Transcripts
1. Algebra for Physics - Introduction and Class Content: Ui NO2, last years of high
school and you took physics. But it is, so it doesn't
have to be that way. Physics is actually quite easy. Once you realize this, you will also realize how
the subject is fascinating. Many of my students
get stuck on math. They have trouble
applying what they learned in math
class to physics. This is why I
created this course, a bridge, a bridge
between math and physics. In this course, I will review
with you all the math you need to feel comfortable
in your study of physics at high school level, there are three sections. Algebra, where you
will learn how to rearrange physics equations
effectively and reliably. Vectors, so important
in physics, of which the manipulation
you will learn to master. Finally, we will dive into trigonometry
and its application to vectors as a bonus
dispersed in the course. There are also tons of
little practical tips to make your life as a
physics student easier. I'm going to show you how to
rearrange equations easily. Two episodes, Earley,
the first one is longest video of this
course, about 25 minutes. And it is full of goodies. It will remind you what a
mathematical term is and why this notion is important in regards to rearranging
equations. The video will also address some useful notions
on fractions. It will reflect to the
meaning of the equal sign, and then it dives in. You will learn how to
view range equation super easily using reliable
tricks and shortcuts. The video concludes
with an exercise isolating a variable in an
equation involving energy. The second video, we'll train your new skills in new entering
a half dozen equations. These equations are taken from electric and
magnetic field, motion, oscillations
and electric circuits. Note that you do not
need to be familiar with these subjects to
manage these exercises. Follow this course
with a pen, paper, and a calculator, and be
ready to pause the videos. Lessons are punctuated with solved examples and questions
for you to train all. This course is end of
students preparing for the International
Baccalaureate Level, AP Physics, or any type of high-school final
examine physics. I hope you will enjoy
studying physics with me as much as I enjoyed
producing these videos. In the meantime, fasten your seat belts and
enjoy the ride.
2. Algebra for Physics - Lesson: algebra is a really important tool in physics. Imagine yourself at an exercise or even at an exam. So how do you solve the exercise? First you analyze a text, you extract the known data, and you also try to find out to identify the variable you're looking for. Then, depending on the exercise in the situation, well, you were defined an equation to apply. And although to find out what you looking for right on this equation, which will be, um, linking the known data to the unknown variable, you'll have to rearrange it in order to have the known variable I subject now in this rearranging Well, you'll need a driver. That's where everybody's important. Take an example. Suppose you're doing an exercise and you identify the equation that you want to use. It's equation would be v squared equals U squared plus two A s. You know, V you know, u you know s on. You are looking for a so you re ranges equation and then you divide both sides by two s to isolate a Now this quite easily. I want you to be able to do the same thing in physics as you blast should be just a tool without bringing any stress. Just imagine. Imagine you have you at an exam and you just solved a very complicated physics exercise. I know really happy you understood everything and slowly by these name. You found out which equation you needed to use. And at this moment, you need to rearrange and you mess it up because of the underground and you don't get the mark. Just imagine the frustration and pretty show you where the experienced it. I experienced it in a student. This video is there to get you a job. Assorted. It's not a full blown math lesson. No, no. The city was a selection, a selection of the tools and nothing but you need in physics so that when you arrive to the step in a problem where you have to rearrange stuff, everything goes smooth. So what I'm doing this video is provide you some tips. Of course, that also swoons to follow so that algebra becomes second nature for you. So what is rearranging equation? Rearranging equation consists and isolating one of the valuables. Often the equations are given in your that The booklet was the subject, but it's not the subject to ingested it. It's one of the variables. Let me give you an example. The universal law of gravitation is written that way. So you have the force here you have the mass of one of the day, the massive, the second object and the distance between them. This is a force between two objects and gravitation. Suppose that I want to find out m I know F began D and jeans a constant. I'm looking for em. So I need to rearrange this in order to put em a subject so I could multiply by d, squared on the science and then divide by G begin on both sides to and then get an usually I like to put in, uh, in front. Why? Because I m is a subject on in English. When I start a sentence, I start with the subject. So I like to say and equals something I like to read it like in English and in this rearranging quite fast, right. I want you to be able at the end of this course to do this kind of rearranging at this same speed we even faster that you're younger than me. so you should be able to do it faster. One notion that I believe is not discussed enough in algebra courses is the idea off turn. What is a term? A term can be a number for lets me right the title term. A term it can be a number like full 32 3000. Whatever. It can be also valuable, like X Okay, but it can also be a product of numbers of their rebels. So two X is a term four. X squared is a term full by x by x seven. Picked up is a term X T is a term. A term is actually valuables numbers which are multiplied by one each other. It's like they stick to each other, right. They are multiplied to each other. They stick to each other. The term is just a group. Seems like a block and look off perimeters which are stuck together So these power meters can be numbers can be variables and they can stick due to limited. Ty Sign can also be a divide site. So this is a trip. For example, X Plus two is not a term exeter to visitor, but express to like this is not true. Terms are separated by plus and minus signs. Another example, A X squared plus seven. How many terms do I have here? I have to. This is a term this is now when you have an equation like a equals B C Class D before we ranging it is essential. You look at the number of terms. Yeah. We had one term on the left and we here we have two turns on the light. This tells you what you can and cannot do when you re arrange, and we will look at this later. The point is, remember what determines its a block or valuables or numbers which are linked by a multiplication or division reflections. I'm not going to give you definitions. They're full of them on the web. What I'm going to do is give you a few tips. If you examples of where I saw some of my students my best to stumble upon really basic stuff. For example, 2/3. This is two divided by three white, 2/3. If you take a calculator, you find you 30.66667 something like this. But listen to it in English 2/3. This means it is two times 1/3 to third with an S because it's proof 2/3 can be written like this, willing that it will be a slight wait when you have 1/2 MV squared, which is kinetic energy. Well, we in this situation when we have 1/2 off the turn and B squared 1/2 of an apple that we can also write it and b squared over two like a fraction. Yeah, it's essential that you be able to mentally go from one to the other without even realizing that you're doing it. It needs to be second nature. Also, for sun of urine might be. What is he saying? Off course? It's obvious, but for some others, it's not that obvious. And you need to make it obvious for yourself. If you don't when you re arranging questions, you might miss some roots. That's an puff to rearranging the equation you might not see, so this equivalents needs to be within you, right? Something else about fraction. I would like to discuss. Think this faction ever be What? What if you end up in an exercise with something like this one over a B. How do simplify this? You see, we have a fraction the fraction able B, which is a denominator off a big a fraction. How do you make this more simple to read? Well, you can take this fraction you will be and flip it. This is equal to be of a when you place from the denominators of the numerator fraction you flip it an example with numbers. What is one of over 1/2? Well, you take the faction in the denominator and you flip it to over one, which is to another example 1/4 3rd What is the answer free? Fourth, it looks very simple like it is. So just remember it. So now it's time to bite into the meat a little. This equation a equals B. C. In my exercise I and see a node B is unknown. So I need to rearrange this equation to be as subject. Let's talk about the equal sign first, what is equal? What does it mean? It means here that a is identical to B. C. If I transform a and that applies the same transformation to B. C, the product of the transformation of a would be equal to the product transformation on BC It's not. Transformation is, for example, adding D. So a plus the it would be equal to B C plus de I can do this with minus one. What or multiply, we'll divide. I can apply also either transformations. For example, it can look a because log BC. I can even different shape the A of a DT, of course. D o B c of a DT. The equal sign is a very powerful sign. It's a very powerful symbol, and it allows us to rearrange our equations. So we want to isolate. Be so what I'm going to do is divide by sea on both sides, and you see that I can be like this, like be misapplied by sea of a C, which is one. So it kind of cancels, and now I put be a subject again. Beak was a F. C. So let's analyze what I just did A equals B. C on. I was able to rearrange it to be equals a C or more precisely, to illustrate one or two say a over C equals B. So I took see here and placed it here. When I write a equals B. C, I'm actually writing a of one equals B C of one and I moved See as denominator. So if I generalize this, you can imagine term one equals term to and I can divide by one. His case is change coming. I can imagine kind off double arrows here telling me I can move stuff around. I can put 10 to here for one term one here one The one that I have here concluded there. Let's explore this. We had a equals B c. So Seacon go. They're giving me a C equals B. But if I want, I can also put a here giving me one of the C equals B of A and I can put the sea there, Put it back So one equals B C o A. And then come back by putting a here giving me a equals b c the complete around like this without each time having to think. Okay, I'm going to plan both sides and then I cancel one. I can just use this idea. Be careful. There's a catch. You can't do it all the time. It depends on the number of terms you have on each side. For example, if I have a equals B C plus the and I want to isolate be so I think don't just like this a The C equals b plus D by putting to sea there. No, that doesn't work because I have to take him to County. I have two terms here. I'm only allowed to do this. It operation with the class when I have one term on the side. So how can I manage to change this into 12? Sadly, wiped it again. I can put brackets and say this is just 12 and I would say this is equal to X say so I could write a equals X, and in that case, I can divide by sea on both sides. Right. So let's do that. I'm going to divide, Am I see and the second to be C plus d I c. Then I can develop this bc of a C plus d oversee and still here Ever see giving me a of a C equals b class d of the sea because I can't solve sees here that we're not done yet we need to isolate Be this term the other side. And this arrives to the second type of arrangement can do. I would come back to this. Let's consider a equals B plus C I want to isolate. Be so what I can do is subtract C on both sides and you see the two seas cancel each other and I have been isolated. My B A minus C equals B. So what did we do here? If you compare these two, we actually move, See here and turned aside. Well, maybe we can use this as a short cut Instead of doing the all this operation. We can just say when I move a term from one side to the other, I just change the same. So giving me a minus e people school. Let's go back to our previous equation. We had something like we were at this point like a C I ever see in Crosby plus the oversea . This is a term I can just move it there and change the sign. Giving me a of a C minus d c equals B. That's it. Isolated. My being the denominator is science. I can also like that way. B equals a my honesty defined by sea. So we started from this equation a equals B C plus D. That's quite a complicated way to isolate be because we started by arranging zig medication . And then we arranged using edition. Sometimes it's better to do it the other way around. Let's take example again, A equals hey C plus D. It might be easier to move this term. This side a minus d equals B C brackets here to make it one term, I guess. One turn in one term and I can take my C and just pathetic as eliminator. Giving me a minus t of C equals B. So there's always multiple ways to rearranging equation. I've but different routes bring to the same result. Only was practice and with experience you will know intuitively which way which passed to take to of your injury question in a smooth way. Let's work on a practical example. Imagine your attendings are on. You are doing the physics of exercise on you end up with this equation, which will solve the problem right so you have 1/2 and the square kinetic energy plus N G. H gravitational potential Energy equals total energy. Said would be hundreds something like this on Imagine you're looking for V. So the unknown is the So you will need to rearrange this to find V. So let's do that. I can take this term and place there by changing the science. I got 1/2 and the squared because 100 minus and gauge. Then I will try to late V. But I have two terms there, so I would put back it to make it one term. Like sticking these two part as a group, they cannot separate from each other now of 1/2 off em. That's like an over to So can we write this and of the two giving me the squared equals and putting em over to bear 100 minus MGH If I did by an over to so have a fraction of the denominator. So if I want to put it on the numerator need to flip it. That gives me V squared. Of course, two of em off 100 minus and h And now I could just develop right. And at the same time, I think Kabila Square So giving me to hundreds of em but minus to M g h of m the end goes away so it can be righted like just to GH And I take the square root to illustrate what I said before about finding different path to the same result when we ranging Let's try to find a different part here. I notice I've got em in both terms So we expect allies him Let's do that. The end fact of the square divide like to last GH equals 100 about one term now because I listened to my kids off active ized. I've got one term and one term so the end can go under the 100 giving me these quite of the two placidity age equals 100 of. Now I can put the GH other side b squared of the two equals 100 the M minus th and then I can put the two on this side if I consider this bracket all right. I consider this like one big term so I can put the two upwards so these squared equals two by 100 and mine's GH. And then I developed this, giving me to hundreds of em minus two GH and I take the square root. Same result longer. I prefer the 1st 1 is here. There was less steps, but hey, sometimes when you're doing the exercise, you do not see the most efficient one. I only experience will able you to see the most efficient way to your engine equation. So it's a good idea to train a lot. You will save a lot of time at the exam if you practice rearranging beforehand. Now you are armed with a mathematical Swiss knife. I suggest you go in the next give you in this video. I will propose some equations on the board on ask you to rearrange them in a certain way and then I will correct them. Understand? Do it seriously. It's a great time investment. We won't regret it because of the exam. Well, it's gonna be smooth fight, but
3. Algebra for Physics - Training Exercises: in this video, we will train. You think the tools we learned about in the previous one? You know how to rearrange equations. So what I'll do, I'll put an equation on the board, ask you to rearrange it, and then we collected together we have three or four lightness and this video, it's a good investment to do it seriously. You'll thank me. And exam. Okay, let's start with this one. F equals K big coup by little coup Divide by D squared. So in the exercise, I was doing right. I know FN okay. And a big clearly to coo and I must to find So after we arrange for could you be arranged this for the for me? So this one is pretty straightforward because I had one term it side off the equal sign. So it's gonna be quite simple. I just going to use this transformation. If he's going to go there, he's going to go there. I mean, d squared equals Okay, 22 f. I just need to take this quote now. So deep was quote or K 22 Suppose you are working on the motion problem and you realize after analyzing the text that the equation you need is s equals beauty. Plus 1/2 80 squared then by looking at data and realize also that s equals zero. That's you know you on t but you're searching for a So could you relay this equation to isolate a Okay, it's about two terms here. Most complaints. So I'm going to put one of the term the other side changing its site. Having museum Will my house, you tea or minus UT equals 1/2 a T squid. I look to you have both sides Second divide by tm, but it's not giving me nine. Issue equals 1/2 a t. I still have one turn on each side so I can do the cross system, right? So I can take this part so I can actually write it t over to but a on the tee over to I put its under. Really, uh do you and thats it basically so I get minus you. Did I buy t of to equals? A. This is a fraction under the denominators are a flip it giving me a equals minus two u of t . That's one way of doing things you want to see the other one. It's very similar, but I'll show you. I could fact allies. This zero equals t because I got t on both sides by U plus 1/2 18 and then divide by t on both sides, giving me zero equals U plus 1/2 18 and then repeat what? I didn t vous, uh, case minus you Because, uh, 82 giving me a equals minus two. You over team in an exercise, an expression for force is given f equals could v me. It is also said in the text that f the same force is equal to n v squared of our The question is, what is value for our So using these two questions, we need to be arranged, um, and isolate our Could you try to do that? Remember, the to force are the same force. Okay, well, if they have the same fools, I can't equate these two terms. And why don't could be equals and v squared of our We've got V on both sides so I can remove one of them by dividing by v both sides giving me to be equals and v of r now I have one term. Either side of the equal sign say it's going to be straight forward I can do is like cost system here. I'm going to put our here and to be there se gives me oh equals m maybe of a to be in this exercise a variable only got has two different expressions. Only God can be either to pie of a big T Only God can be squared off K. So only guys equal to these two expressions. The question is, find an expression for em, which includes K and T. But so only I equals two pi over tea and only Eichel's quote of care. And so we can write down that two pi of a T equals quote off of em. So the first step would be to get rid of the square root someone to square those sites Remember Equal Sign announced this If I transform one side that can transform the other one the same way, getting me to pie of a T squared equals k of em. Now I'm going to get rid of the square by square. What's inside? Giving me four pi squared Divide by t squared equals k of em. I have one term on each side so I can use my cross system. What should I do? Well, I want the M to be on the numerator and isolated. So when I put the AM here as still have four pi squared of it, he's quit. But the T squaring and put it there and the food price quick and put it there. So let's do that. I would have em equals. Okay. The T square goes there, Katie, square on foot by square goes there four pints of late. If you feel uncomfortable doing it, everything into go look inside You can do it step by step. For example. You would write and by four pi squared t squared equals K. Can you pretty please square there so and four pi squared equals Katie squared. And then you put four per square downwards and equals. Katie squared over four. Pi squared, but was practice easily. You can for you out how to go from there to there Dying. One very typical equation and electricity matrix circuit Is this one one of all equals one of our one plus one of our two. I represent the equivalent resistance off two resistors R one and R two in peril. Okay, I want to find an expression for are the most simple possible given to shop? No, easy. So what you could do here is, for example, say, Oh, this is just one turn up brackets and I do my cross sister, so I would put our on the generator and one of the r one passed one of the rto denominator . So giving me one over one of our one plus one of our two schools are right. So I have an expression for arm. It's not really the easiest one, right? There's another way. Let's like it down again. One over r equals one of our one plus one are too. I need to remind about factions. If I have a faction like this, a of a B, it will be is actually you be multiplied by one one can be see of the sea. All right, that I'm allowed to do this right? So I'm allowed to take a fraction and multiply it on the numerator and the denominator by the same number. It would still be the same value. So a way to transform this into one term would be to have the same denominator underneath. I can do that because I couldn't apply this one by our two on numerator and denominator. And this one by our one on that would end up with same denominator that would give me one of all equals are two on one out too. Plus, I want this confusing plus our one on I want to The same denominator woke them giving me r one plus R two on r one plus by our to and this is still equal to one of the And then I can flip another thing with factions. If you have a over B equals C of D, you can fit them, giving you b of a equals d f a c by flipping the mere expression for all here. So oh, equals, I want to On our one plus two, you might be a little confused by what I just said. Down the sleeping part A of a B equals C of d implies that b of a equals the sea. When did this come from? Well, it comes for my close system using this system. Could you figure it out could you prove that? Okay. You see, we have one term on the side of the equal sign so we can use this close system I can exchange seeing me and I nd let's do that So the d a becomes deep, the B becomes c the sea becomes be on the D becomes a Oh, you know, you can also do it inimitable ways. If you want that, you want to go slower. You can decide assault by there again a devil, Bobby, we'll see if I d. You can decide to go only one way, de here, be there. So I end up having a d equals B C. And then at the second step, put a here. I don't see there. So you get, um, the of the C equals B over a Hey, what up? The section about algebra for high school physics is now closed. I hope you found it useful. I recommend that you continue training on this. For example, you could play with the equations in your formula booklet and isolate one by one each of the valuables they contain. There are two more sections in this course victors and trigger elementary. I'm courageous to check them out, too. If you do go through them diligently, you won't regret it on the long term, guaranteed. In the meantime, see you soon.