Today is the concluding session. So what I propose to do is to do a very quick review of the course and then specifically discuss the end semester exam pattern which I had promised I will do in the last lecture and then of course I will have some few concluding remarks. So if you look at the whole course when we started in July we studied the basic principles of computer programming in this course. Fundamentally we looked at computer as a stored program machine and we said it has memory, it has processing power, it has peripheral devices and it has storage. We have learned to handle each of these bits in a limited fashion. We also discussed the development of programming paradigms, how people program machines using machine language earlier and then higher level languages developed. Primarily we have been discussing the third generation programming languages through CLC++. We learned the basic programming concepts. So data representation, values of different type. So we have types for example fundamental types such as integer, real, whatever, whatever. We considered variable as a placeholder for a data value. We looked at expression evaluation, order of evaluation, assignment of a new value to any variable placeholder. Then we discussed two very important concepts in procedural programming. Ordinarily a stored program would be executed sequentially. Each instruction after the previous instruction would be executed till all instructions are executed. We found out that that is not the best way to represent our program because during the program execution in our algorithm we might want to execute some other instructions based on certain conditions which develop during the program execution. For example, if an input value is greater than 25, we may want to execute some other instructions rather than the sequential instruction. It is in this context fairly simple but powerful programming constructs which are called the control structures. The conditional execution embodied by if, if and else, the simplest form, if, else, if, later. And we also said there is a statement called switch. There is a question mark expression. These are all methods of conditional execution. We considered iteration in fair amount of detail because we have to iterate around to get either past several elements of an array or to iterate around a single value to make it better and better and better in several numerical computation problems. In short, then we discussed the conditional execution and the iteration mechanism fairly in details. These constitute the basic programming concepts. These would be available in absolutely any programming language that you will ever study. We should never ever talk about knowing this programming language or that programming language because it doesn't make sense. There are more than 1,000 programming languages. Primarily there are three programming paradigms. The procedural programming which is the conditional programming embodied by programming languages such as FORTRAN, COBOL, C, Pascal, BASIC, whatever. Object-oriented programming which we have not studied in details but programming which is embodied in programming languages such as C++ or Java. These are actually called object-oriented programming languages. And we have a third paradigm called functional programming. Primarily we developed to deploy for building solutions such as in artificial intelligence problems. We have not studied that a paradigm at all. We have primarily studied procedural paradigm and we have very briefly introduced ourselves to objects. However, the fundamental procedural programming concept that we have studied will be there in absolutely every programming language. So you need to be familiar with the notion of the type of data, conversion of types, what is permitted, what is not permitted. Some programming languages are strongly typed such as C++. Some programming languages, particularly scripting languages are very weakly typed. We saw an example of AUK scripting language. Those of you are familiar with HTML which is another scripting language for example. Or JavaScript which is nothing to do with Java programming language although it is similar. These are called scripting languages which are interpreted rather than compiled. We saw that. We then specifically looked at the notion of process of compilation. We looked briefly at the operating system environment with which you are becoming familiar from lab one because that is what we have to use. Initially you perhaps had no idea of what are directories and sub directories and files and file permissions and whatever. But as you got used to using these environments, you learned more and more about. Very specifically we saw how a compiler produces object code. The various object codes can be linked together. We saw that for large software you would use necessarily some header files which are to be included for compilation. We also saw how libraries could be built, functional libraries specifically. And they could be linked together if they are previously compiled. Fascinating, building of large programs. Very specifically we learned that in our endeavours to build solutions, programming solutions to problems, it is stupid to start always from scratch and write and develop the entire programming system from scratch. Why? Because many aspects of the programming which are required to solve any one problem could already have been covered in building solutions to some other problems. And the reusability of already written code or essentially saying do not rediscover the wheel is a paramount objective of every program. Consequently we learned how we could use already built libraries or functions or already built programming systems and construct something more which is required particularly to solve a specific problem. Mishit or enhance an existing system with these and that is how you build solutions there. Amongst data structures we had time to discuss only arrays, one-dimensional, multi-dimensional arrays and structs which are complex objects. We did not see additional artifacts that are built or that are defined using programming language facilities that we have. We did notice that we could define an equivalent of a type when we define a structure, for example we were effectively defining a new type. However, definition of an abstract data type and the features to do so and features to use those abstract data types is not limited to simple things like structure and arrays. We have specifically not discussed interesting types such as link list, queues, trees and so on. There are courses on data structures and algorithms, advanced courses which computer science students will necessarily do. And others who are to practice programming in their own profession will learn on their own. But these are very useful concepts where you extend the notion of a simple data type by including additional types. In fact we object oriented programming whenever you define an object class and whenever you define methods or what we call member functions in C++ you are essentially extending the reach of a programming language which defines certain basic data types but extended or abstract data types can be continued to be defined and you can actually use conventional operators to perform operations which are not conveyed automatically by the nature of the app. For example, plus is an addition operator but when we use it in the context of strings which are members of stream class in C++ plus stands for concatenation. Exactly the same way multiple operators can be overloaded in object oriented parallel which we have not discussed in greater details but we did discuss functions and function calls which are fundamental to programming language and reusability. We discussed some applications, we discussed some computational applications such as matrix multiplication, a larger application for image analysis we in fact had a project but that we will discuss in the next slide. As I mentioned earlier I repeat that we are not explicitly studied linkedless queues, stacks, search trees and these are extremely elegant and important data structures. Primarily on one hand they facilitate easier programming using those particular data structures solving larger complex problems and within these types there are some very elegant algorithms which significantly reduce the computational time. Remember we discussed the computational efficiency coming to the actual use of complete programming in the world. We remarked that very rarely we would be writing 100, 200, 300 line programs to solve a real life problem. Even a trivial application would demand everywhere between 5,000, 10,000 lines of code to be written. The larger and more complex problems of course could extend up to millions of lines of code. Very clearly it is impossible that such software development could ever be undertaken and completed by one individual. Of course there are very creative individuals who contribute to the design of the whole software. They contribute to some very elegant algorithms in some part of it but essentially large software development is a team effort. To get a flower, first hand flower of what large application development is we introduce course projects which is what we have been doing for last one month so that you can understand and practice such development process at least to some extent. I think by now you would have concluded and you would have observed that when large groups and they are not even large groups really, 20, 30 students working in a group, you will find that a large amount of time is spent in coordinating activities in job allocation, in managing synchronization because somebody's activity depends upon somebody else's activity and so on. This is the reason why a group activity is so significantly different from an individual activity. So remember that in future whenever you use complete programming to solve large problems, you will have to depend upon group members. Not all of them will be in sync with your own thought process. This time you have the flexibility to choose members of your own type because they were all CS1 students. In real life, if you are a chemical engineer or mechanical engineer, you might have to work with some team members who are neither that, they may be accountants for example. They may be just good programmers since a programming parallel. As a result it is important to note that group work for software development is going to be the major mechanism of developing solutions to large problems. We also studied some elementary mention of complexity of algorithms. Complexity of algorithms is a topic in its own right and there are full semester courses on analysis of algorithms. What we did is we tried to understand what program execution efficiency could mean, why it is important because it does not matter when a program executes in let's say 0.8 seconds, then to make it more efficient to execute in 0.0 seconds may not be very meaningful because less than 1 second is good enough for me for example. But when you have very large and complex programs and when multiple of such programs are to learn, time complexity becomes extremely important. We had a flavor of that when we discussed some preliminary aspects of algorithm efficiency or time complexity. By and large we have used C and C++ programming languages to discuss our programming concepts here. I will repeat once again that C and C++ are incidental. We could have used for example Fortran programming language or even Komal programming language to understand programming paradigms of the procedural type. We could have discussed Java for example. The point I am making again is that C and C++ are incidental and therefore unlike in most major universities in the country, you will not find the name of the programming language as part of the title of the subject. The subject is computer programming and utilization. And what you have learnt hopefully are fundamental programming concepts with a very brief introduction to object oriented paradigm. But you can build all this and you can learn other programming languages on your own that is the hope. So while we have a brief introduction to objects, it is expected that when you study your things further, either on your own or do specific advanced courses, you should be able to cope up with practically any programming paradigm. To the end I will discuss what kind of programming challenges you are likely to face when you build solutions to more complex problems in this world. But this is essentially what we have done in this course. Now as I promised, I will very briefly describe the end semester examination. I hope all of you are aware of this, the exam is scheduled on Monday 23rd November from 9.30 to 12.30. We will have a sitting arrangement which will be very similar to mid semester sitting arrangement. So we will have the exam in Convocation Hall plus IC rooms plus main building. All of you remember how you start for the mid semester examination? Exactly in the same way we will have allocation, some I think groups up to 7 or here or whatever I don't remember exactly. If there is any change or even if there is no change, the schedule of sitting arrangement will be again put up on the notices and please look for those notices but by and large we shall follow the mid semester exam pattern. Sayobas for the exam. Orally the sayobas for the exam is all that we have discussed in the course and much that we have not discussed in the course. We will follow the same pattern. So the following sayobas is everything that we have covered in lectures in labs except the specific work that you have done in the projects. You will recall that I had arranged some special lectures by external experts and by myself where only the team leaders were invited because specific topics were discussed. Now that specific discussion is outside the scope of the exam. The exam is for all and therefore the material that we have covered in the lectures is what will be the sayobas. However our image analysis for example I propose to give at least a question on some aspect of image handling but purely based on what was discussed in the regular lectures. So nothing outside the regular lectures will be in the syllabus formally. However as I told you in the mid sem, I am repeating this again in the end sem, there will be at least one question about which no student in the class will have any inkling. So there will be one question outside the syllabus and that question will expect you to externally imagine whatever you have studied to apply your mind to solve that problem. Even though the question paper pattern is slightly different in the mid sem you wrote the answers on the same question paper. We found out that the logistics in arranging to Xerox multiple copies and staple them was horrendously complicated and we could not, we could just manage to complete it about one hour before the exam began. That is no more feasible for the end sem where we will have six questions Xero4, we will say three of our exams. So what we have decided is that we will have question papers separately and answer books separately. That is how I suppose you write most of your exams. So you have got eight page answer books or sixteen page answer books. Sixteen page answer books and you will have of course ample supply of supplements and whatever but you will have to tie those supplements and please remember that if you use separate notebooks the top right hand corners of the first page must be your roll number and lab batch number otherwise it will be very difficult to identify in case you goof up. So if you have multiple answer sheets which you tie up together even if you tie them here on each separate answer sheet do not forget to write your roll number because unlike in the earlier exams where we will ample opportunity to discover things, find out, etcetera, etcetera at the 8th sem we will know about opportunity. The examinations will be open notes as in the mid sem. There will be six questions some will be multiple parts. I would try to organize the question papers such that the difficulty level of the questions increases as you go forward however that is not absolutely necessary because I will also have to organize questions roughly on the lines of the material that was developed and discussed. So I will see how exactly you will do that but I will try to organize questions in ascending order of difficulty. Last time there was a genuine observation made by many students that there were some questions which have let's say whatever 5 marks which were extremely simple and there are some questions which are 5 marks which are extremely difficult so is that justified? My answer is yes it is justified the question paper is meant for all students the students who are not very good in programming must also feel comfortable about scoring mainly marks to get their passing grade as good a grade as they can and therefore there must be some simple questions which might earn them maybe 5 marks do not forget that I am a travel programmer and I have been programming for 3 years in my school I can solve that simple problem in 5 minutes but on the other hand whenever I see the computer in my life I may take 20 minutes to solve the same problem I solve it correctly but I need 20 minutes and therefore 5 marks are justified for me to earn from that question while some of you might feel it is too simple a question so this will happen again do not lose your lives for some questions for even to get 5 marks you might have to struggle for half an hour for some questions you might be able to get that in 5 minutes that is that part and part of your life but I will try to arrange questions in ascending out of complexity to the extent that is possible some questions will have multiple parts maybe one or two questions will have a simple thing now here is the important part we used to have I have put quote-unquote discussion session you guys usually call it creep sessions right so if you do get marks that you deserve after you get the corrected paper you find out that some algorithm has not been understood by that EA who corrected that paper and so on you have a chance to go back argue convince and I notice that in some cases marks have been increased in fact I had couple of very specific requests that look with me always it happens that my algorithm is not understood by anybody who examines it not necessarily this year but everywhere so what do I do with it my answer to that is changing the evaluation pattern completely at the back end what we did in the mid-sem was the question papers were by large corrected by the lab group TS so consequently what happened is that four or five people who are sitting together in one group all were correcting different questions and as a result there was no discussion possible so question 2A for example was corrected for lab batch for lab batch 9B by somebody else sitting somewhere else this time I modified and using what I call the pipeline motion of paper correction we will completely give away or throw away the motion of lab batch correcting their own papers instead we will find out how many parts are there in these six questions maybe there are 15 parts ABC whatever whatever now we create 15 groups of TS each group will be correcting only one part so four TS sitting together may be correcting question 1A next four TS sitting together may be correcting question 1B next four 1C some other group of four students will be correcting question 5A and so on that way these four students who correct a specific question will be discussing amongst themselves constantly if they come across an algorithm which one of them cannot understand they can immediately ask the neighbor to check it and there will be specific instructions that for particularly for complex problems if the solution is not easily understood by one TA he should have given marks or two marks of whatever arbitrarily he should consult another TA I should be personally present and in addition to all of this there should be a moderation which shall be done by senior TAS here by and large therefore I expect for greater uniformity in evaluation of questions here this should take care of most of your apprehensions however even afterwards when the marks are declared and apart from the grades while we put up also the marks that individual students have got because after an incident marks should be completely available and there is no reason why somebody asks whether ancient papers are confidential or something like that that is nonsense as I said earlier I used to figure out correcting final exam question papers in front of the students we don't have that luxury now because the number of students are large and the exam is towards the end the paper collection specifically will happen only after my TAS have completed their exams don't forget they are also master students so we will not have any time for discussion session now however please note the last point if any student has ever come here or how much an application can be made for re-evaluation we will organize all question papers in assuming all the world numbers so that academic office will find it easy to extract a particular question paper for anyone who genuinely believes that he or she has got less marks than what he or she deserve we will get that question paper and we will not just re-total or re-check whether all questions are corrected or not but we will actually re-examine for that purpose we will record which TA corrected which question so we will know exactly and the TAS they are also going to be there next semester so those few students who still have a problem with their final exam marks can actually make an application formally there is a procedure in the academic office and we will have this discussion later any questions on this and same organization etc etc so I take it that this is perfectly alright so to recapitulate the sitting arrangements will be more or less same as the mid-sem sitting arrangements the academic office is just about to confirm that it will be a nothing notes exam like last night no books are permitted but you can have copies of whatever matter has been distributed in the class and labs and of course I will bound notebooks or files no newspapers will be permitted I will use a few minutes to discuss the future for all of you by then again there is much more to complete programming than whatever we have discussed in this course what we have done is nearly scratching the surface it is truly an introduction what we have attempted in the typical IIT style of course is that we try to take you as forward in the long journey as much as is possible notice that the kind of programming projects that you have attempted this is generally not done in most of the institution but actually have exposure to what last software is but considering that use of computers is increasing very rapidly what you are studying will only be a preliminary thing to real world problems and their solutions take for example conventional computers what you have seen mostly are PCs and you know that there is a server at the back end to which most of your PCs are connected but if you consider last transaction in system of bank account holders for example continue their credit transactions if you take state bank of India which has 16,000 branches and may be 25,000 ATMs the transactions are happening every time of the day some people are withdrawing money some people are putting money in depositing money some people are transferring money much of these transactions now happen on web consequently the requirement of large servers at the back end is the requirement so the kind of computers that you have seen both PCs and servers are no much for very large servers that you have which pose additional management problems of their own distributed applications we have very briefly mentioned I think that if I do an online reservation then what I get on my screen is a front end program which somebody has written on a web page I have failed my application on various computers from there if the reservation is available I will be directed to a towing gateway which will take me to a server on my bank's computer now these are called distributed transactions before because different parts of the activity are done in different computer systems different computer systems belong to different organizations all together unless I pay for my credit card to state bank of India or bank of the whole city bank and unless that payment is confirmed the Indian way is server by them I cannot get my booking but all of that can actually be handled today consequently the complexity of the programming system which drive these applications has increased in on us how I am computing in analysis is going more rapidly than what we can think how we could do floating point computations matrix inversions on small machines now you are super computers I don't know that I mentioned it whether you are aware of it or not but every year I mean in fact 6 monthly there is a competition of both large computers high-end computers which do high-end computing in analytics last year around this time I think an Indian computer called RECA made by Tata Research Labs actually performed fourth best in the top 100 of the world's fastest super computers so we have come a long way but the world is going faster and faster these super computers are nothing but a combination of large number of processors which are doing things parallely doing the same problem parallely is far more difficult programming wise then having 20 computers parallely executing 20 different things that is much easier to manage because each computer is doing some other program the same computer program to be executed by multiple computers is not an easy job and that is why high-end computing and analysis is of a different kind information repositories are coming in now you will have seen digital libraries where you can download books you can download movies you can watch movies, you can paper movie you have fingerprint collection system you have sensors data huge back-end servers far less are required not just individual servers the stories that we talk in terms of 100 gigabytes 200 gigabytes of this can you think that's a large storage that is peanuts when you consider typical data bytes of data warehouses and data bytes of storage farms which are now very common across the globe few in number but they are very common and this will only grow in future so whatever programming you have learned you have to increasingly apply it to solve larger and more complex problems of this type this is one end but there is another end where computers are being deployed in greater numbers and these are in the form of embedded systems you have seen a demonstration of a quicker a quicker has a processor inside which is almost as powerful as the processor on your PC it has additional signal processing capabilities so that it can handle radio packets transmit radio packets, receive radio packets practically every appliance that you see today in modern world has some kind of computer or the other and you have to write programs for that computer and the programming principles don't change the only difference is after you compile that program you don't load it from a desk but you load it permanently on a non-reliable memory inside the appliance so if you have a washing machine that gives you that to your house it actually has a computer which contains a program it has been tested rigorously and it has been put permanently inside that consequently when you operate a modern washing machine the computer takes over sensors from all the sensors you have activate motors and model so if you take any modern equipment for example a car or a ship or a rocket there is a large number of computers embedded and writing program for those embedded systems has become a very very major challenge manufacturing processes mobile phones personal digital assistants these all have very complex software if you take any mobile phone that you use the internal software that a mobile phone today has rivals the complexity of a full-fledged operating system and application software millions of lines of codes are written actually before they are squeezed into the small, non-reliable memory that you have on these gadgets and you can imagine since you have done a lot of programming yourself how long it takes to guarantee that your program works correctly how many times you compile how many times you modify and when you submit your assignment you are still not sure whether your program will work under all circumstances if somebody gives you wrong data whether your program will work or crash is not wrong appliances on the other hand have to guarantee that they must always work they must give a reasonable response when wrong data is given like if you key in a wrong telephone when your mobile phone should say phone number is not correct or something imagine if the mobile phones operating system was to crash every time somebody entered a wrong mobile you have huge problem so the appliances and embedded systems therefore pose an entirely different kind of challenge complex software will have to be written I am sure some of you have contributed to such development making these appliances better more comfortable and convenient to use even at children the software complexity continues to grow maintaining already written software maintenance is not in the form of like you maintain a bicycle by holding it every now and then maintenance of software development is actually extending the existing software new functionality is required new modules are to be added so maintenance is a wrong word only got stuck with the software business it is actually not maintenance but extension of software and that is perpetually required till the extended software becomes unmanageable you throw it out and start a new software development project effectively the life of a software really good non-trivial software is considered 15 years class it must survive for 15 years of maintenance and consequently software engineering has evolved as a major branch of engineering just like mechanical engineering electrical engineering and they are not programming software engineering for example emphatically raise down methods of developing projects in groups how group communication should be established how group hierarchy should be established how testing should be done there is a huge amount of research and just testing white box testing, black box testing the literature is about fortunately due to the internet you will be able to get very concise but correct introduction to most of these topics you just have to go to Wikipedia and find out what these things are it will be very interesting reading even in the story book reading but subsequent when you go ahead you will in your own fields when you use computers you will need to understand some of these things as well as you can so that you can produce absolutely top quality professional great software in whatever endeavors that you do so this is my concluding slide I believe you all know how adequate exposure to learn more on programming on your own and use the knowledge in your own fields and please understand one thing traditionally computer programming was considered to be computer science students preserve earlier it was electrical engineering preserve that is the biggest nonsense in math every individual scientist and engineer is required to be a good programmer to be effective in one's own field that's the reason why this course is compulsory practically for all human science students I believe now you have enough exposure so that you can learn things on your own if you know about the course as an engineer I hope you have enjoyed it for me it was really a great experience I had taught programming earlier but for 25 years I had not taught it almost all the things that I like is the level of enthusiasm and energy although the students were slightly worried and concerned at the beginning particularly those who came without any background but I am happy that everybody picked up no simple thing I like is that when I noticed some unethical behavior and I mentioned that I am not happy with it all students came up believe me in the history of teaching anywhere in this country I have not seen about 90 people confessing that they made a mistake and they were willing to correct themselves and thankfully to you and I it has been really a privilege to have all of you as my students so best wishes for the exam and best wishes for very effective use of computers in your own fields thank you so much


So this shows a rough track, a portion of which is in the form of cylinder of radius are capital R. With what minimum linear speed should a sphere of radius small r, it's a sphere of radius small r, solid sphere, it should be set rolling on the horizontal part so that it completely goes around the circle on the cylindrical part. You have to find out with what velocity you should project it so that it completes the full circle. Simple? It will roll without slipping, throw out. So can you say that this radius is a lot smaller than that one? It is not small, you can't ignore smaller components. Where is the highest chance the sphere will leave the circle. So if the sphere doesn't lose the contact at the topmost point it will complete the full circle, that is the hint. Condition for the sphere to leave the surface is normal reaction becoming zero. Just do the force balance for the put normalization zero so you get something. And then apply conservation of energy between this point and that point. Simple? Same thing we are doing again and again, conservation of energy, torque equation, there is just hardly three or four concepts. Once again topmost point or the force diagram equate normalization zero you get a relation between velocity and gravity, topmost point. Then apply conservation of energy between this point and that point. Okay? Try attempting it, do it your own way. You may be wrong, it's okay. So is it 20 into capital R minus small r by 700 root? Which under root 20? 20 by 7 g into capital R minus. You might have done silly or somewhere. Oh it's it's so. Root 27 by 7 g r minus r. Won't this just be the same thing as when we are using a string to push it out. What is string? What is string? String and the circle. Is there a difference? Difference is there or not? Sir, over here it's going to rotate. Force, string, the force, string applies is a pull force. The force, the surface applies is a push, normal reaction. Why are you quitting two scenarios? You are oversimplifying it. There was no law that one scenario is equal to the other scenario. Okay so see the thing is that many a times you don't have to learn, you need to unlearn. You need to throw away the assumptions from your head that okay fine, you have to keep on reminding yourself that these kind of assumptions should not come in your head. Otherwise mechanics will really be a problem. It will keep it straight forward simple the way it is. Just three or four equations, same thing you have to do again and again. That's all. Read every question on its merit. Don't compare one question from the question which you have solved earlier. Compare it with the concepts. So easy to say like this. Got it? Alright so normal reaction will be downwards. This is normal reaction. MG will be downwards and acceleration. How much into the acceleration? vcm square? No, by r minus small r. Center of masses radius is r minus small r. It is moving in this radius. This is capital R minus small r. So I will write n plus MG net force is equal to mass times acceleration of sensor of mass. How many of you got this equation? This is not this. We haven't learned in this chapter. We have learned in not work by energy. Leave a little other motion to write this equation. Net force equal to mass and acceleration. So what happens is if it is a point mass, then you have to check the radius. But if it is a rigid body, it is a big object. So whose radius will you take? Radius of the center of mass. Center of mass is travelling a radius of r minus r. So r is not radius of the center of mass. r is the radius of the path. You have to check the radius of the path of the center of mass, which is r minus r. This equation and normal reaction will be 0 if it just leaves the top surface. So then you put normal reaction 0, you get a limiting condition for it to leave the surface at top most point. If normal reaction is little bit higher, it will complete the full circle. So condition for it to complete a full circle is such that velocity of center of mass over here should be equal to how much? vcm should be equal to root over g times r minus r. This is the condition for it to complete the full circle. This velocity is velocity over here, not over here. Now I am going to use what is the theorem between this point and that point. Why I am using these two points? Because I have velocity at that point. Which is this? W is 0. U2 is what? Stop talking. Mg what? U2 is? This is 0. Mg into, this will be capital R, capital R plus r minus r. Let's take this line to be 0 potential energy. It will be easier. So this will be Mg into?  This will be U2 plus K2 is half icm 2 by 5 mr2 vcm2 by r2. This is half icm omega2 plus half m into vcm2. This is K2, this plus that. Minus U1 is what? 0 plus K1. Small r. U1 will be Mg small r. I am taking this to be 0 potential energy. Passing through the center of the sphere. Half into 2 by 5 mr2 initial velocity by r whole square plus half m into initial velocity of the center of mass square. From here you get initial velocity of the center of mass. You understood your errors? Your mistakes? Whatever you have done? Any doubt or any trouble? This chapter is difficult or Fluids was? It was not hard. I like this one more than Fluids. I like Fluids. Both are equally hard? No. This one is harder but it is more fun. Fluids. Fluids was not doable? Advanced level. Okay, whatever we are doing is advanced level only today. Now if you look at the main of the leg O's. All these see I am looking at the last questions of HCRM. Even those friends we have done already. So I am not able to find a new type of question. Alright, here is a question. It is a disk. It is a disk which can rotate about this axis. Alright. In fact it is rotating already. Omega naught. Alright. Now gently you have kept two masses. M1 and M2 at the edges. Okay. And M1 and M2 immediately when you keep it you have attached a favor quick on it so that when you place it it sticks there. You need to find the final angular velocity. It will attain after you have placed M1 and M2 over the edges. They are point masses. Not required. The mass is M, radius is R and it is a disk. It is like this. Disk is horizontal. Like this. Disk can rotate horizontally. Give me that worksheet Who had that? Solve this question. What I can use here? And you want them to use. But isn't there an external torque because of the weights of M1 and M2? Who said it is like like this? Torque is there or not? Right? Normalization because of M2 and M1? No, not normalization. The weight of M2 and M1? Torque because of M1, G and M2, G is about the axis that passes through the diameter of this disk. And this axis is perpendicular to it. So torque because of the weights of M1 and M2 M1 and M2 that torque doesn't pass through this axis. Understood? So torque about this axis is zero. But net external torque is there. But not about this axis. About that axis it is there. I can consider about this axis. Fine? So initial end momentum is what? I omega which is M R square by 2 I into omega this is initial angular momentum this will be equal to final end momentum which is what? M R square plus capital plus M1 R square plus M2 R square into omega. So you will get omega. Can I consider mechanical energy? No. You can't. There are more masses. What? There are more masses. Understood? Alright we take one final question. It's a paragraph type question now. From this only. So most of you got most of the questions wrong from this paper. Okay do this. Stop talking. And listen here. Finish this question. Then we can all go home. A uniform rod of length L and mass M is fitted freely at one end as shown in the figure. This angle is theta. This angle is theta. This angle is theta. This theta. Whatever is drawn I am drawing exactly the way it is. Okay. Alright the rod was initially vertical. Nursed it and it start falling down. Rotating about this fixed axis. Alright. There are three questions on this scenario. You need to find angular acceleration when the rod makes angle theta like this. You need to find angular velocity when the rod makes angle theta. And you need to find the tangential acceleration of the free end of the rod. You should be able to solve it. Initially the rod is like this. Initially it is vertical. Like that. At this theta where angle is theta find out alpha, omega and tangential acceleration of the free end. Same thing we have done. Similar thing on the second class of the rotational. Fourth. How many class you missed? So it is sad that you are not in it. Sad for you, not for me. You are not looking sad. You have one more week to practice rotational. Mark my words you will not get time later on. Tell your class 12. You will not get time later on. When is the syllabus going to be bad? It will be two weeks. One month we have spent on this. Already. In between like the J advanced one. How we can have it? I will call you guys. Find all three and then answer. Next all chapters are straight forward like the thermodynamics was. This was little tricky. Understand it takes lot of practice actually. You cannot sit here and think that I will understand everything. Okay. Done. Alpha all of you might have got. Talk about the fixed axis. Is how much? This is mg. Papandika component of mg is how much? Cos of sin theta. Cos of sin theta. Mg sin theta is Papandika component. Mg sin theta into l by e2 is a torque. Mg sin theta into l by e2 is a torque. So mg sin theta l by e2 is a torque. This is equal to i alpha. Which is m l square by 3 times alpha. Torque into i alpha about the fixed axis. Alpha comes out to be 3g by 2l sin theta is alpha. How do you get omega? Multiply with no omega e. Other than that you can conserve energy also. That's better. Please find out using conservation of energy. Quick. So it's root of mg cos theta by m. Conservation of energy all of you please apply. Strange answer. Is there any answer? Conservation of energy? Energy should be conserved. Under root of 3g into 1l sin theta by 2l sin theta. I don't mind. I don't mind. It's not a different thing but it would be simplified. I'll do it now. For omega using this s by 0 potential energy. So final potential energy is what? The height of sensor of mass from here is what?  So m l square by 3 i omega square. Minus u1 is mg l by 2 k1 is 0. Same thing we have been doing for entire class. So omega will be how much? You can integrate this also and get it.  This is equal to 3g by 2l. Probably when you are integrating you are forgetting that limit is from 0 to theta. When you put cos 0 it is 1. Integrate sin theta with minus cos theta. So when you put 0 as theta cos of 0 is 1. All right? Tangential equation of free end is how much? So it's just 3 that alpha into l. Alpha into l? 3g sin theta by 2. 3g sin theta by 2. Okay now you are able to solve those kind of questions. We have couple of more minutes. Because I am a workshop. So let's leave it. Try attempting the homework questions. Those who have not done the homework probably was feeling totally out of sync today. And this is going to grow. As you move slowly and slowly class 11 syllabus will be over then class 12 will start coming up piling up. So it becomes very difficult to catch up. So open your eyes. Open your eyes. Accept the reality. That it is not straight forward the way it was in class 10. Already damage is done. And probably it is permanent damage. You can't do anything about it. But if you keep ignoring it that permanent damage is going to increase only. And you cannot do anything. When you are in mid of class 12 if you are not doing the homework it will destroy your chances completely. Just because you are not doing the problem doesn't mean that others are not doing it. Others are solving many difficult questions. And you have chosen to sit with them in an exam J or whatever you are writing. And they are better prepared than you if you don't practice. So they will naturally beat you down. It is natural. Now you can choose to close your eyes and feel that I don't want to do it or I am very happy playing video games and chatting with you whatever time pause you are doing. That is completely foolish because soon you will realize that after class 12 and I am seeing it every year every year I am seeing it for past 10 years I am seeing this every time I say this there are people who take it seriously there are people who ignore it and then same people who ignore they come back mid of the class 12 and mark my words they will come with all crying and everything they will say that they are depressed whatever nonsense but we can't help that point in time even we can't help. We can console you saying it is okay and things like that but then now time is going to run away and destroy it completely permanently fine. Waking up means that at least get where you deserve. I am not saying get more than what you deserve I am not saying anyone that be in rank 1 in J mains or J advanced if you deserve to be in 90s suratkal don't take admission in local colleges in bangalore you understand what I am trying to say if you deserve something better then you go and get it okay it will be sad that if you deserve let's say a college like like 90s suratkal and you land up in some third grade college in bangalore or somewhere else then you have to naturally prove yourself to the world and listen even though I have land up in some not so good college but I am good for that you need to prove to the world otherwise world will not accept you you have to work hard some point in time better to do it now otherwise once you are in some third grade college all of it is known to the world the world doesn't know what kind of students go where they know it okay so make your life easy by working hard in next couple of months and you have another one weeks time practice this chapter which is naturally very difficult I know very difficult because a lot of concepts are there so it requires practice practice and get what you deserve I am not saying get something more understand the difference right I am not saying get let's say 360 or 360 but if you can get 150 don't get 50 and if you can get 200 don't get 100 at least be around and if you are around 100 there might be a score of 30 or 20 if you think you are at 100 maintain that later on it can go up to 120 or 130 whatever it is okay so don't make it worse just maintaining your status also requires lot of effort otherwise you may think that you are there only but others are going ahead of you so not doing anything doesn't make your place stable it makes you go down not doing anything because others are getting ahead of you and it is all relative ranks you are going to get right you don't want to see your ranks in lakhs but somebody will get it 20 lakhs it will write the exam 4 fifth of them will get a rank less than more than 1 lakh right so probability of getting rank more than 1 lakh is what 19 out of 20 which is close to 1 competition is high alright that's it


Education is a valuable part in life that continues to challenge and intrigue individuals until the time of their passing. A popular question for parents is when to start formally educating their children. At Naval Air Station's Siganella Richard Aubrey, the librarian answers that question with a weekly story time aimed to form an interest in literature for young children in the community. The thing is, it's been proven that the younger you start with children reading or being around books, the farther they go in life. So it's really one of our strongest and one of our best programs. The library puts a strong emphasis on reaching out to youth to engage them mentally, but they also offer many tools to help aid the community. The library has computers, Wi-Fi, a cafe, and of course over 18,000 books and magazines for the community to use. From Naval Air Station's Siganella, I'm Petty Officer Sean Hillier.


Welcome folks, this is Tom O'Brien of TFNN. We have five days a week, we have seven hours a day, we go 24 hours a day in the internet at tfnn.com. Always remember folks, what if you think about, you bring about whatever you focus on grows. Hope everyone's having a great day, safe day. It's making a great night, folks. Don't take anything personally. Your truth is personal to you. Your own opinions and point of view reflect your own agreements and are personal to you. It's no one's truth but your own. Market wise, let's take a look at it out here. We have the Dow Industries down 62. Nasdaq off 78, S&P's off 10. Gold, gold contract up $12, trading is 2,031 an ounce. We have silver up 45 cents, $25.64 an ounce. Light sweet crude up a buck 75, trading $83.28 a barrel. Notes and bonds, a 10-year note. Up 12 ticks, trading $1.15, $24, the 30-year. Down two ticks at $132.10, a king dollar. King dollars, where are you, baby? Maybe just a bit, there you have it. King dollars down 710 ticks, trading $101.494. The euro's at 109, the yen is at 133, and the British pound is at 124 to one US dollar. iPhone number's 877, 9276648. Give us a call, folks. I don't know what's going on in your world and the world of the S&P's, let's take a look at it. Well, first let's go to the futures because it's gonna get really interesting here because ES, what you're looking at here is that you're building cars to break this low right now, enter day. That's how this is shaking out right here. You know, we've been here for 30 minutes and we'll see how this shakes out. The low of the day here is 4121. If you get the break, it's gonna get interesting because you can get a small ABC down coming into the close. It doesn't have the juice to go top side. Each one of these bounces today, you can see if we just pull this up. In fact, I think it was a 0.618, the whole thing in general, almost. It was almost a 0.618. The first one was a 0.382 of the day. Second one, almost a 0.618. So we'll see where those shake out coming into the next hour. Gold, gold contract out here. Bottom line is that this had turned into a complex ABC structure up because it went under the B point, did it with light of volume, got above the B point again, has volume again, so bottom line. The game is on, still in the gold market. Even though, that would make sense because the dollar's breaking down. Yeah, that makes sense anyway. So the bottom line is that you're at, the B point on this was the 2031, we're over the 2000, we're at 2031.30. You have 216,000 contracts traded. You can see yesterday, it sideways 126,000. We went lower the day before with 136,000. That's what you want. That's what you want when you want higher price, folks.  King dollar, now check it out, man, because this could get really interesting here with King dollar. Bottom line, you are going after the lows, man. So the low in the dollar index is 100.83. The strength, however, as we come off that low is 100.546. Now we're into it, we're at 101.496. So that sets up, it's gonna go after it. And we'll see how that shakes out, man. We bring this into a longer basis and what you're gonna see is that the next move down in this baby, you know, you break this level, you break the 100 level and your next level would be like 99. The bigger level there is like 96, 98. The 96 is game, man. That's what's pretty incredible, so. Notes and bonds still want higher price. Higher price, lower yield. This is gonna get wild. The Fed minutes come out at two o'clock today, folks, okay? You can see here's a volume coming in again. 141.4 million contracts on the way up. Yesterday, let's take a look at what went down. You can see this yesterday. Yesterday you go down with a million contracts. You're up at 1.4 million. What that's setting up is that setting up higher price, lower yield. Inside the Fed minutes out here today, what you had, we went from the aspect of the, you know, higher rates to the aspect that they actually were bringing up to the point that, yeah, they're looking for a mild recession now. And so that is the first, folks. That is the first heads up that the Fed itself, okay? There's plenty of the folks out there that have been saying, yeah, we're gonna get a recession. You know, some people say it's a hard land and some say it was soft land, but at the very top of the Fed minutes out here that they're looking for a recession now. That's what they're looking for. So the market's gonna get interesting and the market's gonna say, well, if you're looking for a recession, well, if you know what a recession means, a recession means we're all gonna make less money. So we'll see how this baby's gonna shake out. Let me just go over to the SMP again, because if we break this low, you get plenty of time to really get some juice going here. Okay, so I just went after it. That, the first low, let me see what time it is here. Okay, we got, we're two minutes into it. The first low had 41,000 contracts. Right now, you're at 17. We're gonna blow that away, man. We're gonna blow that away. So, you're gonna get lower prices coming at you, man. Some of the higher volume equities out here, let's take a look at it. You get Amazons down to buck 60. You got Teslas off 584. You got American Airlines down to buck 36. Marathons off 40 cents. Excuse me. Let's go inside the NDX 100, Strength versus the Weakness. Crowd strength's up 3.5%, data dog's up 3.5%. Taken away from it, JD.com's down 7.5%. Holy cow. Pinduoduos off 5.5%. You got Walbrings on a Warner Brothers off 4.2 and Chattac Communications is off 4.4%. Inside the Dow Industrials, the Strength versus the Weakness. Point wise out here. Excuse me, folks. We have Goldman putting 13 positive points, Microsoft 7, Merck 6. Taken away from it. Home Depot minus 17, American Express minus 16, Disney's minus 13, and IBM minus 12. The volume out here today, when we take a look at these indices. So, right now you're at 450 million on the NYSE on the composite. We are, composites can have some volume. We're already at 3.9, 4 billion inside the composite. Dow, Dow Industrials right now down 41. We get the NASDAQ off 81 SNP.  Stay right here for folks. Good job, man. Mr. Tim Ward coming up with the odd oracle. Coming right back.


Hey everybody, Dr. O'Hare. We just got on talking about the apricot and American sweat glands. Now we're going to talk about primarily your sebaceous glands. I got a couple more I want to mention at the end just because they're not worthy of their own video. Let's put it that way. So sebaceous glands are going to be oil glands and they're going to produce sebum. So sebum is this rich, oily substance that lubricates and protects the epidermis, inhibits the growth and movement of bacteria, and also waterproofs your skin and your hair. So sebum is very, very important. So sebaceous glands, the first thing to note is that every hair follicle has its own sebaceous gland. But then there also are sebaceous glands that just dump sebum right onto the skin as well. So there's kind of two types of sebaceous glands, the ones that are lubricating hair as it's growing, and the ones that are just on the surface lubricating the rest of your skin. The production and secretion of sebum is stimulated by hormones, which is why they're not very active until puberty. So puberty, we already talked about how you're going to start to produce apricot and sweat, which can lead to body odor. But also your skin and hair are going to get a lot more oily at puberty. The androgens, the male sex hormones will produce a lot of sebum, but all of the sex hormones do as well. So that's going to be sebaceous glands, where they are around a hair follicle and just on the skin surface, what they produce is sebum, which waterproofs hair and protects your epidermis, et cetera, that also can lead to problems, which we'll cover in the next video, which is acne. But I do want to mention just the other glands. We talked about sweat glands and sebaceous glands. There are other multicellular exocrine glands that are associated with the skin or the integumentary system. Now it would be mammary glands, which produce milk, will cover milk in our last chapter together, breast milk. And then ceruminous glands are the ones that produce cerumen or earwax. So I'll cover those when we talk about those structures, but I just want to mention them here as well. That is sebaceous glands. There's a couple other ones as well. I hope this helps. Have a wonderful day. Be blessed.


Our main subject is the morality of capitalism. And really, I think to many people, the main force of capitalism, free markets, this is the morality. It's the ability to produce wealth and we've had this incredible wealth engine going on for at least 200 years. But to many people, the dis-oppositional results are not just. And so, but you claim that it is the moral aspects of capitalism that is really the major case for capitalism. Absolutely, and I think one of the reasons we're losing capitalism, that is capitalism I think is in decline globally in the world all around us, is because its defenders have focused only on the economics and have kind of accepted the morality of its opponents. I think capitalism is the only moral system because if morality, as I see it, is about human flourishing. It's about individual human flourishing. It's about individuals having the ability to make choices for themselves, pursuing their own values, using their own mind to figure out what kind of life they want to live and living that life, then capitalism is the system that protects their ability to do that. It's not primarily an economic system. Capitalism primarily is a political social system and it's a system that basically relegates the government to a very narrow job and that narrow job is to protect us, protect us from crooks and criminals and terrorists and invaders and fraudsters, importantly. And other than that, leave us alone. And then we all live our lives based on our own mind and pursue our own values trying to achieve our own happiness. That's what morality to me means is individuals living their life based on their own terms in pursuit of their own happiness. That's what morality is. And what capitalism is a political system that allows you to do that, leaves you free to do that. Every other political system wants to impose on you certain values, certain standards, tell you what you should or shouldn't be doing with your life and whose happiness you should be pursuing. And I think that's morally corrupt. I don't think you can impose morality on people. I don't think you should use force and coercion to achieve your vision of the world. And remember government, government sounds like a nice word. And I'm all for government. I'm not an anarchist. That might disappoint some of you in the audience. I'm not an anarchist. Government is force. Government is a gun. Just if you're not sure, try to not follow the law.  So government is force, coercion. Law is not optional. Once a law is passed, no options. You have to do it. So I think that morality demands that we not use force against one another. Even if we vote for it. I think morality demands that we leave individuals free to pursue their own values and impose values on them. But a lot of people would see the capitalist system as one that's producing a lot of inequality, arbitrary income distributions, which needs to be fixed. Even if they accept your point about pursuing your own values, they would claim the result, the income result is not just, why does one apply justice to income? What is the standard? And again here, I think conventional morality out there says that the standard is some form of equality of outcome. Why? Why should people be equal in outcome? And there's, I don't know, any objective reason for that to happen.  We have different talents, different skills, different abilities, probably different levels of morality. Some of us are ambitious and hardworking, some of us might be lazy, I don't know, I'm just guessing. Why should the outcome be the same for us? And I think it goes to one of the points you made, which is arbitrary distribution of wealth or it's not arbitrary at all. The distribution of wealth is determined by what you produce. You produce, you have stuff. You don't produce, you don't have stuff. Seems just to me, right?  I don't have a right to take your stuff, you don't have the right to take my stuff. You'll produce a little maybe, I'll produce a lot or I'll produce a little, you'll produce a lot. Why does anybody care? How much somebody else produces? And the beauty of the system is that the only way for me to make money, the only way for me to become rich, to become part of that 1% or whatever, however we want to define it, is by making your lives better. There's no other way to do it. How does Apple make money? It's the biggest company in the world, or second biggest, maybe the Saudis are the biggest, but how does Apple make money? By selling me a product that I want at a price that I think it's worth it because the iPhone is worth more to me than the thousand dollars I give up for it. I celebrate when I buy a new iPhone, I don't, oh God, I lost a thousand dollars. When I lose it in the stock market, I lost a thousand dollars, but when I buy an iPhone, I'm like, I'm happy. I got something that's worth more to me than the thousand dollars I gave up. And Apple is happy because they just made a really nice profit off of me, right? We're both happier. The world is better because Apple made the iPhone and made a profit and traded with me. They got rich. I didn't get richer, but I got more fulfilled. I got more potential in my fingertips. I got more music to listen to. I got, you know, I got an iPhone, which is of value to me. I can give a two-hour lecture on why the iPhone is of value to me, but put that aside, but it really is otherwise I wouldn't have given up the money. So the only way to achieve this is to drive everybody up, and indeed, that's the history of capitalism, to the extent that we've practiced it, inequality increases, but the poor get richer, fast. Indeed, the only system in all of human history to eradicate poverty is capitalism. It's, you know, to the extent that we practice it, private property and freedom of contract and people buying and selling stuff based on what they want. That is the only way to alleviate poverty. There is no other way. And what I care about, what you should care about is poverty, quality of life, standard of living. It shouldn't be relative, should be are they poor people? So basically what you're saying is markets and transactions are not zero sum, they have plus sum. So everybody wins, it's their win-win. So is it that so many people see the market and other interactions are zero sum? Is there a good explanation for this? I think economics professors have done a very bad job explaining it. I think our politicians have an incentive to present it as zero sum because they want to play us off of each other. And I think that unfortunately, thinking is an achievement and a lot of people never achieve it. And the reality is that a lot of people out there who don't think, we want to think well of our fellow man, but a lot of people just don't engage in it. They have the capacity, everybody has the capacity. But all they have is a, you know, there's a perceptual level that human beings have, that all animals have, we see what's happening. And what we see is iPhone $1,000. And we think the two are equivalent and then we see Apple getting richer and I didn't get richer because the value I got from the iPhone is you could argue spiritual is not material. The whole, you know how Piketty measures, Piketty is the French economist who wrote the book about, think about how he measures inequality, right? He measures inequality by looking at my bank account, right? I have X amount of money in my bank account, Apple has a lot more money in their bank account, so they're richer than me. And every time I buy an iPhone, I get poorer according to Piketty and according to most economists. Because my bank account goes down by $1,000. There's nothing in his equations that includes the value of the iPhone to me. What we call an economics consumer surplus is not captured in it. So I just look like I keep consuming stuff and getting poorer and the manufacturers keep getting richer but that's bizarre. And I'll give you my favorite example for this because, you know, I don't know, there are not that many young people here but how many of you have read Harry Potter? I mean a few of you have read, well actually some of the older people have read Harry Potter, that's good. I mean Harry Potter is terrible because Harry Potter led to J.K. Rawlings becoming a billionaire. And I became much poorer because of Harry Potter. I don't know about you but I had to buy three copies of every book because both my sons wanted one and I had to buy one for myself. And then there were rides in, you know, in the theme parks and there, what were they, seven, nine, 12 movies that we had to go see all of them. I spent like $3,000 on Harry Potter. I got poorer, poorer by $3,000. J.K. Rawlings became a billionaire. That's not fair. And Piketty would say inequality exploded. She went from a welfare recipient to a billionaire. How horrible is that? And I got poorer and that seems like zero sum because a lot of us got poorer because we all bought the books. But how do we measure as economists, and this is the challenge that we have, how do we measure the satisfaction of reading your children a book or watching your kids in this day and age actually read a book or going to the movies with your kids or doing all that, how do you measure that? There's no measure. But that's the win on my side. The win is the spiritual satisfaction of reading Harry Potter. And she won as well. Good for J.K. Rawlings. I mean, that's wonderful. So we have a challenge of explaining that because it's not perceptual. The benefit I get, and this is why I think Harry Potter example is a good example because everybody's read it and understands the value they got. But they never think of it in terms of economics. But it's all part of it. And Piketty and those economists pull one over on us because they show us statistics which is missing the most important feature. What I got out of all the stuff that I've bought. I have to buy artwork and you get enormous spiritual value artwork. You got poorer, I tell you. And you go, no, not really. Not if you count my spiritual wellbeing and so the whole inequality debate is bogus. There is no issue, there's no problem, there's no reason to discuss it. We need to explain the basic economics and how as people get wealthier and if we are participating, and it's important because participating means we're working, we're producing something, then we all get richer.


The skills you need that I think you need to be a foster carer is a sense of humour, not to take things personally. You need to be very understanding, encouraging, just a normal person, just be you. My name is Michelle and I've been fostering for West Sussex for about 26 years. I had a young child of my own and didn't want to go out into work, back to the office. So I decided that I would work from home and look after teenagers. And it worked really well because obviously I could give individual attention to my child during the day. And when my child was a bed, the teenager had me to themselves. A lot of them just need a safe place first, somewhere where they can feel safe, secure. Someone that's in their corner will listen to them, fight for them, encourage them. Simple things we take for granted with our own children that you just do instinctively. Sometimes I've never had that before. So about 95% of my foster children keep in touch with their families. They'll come to see me, some call me Nan, which is lovely. I've actually seen a foster child that I had give birth, so that was pretty special. To me the rules are successful in their own right. Whether it's going catering college or whether it's going to university, it's more a case of what haven't I got. Seeing all these children that come in through your door as one thing, when they leave, they're totally somebody else. I like to give them a sense of being, a sense of self-worth that they can be. Whatever they want in life, it's there if they want it. A lot of people do think that fostering teenagers is going to be really hard work. Trouble, police at your door every day and that's really not the case at all. Once they feel safe and secure, they slot into your routine, they just want somebody that will vouch for them, care for them. What I would say to somebody thinking about fostering that was in my position all those years ago, is go for it. There is help out there. You can work from home, be with your own children. I've had lots of support really over the years from West Sussex. Lots of training on probably every subject under the sun that you need. There's always help or a training course to go on to. You don't have to be a standard nuclear family well off in your own home. There's lots of different families, lots of different children. That's all they need is a chance. They just need somebody to be there to know that they're not going to give up on them. It's just nice to change lives and we do as foster carers.