Some scientists argue in favour of abolishing leap seconds...stay tuned for 2023 to find out more! Although we use a measure of 60 seconds per minutes, 60 minutes per hour then 24 hours per day when dealing with real world time, we still break seconds down decimally in science and talk about milliseconds, nanoseconds etc with standard prefixes. Temperature - Kelvin (K) The Kelvin scale is an absolute thermodynamic temperature scale in which 0K represents absolute zero. We don’t use the language of degrees when referring to a Kelvin but it shares its scale of magnitude with degrees celsius which at least makes conversion fairly straightforward, The Kelvin used to be defined by the triple point of water but now relies on the Boltzmann constant. Thus it relies on the kilogram, metre and yes, the old reliable second. Current - Amp (A) The amp or ampere is a measure of electrical current. It is defined in terms of the elementary charge constant (the charge on an electron, e) and the second. Amount of a substance - Mole (mol) A mole is the measurement of an amount of a substance in the SI. A mole is defined as 6.02214076×1023 of whatever the substance is; atoms, particles, electrons etc. (In the same way that a dozen cows is 12 cows, a mole of cows is 6.02214076×1023 cows. The mole used to be defined as the number of atoms in 12 grams of the isotope carbon-12. Luminous intensity - Candela (cd) Luminous intensity is the luminous power per unit solid angle emitted by a point light source in a particular direction. A common wax candle emits light with a luminous intensity of roughly one candela. Derived units - Special names Derived units are SI units for physical quantities beyond the 7 base quantities. These quantities have units that are either given special names such as Joules or Hertz or expressed as products of other derived units or base units (metres per second, joules per second etc). All derived units can be represented by products of base units. There are 22 physical quantities with derived SI units that are given special names. Unit names that are named after a person (generally a Scientist) are given uppercase letters, such as N for Newton. Those that are just from words are expressed as lowercase letters (m for metre).  Special names - full list! Quantity Symbol Unit name Unit symbol Frequency f Hertz Hz Force, weight F, W Newton N Pressure, stress P, σ Pascal Pa Energy, work E, W Joule J Power P Watt W Charge Q Coulomb C Voltage, potential difference, V Volt V emf Resistance R Ohm Ω Temperature relative to T Degree Celsius °C 273.15K Capacitance C Farad F Magnetic flux density B Tesla T Magnetic flux ΦB Weber Wb Radioactivity A Becquerel Bq Equivalent dose of radiation H Sievert Sv Absorbed dose of radiation D Gray Gy Electrical inductance L Henry H Electrical conductance G Siemens S Luminous flux Φv lumen lm Illuminance Ev lux lx Catalytic activity kcat katal kat Angle θ radian rad Solid angle Ω steradian sr Derived units - Compound derived Compound derived units are expressed as the product of other units. They frequently contain superscripted numbers and often at A level follow the convention of using a negative sign as a subscript to represent ^-1 instead of /. e.g. at A level, m/s (metres per second) is commonly written as ms-1. Expressing units in base units Primarily our focus on units in A-level Physics will be learning and using them. Being able to instantly recognise quantities, symbols and units and use them in our own calculations. However there is another skill we need that encourages us to be able to compare dimensions of different quantities. This is the ability to express derived units as their equivalent base units. If an excellent memory is one of your strengths, you may wish to learn the base unit derivations for common derived units. Otherwise, there are methods we can use to figure out the base units of any derived unit combination. Either method is acceptable and your choice will depend largely on how your brain works and how you go about solving problems. Some people will find themselves doing a mixture of the two methods which is also fine, just be really careful to keep track of quantities and units, getting the 2 confused, particularly if you start to work in symbols, can lead you down the garden path and straight into the river. The most important thing in either method is to show your working, partly so examiners feel confident in giving you the marks, but mostly so if it goes belly up towards the end you can trace it back to where you went wrong. Both methods will probably require the use of a formula sheet, at least until you become overly familiar with the formulae. - Method 1 The first possible method involves converting into physical quantities, looking out for base quantities then converting back into units at the end. Let’s take the Joule as an example. Question 24 part b on your A level paper could be: 24. b) Express the Joule in base units Ok great so: Method 1 Step 1 - what physical quantity is the joule? - Energy Step 2 - What formulae do I know with energy in? Energy = mass x g x height kinetic energy = ½ x mass x velocity2 Work = force x distance Now from years of experience working with these formulae and converting units, I would instinctively pick the middle one to work with as I can see the simplicity in the quantities it contains. The method works with any of them though so we’ll try with each Step 3 - Identify base quantities and repeat step 2 for any quantities that are not base So now we need to break acceleration down into base quantities…. This continuing process is shown in the images below and repeated for the other 2 formulae.  - Method 2 The second method involves converting straight into units from the initial formula and then working with units until they are all base. This method is highly effective if your initial formula breaks into quantities with compound derived units or you have a solid understanding of derived units. Same question, method 2! Step 1 - Identify the physical quantity in question - Energy Step 2 - Which formulae do I know with Energy in? Energy = mass x g x height kinetic energy = ½ x mass x velocity2 Work = force x distance Now from years of experience working with these formulae and converting units, I would instinctively pick the top one to work with as I can see the simplicity in the units it contains. The method works with any of them though so we’ll try with each Step 3 - Identify base units and repeat step 2 for any units that are not base This method can get us an answer quicker for some situations than the first method as any quantity with compound derived base units doesn’t need to be broken down any further and we can jump straight to simplifying! The best way to get better at this is to practice. A lot. Go through every quantity on your formula sheet and change them all to base units. Go through all 22 specially named derived units and express them in base quantities. (The radian and steradian are particularly straight forward).  Prefixes Prefixes are used with units to indicate that a multiple or a fraction of the unit is being used as a measure. This can make dealing with numbers easier on different scales rather than always just relying on standard form and powers of ten. There are in total 20 standardised metric prefixes in use for the SI, not all of which are commonly used in Physics A -level. Descending https://en.wikipedia.org/wiki/Metric_prefix Ascending Space is massively big and you might imagine that this would call for frequent use of the larger prefixes. However astronomers have their own set of units for dealing with the size and scale of the Universe such as Light years, parsecs and the astronomical unit so the concept of Mm or Gm is rarely seen. BEWARE: read the question carefully and always think about context. As discussed before we lack distinct letters and symbols to work with and 4ms is very different to 4ms-1. What have we hopefully learnt? That units can be fun! Or at least marginally entertaining The difference between physical quantities and units. Some examples of Physics-specific quantities and units. The 7 SI base units. How to express any derived units in terms of equivalent base units. Examples of commonly used prefixes in Physics and what they mean Time for a cup of tea and a chocolate biscuit….