 Alright so this chapter name is first item. So if ever you find this name will come first system of article. So why students find this chapter difficult? Because there are multiple things here. In this chapter they have like n number of things. So just mugging up the document of the exam preparation. So what happens is that if lot of information is there you do not understand the link between the information or you do not do enough problem practice. Then you get confused in this chapter which concept to apply when you might be still confused with the other chapter because of lack of problem practice. This chapter will add, will double it if you do not pay attention. If you ever miss let us say 30 minutes of the class you did reading about something or someone told you that you were thinking about something. And you do not pay attention. Then this is like a chain. Why I am telling you all this? Because the basic chapter is there. So these will form a basics. And then here is a chapter which tells you that studying a special case about the motion of an object. For example you always assume and some velocity because moving like this. You never consider that while moving it can rotate. For example when you are in a pulley system you draw free body diagram with the answer and you feel happy about it. But then going forward you are considering multiple particles together. For example if there are like zillion molecules in this room you are not going back to what this molecule is doing. It becomes senseless. So you need to understand how collective behavior is what as a collection of this entire all the particles what are they doing collectively. So this is what this chapter tells you and this is closer to the reality basically. So we have learnt the basics from special cases. Now we are making it slightly generic. And when it comes to the system of particles each and every thing this theory itself, multiple point masses you can think of it is made up of multiple small small small masses. You can go to the atomic level. The atom is let us say smallest particle of this. You can say electron and this thing also. So there are zillions, millions of those particles are there of which the TV is made up of. So this is one entire, it will look like a single object but this is actually a system of particle. But this is a special kind of system of particle. There can be system of particles like this cap and the pen. This is also a system of particle. When I am studying cap and pen together. This is also a system of particle. The motions are not this point. So their motions are related in some way. So studying this kind of system is easier because knowing the motion of one particle you can predict the motion of the other particle. But if system of particles have loose particles like this then you can predict knowing one particle's motion. This kind of system of particle which doesn't get deformed or there are some relation this is called rigid body. So we are going to study a special kind of system of particle which is a rigid body later on. Right now I am going to just introduce a concept of system of particle. How to study any system of particle. Whether it is rigid body or this they are moving depending on each other. I think we have already started studying the system of particles. We have studied the entire all the gas molecules together what they do. So we have already started studying the system of particles. But here we are going to study it in a different way. We are trying to apply the neutral second law of motion. Then we are trying the system as a whole and so on. So this is slightly different but we have already started understanding the system of particles. Where else have we studied the system of particles as in multiple particles together. Where else? Collisions. Two particles coming in. You have already studied the system of particles. What is fluid? Is it a single particle? No, multiple particles are moving. So even fluid is system of particles. So we have already started studying system of particles. First time we are studying it exclusively. So when we are studying system of particle exclusively we are going to assume that we do not know anything. So we will start from the scratch. So whenever suppose I have to start studying let's say particle. Like you remember when we studied kinematic if you were there. What is the first thing about the motion that we should study? It's a point of it. So what is the first thing you study? In kinematic? No, see that is different. But that is an assumption. How you start studying it? It should first know the location, where it is, is the location. We have a location of entire system and you should tell me, you can't tell me location of a system is starting from 0, 0 to 2, 0 and 2, 2 and 0, 2. So you can't tell me that. Location is a coordinate. So first thing we are going to learn here is how to quantify our system. Suppose there are multiple masses scattered in our system. So please write down location of a system, center of mass. Have you heard of center of mass? This is called center of mass. It is a point, mass here which is 1000 kg, these two masses, only these two masses. Please write it down. The location of a system should be the mass. So basically the weight on the location. This is the only chapter in which I don't follow the NCIT way of writing the content. I have my own way of. So don't match it up with this we have learned, this we haven't learned. We cover everything when the chapter gets old, then you can see and yes. So the location is closer to location. So other than finding suppose this is my coordinate axis, x and y it is same and the position vector of this mass is r1 and position vector of that is r2 and trying to find the position vector of center of mass. So position vector of center of mass will be the weighted average so that the position vector comes closer to the heavier mass. So it will be m1 into r1 m2 into r2 divided by m1 plus m2. Does it make sense? Suppose m, like for some of you, could be 9. No. This is the weighted average. You have 500 rupees and you have 100 rupees not. Total amount of money what is the value to 10? Which else you have? Similarly here you are finding the weighted average. So the weight of the position vector r1 is more. So you are multiplying m1 with it. It is weight getting it. So this is the center of mass location and this is for only 2 particles. Suppose there are multiple particles. Suppose there are like 10 particles then going to the formula m1 r1 particles and then infinite particles also. So how do you know this? This summation of m1 r1 summation of m1. This is the center of mass location. Wexons is in terms of vector. It is of these particles. So let us try to see whether we can find, given the x, y coordinates of 1000 kg and 1 gram, what will be the x and y coordinates of the center of mass. So if I know the position vector, if the coordinate of a point is x, y, what will be the position vector? x i cap plus y j cap. Similarly that is what I will do. r, c, u and vector will be x center of mass i cap, y center of mass i cap. This will be equal to summation of m i x i i cap plus y i j cap divided by summation of m i. So this I can write as summation of m i x i divided by summation of m i i cap plus summation of m i y i divided by summation of m i j cap. So what will be x center of mass? You just equate the i component from left hand side to y component also. So x center of mass 1 plus m2 x2 and so on divided by m1 plus m2. y center of mass will be equal to m1 y1 like this divided by that total mass of the system. Is it straight forward? So you must know what is center of mass formed up because we are going to use this