Mastering Physical Quantities, Units, and Estimations in A-Level Physics

welcome to a-level physics i am miss ali and you'll be seeing me a lot as we journey through learning physics

together but before we go into all the fun stuff we need to agree on certain language that we use to describe the

world around us physics is the study of things around us that we can see and measure and that's why the very first

chapter is just about physical quantities and units so what are physical quantities we need

to we need to agree why it is okay if we are to study it together physical quantities basically you can say this is

not a formal definition but this is something that can be measured can

be by the way you can take down notes you can follow along as i am writing

write down notes so you can keep track and stay keep your brain active as you're following along but anyway yes we

study the world by measuring it so we create things called physical quantities and you can if you discover it first you

name it after yourself anyway whilst we need to know about physical quantities every quantity

must have two things right here every quantity

as well we say a numerical value oops new me well i can't spell ah

numerical value like a number and what we call a unit and we'll learn

more about what the unique numerical value is but for now just know they gave us a value must have unit

by the way if you're still not sure what physical quantities in here uh here are some examples of what ex what kind of

quantities we are going to study together in physics for example we have energy

we have what else we have power we have density have you heard of some of these sound

familiar we have area we have momentum very important one that we measure all

the time is time exactly time what time is it now quite

late quite early i don't know we have a weight which we measure things like our weight to keep track we are

healthy or not how are we growing but there's also mass there's resistance there's angle there's

so many quantities i'm just going to put dot dot these are how we quantify the world

there are going to be two types that we're learning later miss lee will be showing you the types of quantities but

there are two one is called base quantities and one type is called derived quantities

two types we're gonna focus more on base quantities and base sr units

specifically so let's see what are the this one you got to memorize okay uh there's no

there's no there's no loop around it base called sr units there are i think seven

the first ones very common is the quantity of length how long is something you take a ruler

and you measure it so the si unit is meters the symbol we use for meters is m

other quantities mass we mentioned this one is also a base quantity remember this basa

base everybody agreed that we'll keep this as our base the si unit is going to be

kilogram and we use a symbol kg okay this one hopefully you know uh time

what time is it time we measure the sr unit is in seconds yes there are minutes and hours

but we that's not s i uh symbol for seconds we use s everybody agreed

next one electric current electric current you know electricity is a pretty important field of study now

this one was discovered by a person called ampere i think i i don't know

it's a foreign name i may pronounce it wrongly but the guy discovered it so he can name it after himself so empire a

ampere if you discover something name it after yourself temperature

another s i base unit temperature this is in kelvin

why is it called kelvin such a fancy name for temperature that's because once upon a time there was this dude called

lord kelvin and he did some very good work in temperature so they named they chose his unit to be named after

him so kelvin is a big k that's celsius and fahrenheit and other kinds of temperature but the base unit

is kelvin xr unit okay

there's two more perhaps that we will learn a little bit more in a2 so all these friends here these five

are what we will see a lot in the as the first part of your a levels the last two we'll see more in a2 the second part of

your a levels the very first one is the amount of substance let's say i have carbon

how much carbon if i have oxygen how much oxygen if you take chemistry you will see this

a lot is a good friend but we quantify amount of substance by moles or the mole the symbol for this that we often

write is more just mol so like three mole you can't see my head is blocking three

mole of oxygen what does that mean that's just quantifying the substance then the last

one we have luminous intensity

how bright is something how do we measure that so

last time people's source of light before they had light bulbs they had candles so they would look at the candle

and they say hmm what should we how should we quantify like i use candela okay we use candela

so hence the unit is candela i mean there's probably a nicer history to it but i didn't go and

find it so the symbol we use for candela is cd to quantify brightness

so you need to know these physical quantities and you need to memorize the the name of them this one because the

parties can ask you hey tell me three physical quantities that are base quantities so you need to be able

to say at least a few okay so that's quantities let's go and try exercise our brain a little bit to

think about quantities here's one first question for us to look at here they are asking us

what is the approximate kinetic energy of an olympic athlete when running at maximum speed during 100 meter race

how are we supposed to know this is this a fact that we must memorize well you see physical quantities right

we have to have a sense of estimation guessing game in other words so let's

calm down and think of okay what are we looking for kinetic energy but remember maybe once upon a time we knew that

kinetic energy was found with the equation half mv square remember but we we don't have much

information here other than a hundred meter race how we supposed to know what is m what is v

maybe we can maybe we can do some approximations okay let's let's try to approximate v

velocity if you assume that there's no acceleration assume there will be a distance over time

and this is a hundred meter race we are looking at olympic athletes so maybe if you've never done this before

you can go and try google a bit of stuff and you see facts like for the olympic the world record i think

currently is held by usain bolt 9.63 seconds is about 10 seconds so the fastest a human can run 400 meters race

is 10 seconds so maybe we'll say okay let's say maybe it's 10 seconds somewhere there about

so it's right here 10. so this will give me a speed of roughly 10 meters per second

the fastest human can run now this is the first time you're seeing it write this down the fastest a human can

run maybe if you were athlete in school before you could calculate what was your personal record your best the fastest

you can run get a stopwatch run a distance time yourself uh okay we got v whilst we don't have m we need to

estimate m so an average athlete or average human mass is about

about 80 kg roughly we get a mass of 80. i'm gonna assume this is a average guy maybe a girl could be at

this heavy as well who knows somewhere around 80 70 to 80 can pick any value now we are good to plug in our half mv

square so now i'm going to say the kinetic energy ke will be

half mass make sure this is in si unit

and v square where is my velocity uh 10 meters per second so 80 times 10 squared this is in meter per second

and pressing calculator later you should get about do i get four thousand let me check my

calculator again four thousand joules that's a unit for energy so four

thousand would be the best estimate now you may be suspicious i'm wondering about what about a

what about c what about d try play around with the value see if you use slightly different values would you go

very far from four thousand the number of zeros matter speaking of the zeros

it sometimes is a bit troublesome to write too many zeros like this like four zero zero zero zero zero there's a lot

of zeros so what people come up with is another way of writing up the zeros we come up with this thing called

prefixes to make our lives a little bit easier so instead of having to write one zero zero

zero zero zero zero zero zero oh my goodness too many zeros i can

combine all the zero into a prefix i wonder which one it is let's look through if you don't remember them the

first prefix is terra starts with the t please make sure you know your spelling okay don't spell

wrong in the homework or is that and the multiplying factor is 1 times 10 to the 12.

giga is g have you ever heard of gigabytes how much storage does your phone have this one is times 10 to the

nine next one mega is a big m this is 10 to the 6

kilo kilograms kilometers 10 to the 3. deci oh this way it starts to get a little bit foreign let's see we use d

not so common but this is 10 to that negative 1. so you're getting smaller now

we scroll down some more centi is centimeter cm we use a c and this is times 10 to the negative two

milli millimeters for length as well milligrams sometimes this is 10 to the negative three

micro is a mu this that curly curly thing is a mu shape this is 10 to the negative six

nano n for ten to the negative nine and the last one pico

i think we've gone all the way to twelve okay so this is ten to the negative twelve

whoo that is a lot of okay how do we use this thing remember it's not i say writing a lot of zeros is a bit

troublesome how many zeros are here let's count one two three four five six seven eight

nine maybe i could write this as

0.1 times 10 to the 9. and this is a method of arranging a prefix because i say okay i start from

here my decimal point is supposed to be on the right but i go 1 2 3 4 five six

seven eight there's no eight in my list here so i'm gonna go to the next one nine so i go

nine and i put my decimal point now here so that's how you can use this to

simplify your life a little bit make sure you memorize the prefix name okay at least not the name but you

recognize the symbol and of course the multiplying factor because you will need to do conversions

throughout your entire a levels and if we we need to be able to communicate the common way of writing out things

so one way of writing a physical quantity let's write it out down here is to use the symbol so for example

let's say i like to measure the length of my phone so you can take out a phone try and

measure what's the length you know what a phone is right phone smartphone see how long it is and maybe

i say okay the length of the phone let's use the symbol l big l okay and i measure to be 12.3

centimeters in my ruler this centimeters is going to be my unit

but not just a unit it has a c stuck to it this is the prefix so the c and m and of course your

magnitude or your value is a 12.3 over here magnitude

this part okay what's this l here this is what we call a symbol

just a symbol that i choose to represent length another way you may write down the physical quantity is to use the

multiplying factor like one of these factors over here so maybe instead of writing centimeter i could change my

mind and say well i think i want to write 12.3

times 10 to the negative 2 meters so i just converted this c into it is its multiplying factor and i

write it out that's also fine so there's few ways you can write out these uh things like this and this this prefixes

helpful in helping you to estimate values we'll look at some estimations later but first let's practice

converting i'll tell you a shortcut that you can use in your calculator so this question here is asking us

which time interval is the shortest we have a problem here we know the prefix i mean we just look

at it melee nano okay melee is 10 to the negative three nano is 10 to the negative nine and for nano pico is

negative 12 mu is 10 negative six that one we know but the difference is

if you look at the value the magnitude it's not very consistent two decimal place no

decimal place many extra zeros and one decimal place how we need a standard form so this is why we

convert things into standard form for example i want to convert this into 5 times 10

to the something maybe i should do this first the first

thing is to recognize that i can move this decimal place by two spots one two move

it over that'll give me a five but i need to include the negative two then i include the melee which is times

10 negative 3. then next step i combine the negative 2 and negative 3 and if they are

multiplied together i am adding together their powers so this will give me a value of 5 times 10

negative 5 very good we can do this step for all

the other abcd and compare but important thing is now it's a standard form we start with a 5.

so grab your calculator we're going to look at a shortcut right here your calculator may look a little bit

different uh but as long as it's a casio model one of the five casio five seven zero models maybe it's a black color one

the more newer one but it's okay uh the newer one looks kind of like this okay i see that right so but they generally

have the same buttons just different color so what you want to do is let's do convert into standard form

50 we're going to key that in right now so 50 then for prefix times 10 to the nine i

recommend that you use the built-in prefix button on the calculator itself and you can see that it's going to be

this button right on top of my head here times 10 to the x so we're going to hit times 10 to the

negative 9. hear the equal sign if you get a fraction stay come hit the s d button

somewhere around here my mouse is hovering let's hit that and it will convert it into a standard form nice for

you hey we already have 5 times 10 to the negative 10 the negative 8 so we're gonna write here

5 times 10 negative 8. done blast calculator and we have the rest so why don't we go

through it let's go to the next one five zero zero zero zero zero times ten

negative twelve hit equal i get a fraction i hit sd and i get my standard form right up there oh

beautiful let's try the next one so this will be converted to 5 times 10 negative 7.

last one clear 0.5 times 10 negative 6 equals to

sd 5 times 10 negative 7 done so if i compare all of these the smallest

shortest time shortest value will be times 10 negative 8 more negative more decibels so that's

going to be b over here one other thing i want to give you a heads up though is that this

uh calculator will give you in standard form the first line keyed in but you can

change the prefix how do you do that look carefully at your calculator

you should see a button that says eng i call it the end button right here

what does the end button do try hit it on your calculator you will notice that this is 5 times 10

negative 7 if i hit n it goes to 5 times negative 9 becomes more negative

but it goes to the nearest multiple of 3 so this is converted nano hit it again it goes to pico

here again it goes to femto i think it's femto hit it again oh negative 15 is the maximum we can go

what if you want to go backwards you want to convert this to a unit of kilo seconds okay sure kilo seconds

what is this answer d in kilo seconds you hit shift and the n button which is the

engineering button so shift n it goes to negative 12 shift n less negative

shift less negative all right less negative shifting and shift a

oh man oops i hit too many buttons don't think i can go to yeah i can't go any bigger maybe never mind so if i want

to convert this to the full no prefix form this will be 0.00005 too many zeros okay so play around with

this until you're comfortable with eng and shift and be very helpful for you in your journey in a level

or i guess the other way is to make sure you know your indices and prefixes laws to know how to

manually calculate it without your calculator okay

that's all for this question so these these quantities often help us to

guess and make estimates which is what this whole first part is about this table shows some measurable

quantities which row gives the correct order of magnitude of the measurable quantities in the correct unit

wow lots of things to check let's check first one mass of a coin i've never measured the coin before have

you if you don't know maybe try to compare it to something that you do know this magnitude 10 to the negative 4.

how many okay let's assume that this is 1 times 10 to the negative 4. so 1 times 10 negative 4 used to

calculate the skills converted to grams will be about equivalent of 0.1 grams that's

really like i don't know maybe it's correct maybe it's not i'm not very convinced so i put a question mark here

thickness of a sheet of paper this is in 1 times 10 negative 2 so this is actually 1 cm kind of equivalent

is a paper that thick 1 cm okay we can use ruler and check one cm is about this much

no no this is definitely out paper is not so thick wrong

weight of an apple 10 to the zero 10 to the zero is just one so one newton

huh what is what is it in grams for newtons you gotta remember that weight is mass times gravity so to find the

mass i think i will need to take that one newton divided by 9.81 to find that so 1 divided by 9.81 i'm

going to convert that to grams with my calculator and it's about 100 grams

pretty accurate i mean this guy newton had an apple hit his head so i think the heat that's where you got the

inspiration from partially maybe okay this one is likely i like that temperature of a person's body

10 kelvin 10 kelvin ah that's really really really cold

really really really cold kelvin is a skill that is very very different from celsius so 10

kelvin if you convert to celsius it's about negative two

six three celsius that's way because zero kelvin is absolute decoders beyond freezing

so hmm something's not quite right there because for celsius you need a plus 273 to get a kelvin so no that's way too

cold not possible that leaves us with a and c i would bet my sense on c

because c is why i'm more certain of whereas the coin seems a little too light for a coin

uh and yeah you might be wondering i miss how old am i supposed to know all of this

well one way is to have a lot of hands-on experience on the world around you if i ask you what's a

mess of an orange have you been to the supermarket have you bought orange before you see i have orange here you go

and hold the orange in your hand and bounce it measure it put on the scale follow your

parents to the mark just you know have a hands-on feel of how heavy things are and then you compare it to your phone is

the orange heavy or is my phone heavier orange is heavier so oranges and a lot of fruits apples around this hand size

is about 200 300 grams so i guess you say for apples oranges while the fruits are that size they're

all about oh where's my pet oh about maybe 100 if it's a really tiny orange

200 grams if it's a really really big fruit like your whole hand can fill this might be

300 grams somewhere there definitely not 100 kg see something's wrong with

the prefix the prefix will give you a hint whether it's correct or not this is just grams kkg is like whoa

let's have it in a human not possible no no no adult human

depending on whether you're a guy or a girl you might have a very different range so somewhere between anywhere from

fifth kilo let's say median 6080 somewhere there also depends on which country you are

from uh kg is what houses if you see something that says 60 to 80

micrograms for human nah the prefix is wrong so the prefix should

give you a sense of how heavy things are height of a room go and measure the height of your room i dare you take a

wrong ruler climb up to the ceiling measure it's about it should be about two to three meters i shouldn't be any

taller or any shorter again the prefix meter no millimeter no kilometer that's way too long or too

short diameter of a pencil grab a pencil go and try and measure that it's roughly

about 0.5 to 1.0 cm yeah go ahead and measure your pencil

lamp post go outside the road and try to measure the lamp post i guess the lamp post is about how do we

draw this man lamp post human

maybe two human or maybe three human okay one human i assume is one meter so three humans may be about roughly three

meters depends on your country depends on your location but it should be in

meters that's an important part not kilometers not millimeters

we stay in meters okay so that's all for the first part make

sure you know your units and how to estimate quantities and use your prefixes to help you with that so

that's all for this first video we'll see you in the next one we will look at uncertainties units

and scalars and vectors bye bye