And before I introduce the panel, I'd like to draw your attention to the commitment cards that you'll find on your seats. This is actually very important. Yesterday, a number of people expressed concern that we might be repeating the same message year on year and not making really sufficient progress. So this is to ensure that we do, that we stress that we should hold ourselves accountable to act on the issues that arise from D&C days and show progress from year to year. So this is our commitment going forward. So to give you the opportunity to do this, please fill in the commitment card with one action you will take on your work to progress one of the issues that you've heard and has resonated with you during these D&C days. And you can post your card anonymously in the box up here in front. Where's the box? Don't see a box. It'll be there in a minute. It'll be there in a minute. Box will come. And actually, even better, take a photo of it and tweet it with the hashtag at DC days 17 because that will resonate with people. So we're into commitments into being accountable. That's a good start. And as Ruth Spencer of Antigua reminded everyone this morning, we have to be the change that we want to see. It starts basically with us. And each of us can then revisit these commitments in 2018 at the COP24 in Poland and see how, in our own sphere of influence, we've acted on what we said we would do and what we've heard. I'm delighted to be moderating this closing session where we bring things together in a very human conversational way and to have such a diversity of perspectives and lived experiences on this panel and to make sure that we keep the strong links between the grassroots and policymaking that have been the core characteristic of D&C days. Our panelists are paired, as you can see, to represent those different perspectives. So I'd like to begin by introducing the panelists. And I'll start with the panels on the far side here. I'll start because being a woman, I'll start with a woman. I'll start with Agnes Lena, who is Executive Director of Inamatic Community Concerns from Kenya, Pastoris from Kenya. And to the right of her, maybe appropriately enough, right of her, is Hart Schaefer, Vice President of Global Themes in the World Bank. And coming closer, we have not a minister from Fiji, though if a minister from Fiji arrives, we will give her a space, or him or her space. But in the meantime, we have an Irish volunteer representative, Michelle Winthrop, who is the climate and resilience policy lead for Irish aid. And nearest to me is Esther Nabuti, who is the youth representative from the Kiribati Red Cross Society. Apart from anything else, Esther will be reading her poem later. So you have a double task here today, Esther. And on this side is my good friend Sheila Patel, the Chair of the Board of the Slumman Track Dwellers International, SDI. And beside her, Munima Bonaya from the Kenya Adaptation Consortium. And finally, on the shared results, we have Magali Pawwane of South Africa, of the Rural Green Development Implementer, and Diane Holdorf, Chief Sustainability Officer at Kellogg's. These four themes are at the heart of what you've all been discussing. And there will be time for you to make comments and even pose questions or take issues or whatever you may do. But let's start with the panel. So I'm going to start with Agnes. Agnes, you've seen all the key messages related to resilience for empowerment, that first theme. And can you tell us which one of those resonated most with you and why? Thank you very much, Agnes Mary Robinson.  I'll tell you why I say that. It's because when I went to Ireland the first time, she was the president. So to me, she still is.  I just want to say that, first of all, the discussions that you've been having the whole of this week, the two days have been really, really excellent and touching to my heart and closer to the kind of things that we do and closer home for especially a grassroots person like myself. I must say that one of the things that really touched my heart is the fact that building resilience, it's building resilience through deep and meaningful participation and inclusion of local voices from the communities that are directly faced by the high impacts of climate change. We come here and we talk about climate change and we have all these technical words that we talk about. And in reality, when you go down to the communities, who is being faced by this reality? It's the people themselves. And we do not have their voices. We need to learn from the indigenous knowledge that they bring to us, especially being a nationalist myself. There is so much that we learn, especially on issues of mobility and moving from one place to another as a nationalist woman. It is us who actually advise ourselves. It is the elders who have this knowledge. It is the elders who know when it will rain. It is them who will tell you the acacia trees are now becoming green. They are shedding green leaves, meaning that they sense the rain. It is therefore time to move back or to move to a certain place. Those are the important voices that I mean when I say, when we talk about policies and we do not have these voices coming to advise and to talk to the high level meetings like this that we come to, then we do not actually reach the people and it is meaningless. That participation is what I really, really look forward to. The participation of women, not just men. The participation of the youth, the participation of young girls, the participation of young boys and how climate change affects them daily.  And therefore when we talk about national adaptation plans, we talk about policies, we talk about NDCs, we need to hear the voices of those indigenous people, the women themselves, the grassroots women themselves, so that the community is involved in what we do, involved in the policies that we make. And we talk about policies and then we bring the policies to them and they ask, so where was I? Why was I told when this policy was actually being enacted? We need to be part of that policy. My minutes have not yet finished so I can continue. So that's the kind of resilience that I'm talking about because we live with resilient communities who understand what resilience means. They move from one place to another because they understand that is what will bring that.  Thank you. Well done, Agnes. That was a very powerful question. I'm hoping that the gender action plan that's to be adopted at this COP will include the participation and voices and knowledge of grassroots women in particular as part of the gender action plan. Hart, you've had a lot of experience in your work in the World Bank on the issues raised under this theme. And which message resonated most with you and can you illustrate with a story how the World Bank has taken it on board? All right, thank you very much and thanks, Mary, for having the World Bank here and congratulations to all the organizers. Before I answer your question, let me say, I actually have a lot of things in common with Agnes. I grew up in a small community of 750 people. I was a farmer before I did all this stuff studying and being at the World Bank. And one of the most rewarding things that I do is to meet with communities. So for me, empowering the communities, making sure that they participate in the planning, in the execution, in the monitoring of projects is absolutely critical. And I have a couple of very good examples. But from the World Bank's perspective, I want to share three aspects with you. One is, under our new environmental and social framework, this is our new safeguards. We are mandating all the projects to have community and beneficiary participation, stakeholder consultations during the design phase, during the implementation to make sure that we constantly learn from the communities that we actually want to help and want to improve the livelihoods. And that makes for a better project that makes for more robust outcomes, that makes for more sustainable outcomes. The second one is, our engagement with communities started about 10, 15 years ago with community-driven development. And it's still going very, very fast and is a priority. About $2 billion a year are going to community-driven development. That means that we are actually engaging the community in prioritizing what is it that they need most. And with the risk mapping and education on climate change risks, we are seeing more and more that these communities are actually choosing resilience efforts and resilience projects. I can give you a couple of examples of how, when I was posted in each of how we work with communities who wanted to protect the Nile River banks from erosion. And this was supported through a community-driven development, a cash flow works program, to make sure that, in this case, the youth in the villages was actually getting jobs and an income, but at the same time, protecting the environment and making sure that the flooding of the river banks was not eroding and destroying the fields. The last one is how we engage women as champions of resilience. Because we know that women are normally very often more vulnerable. When it comes to water, to trout, to tending to the fields are more vulnerable to climate change risk than the rest of the community. And we are focusing in particularly on women in terms of training, engaging them in projects that range from forest governance projects in India and Nepal, where we know that if women are involved in the committee that oversees illegal locking and so on, the results are better. When women are involved in these resilience measures, the results are better. So from our side, from the top down in terms of what we want to achieve on climate change, we have made a commitment that by 20% of our lending will have climate change co-benefits, both mitigation and adaptation. That's a corporate commitment. Same way, we are making sure that our projects have our gender, not only gender-informed, but they have a gender tag, which means you identify the gender gap and you have appropriate measures in there to close that gender gap. So what we are doing is from corporate messages down, but also from the bottom up involving communities. And one of the most moving example was when we helped the community farmers to get access to crop insurance. It was a trial, but it helped the farmers to maintain their livelihood even during the year of drought. And that makes me proud of having been in the World Bank for so long. But again, deep down in my heart, I'm a farmer. I feel it, I think like I'm... Thank you, Howard. It's good to see that this is now the approach and policy of the World Bank because there have been problems, problems in particular of mega projects with no consultation with communities, projects of, I mean, look at the figures that the Guardian is monitoring this year. I think it's now 161 defenders of land and water rights have been killed this year alone. I mean, so the need to change completely, and so it's good to hear that the World Bank is putting these values to the forefront of your planning and of your implementation. Michel, I'm telling you now, you're stepping in for the minister from Fiji that we hope we might have for obvious reasons, but we really wanted a voice from a more authoritative government source to talk about the value of lived experience and local knowledge that brings different perspectives. So having seen the messages that were merged from the last two days, which message resonated most with you and why? Thanks. Thanks very much, Mary. I think the one that left off the page, if you like, from me was the combining traditional Indigenous and scientific knowledge, and really valuing local knowledge and using it as a tool to bring about change. I'm going to go slightly rogue and I'm going to talk about forests, and I know they're in a different hotel having a different meeting, but that's okay. Just a bit of an experience. If I could transport you all momentarily to a very special place in Ethiopia called Bale Eko Region, and it is honestly one of the most beautiful places on Earth, but it's also a very fragile forest system, and many organizations have been investing for many years in mobilizing the community to manage that forest and to own that forest and really to bring about its restoration. And in a previous life, I worked for an NGO called Farm Africa. We were very committed to Bale. We were very committed to bringing the scientific community in, mapping the water resources, mapping the coffee in the forest. It's got amazing coffee. Our argument, if you like, was that Bale Eko Region was the water tower for much of the arid lands of Kenya and of Southeastern Ethiopia. So saving Bale was not only important for the people of Bale, but it was important for lots of other people who relied on that water downstream. So many, many years of community-based forest management, lots of people, myself included, trying to find ways to mobilize the value, if you like, from the forest. Let's make the coffee really expensive and lots of rich people will buy it. That can be reinvested into the forest, or let's bring lots of really rich tourists there, and that will be really powerful. But at various points on visits to Bale, I was always struck that there was a local organization called Melka that used to run youth environment groups. And the purpose of those youth environment groups was basically to sit down, sit the young people down with the elders of the forest and have that transfer of knowledge from the old people to the young people about different species of trees, about medicinal plants, about how, how they could harvest their firewood in a more sustainable way, and really about some of the real spiritual aspects of the forest.  And if we don't learn this stuff, and if we don't really try to capture this stuff, it will be gone forever. And no amount of scientific data gathering, international conferences can bring that back when it's gone. So to the best of my knowledge, those youth groups carry on. And to the best of my knowledge, it's no longer donor funded. It's just a purely indigenous movement that really values that resource. So I leave it there. I can see how Agnes enjoyed that story. She was nodding throughout. Esther, you're the youth representative. So you could actually have a little extra time if you needed because, in fact, Michelle didn't take her full time. So let's hear how you have felt. This is your first cup. We're asking a lot of you. So relax. But you'll just speak from the heart. What is it that has really struck you as being something you really want to remember and to value and to think about? OK, I'm just going to share an experience that I read two years ago. 2015, Kiribati struck a TC-Pan truck called and two islands had been really destroyed. And one of the most destroyed island is one of the smallest and really isolated island, outside. And I was one of the lucky youth who went on and do the response. We got from abroad. And the funders, the donors, I mean, the donors designed everything for the people in the island. So we went with everything, the materials and the design they had for the people to rebuild their houses again. But the thing that I found that when we went to that island, all the materials that we brought with us are not relevant. They, like the people in that island are complaining because, you know, in my island, Kiribati, we don't have soil. It's just sand. And the materials that we brought to the island is like one of it is art wood, the timber, which is very big and very heavy. So if you want to build your house, it will fall down maybe just two or three days later. So can I just ask, so it is because the donors decided? On the material. It was the wrong material. Yeah. So we've tried everything. We can, with all the materials, but it just doesn't work out. So what the people in that island did was combine the things that we brought with their own materials that they can find in their island and rebuild their house. So we built two examples, like two houses. One is the, we used the design for the donors and one we used their own design. So the one that we used for the, I mean, we used the local one is still standing now. But the one that we used for the donors, the design we got from the donors, I think it lasted just after a month with no wind and sea coming to the island. So that was the lesson I learned from the response I did in that in 2015. Thanks. So if you could just pursue this a moment, because it's a great story. So how in Kiriba, especially young people in Kiriba, are you going to deal with the donors? I mean, how are you going to get them to listen more to you? Well, I just wish the, I just wish that donors will listen. Yeah, and then have some local people in their meeting before they get in. OK, thank you. Amina, I gather you also made a very powerful intervention yesterday. I wasn't here, but my colleagues told me in which you talked about accountability. And we need to make sure that we are accountable ourselves really, Jane. So I want to really ask you to tell us what other either inspiring story or challenge you want to give us here today at the end of this DNC days. Having listened. All right, thank you. My story would be actually to show the importance of having the right kind of information in a timely manner to the local people and the planners and also collective action in terms of making action and responding to a climate risk. It was in 2013 in one of the counties that we are piloting the devolved climate finance, where a lot of emphasis on the local people to decide on the resources and do the planning themselves. So the weatherman, say, gave information, of course, that it's soon going to rain. And of course, the technical people and the local community could make meaning out of that. If the rain is coming, then most likely it will come with a disease outbreak. That if actually action is not being taken by anyone, then the livestock might die. So what they did is having known the budget that is available to them. Most of the time, the budgets never get to be known. But this time, they know how much is available. So they sat down and looked at it and engaged and consulted widely and decided that they probably need to have a vaccination program. But this time, the vaccination program is coming from different words, saying you want to do a vaccination program. Another word saying you also want to do. So that idea come to the technical people at the county adaptation planning committee. They looked at it and they saw the community actually need to have a vaccination program in anticipation of the rain that is likely to come and might actually cause livestock death. So they said the advice from the technical people to strengthen the idea from the community is that one vaccination program in one section of the county may not be useful, because livestock moved from one place to another. And if one section is vaccinated and the other is not, then it's as good as not doing it. So their input was that they come together, do a program that covers the whole county in a way that all the livestock are safe. They are all vaccinated at the same time. So the proposal was actually improved in that way with advice from technical people. And they undertook an intensive program that went around the whole county to undertake vaccination. And the rain came and the livestock was saved. So that is the story that actually shows the collective action, timely information, non-budget that can actually help people take action. And be safe, identity, climate-risk. That's very interesting. So it was a mixture of local knowledge, technical agreement, a budget that allowed you to plan, and then knowing that it wouldn't be enough to do a vaccination. In one part, you had to do the whole region in order to. And that was possible because of ability to plan, basically, and good cooperation. OK, thank you very much, Melina. That's a very good story also. Sheila, I've known your work for years. And I've known how you have to push back sometimes. Most of the time. Most of the time, OK.  So tell us, A, what sort of messages that you might have picked up here, but also your own experience. Everybody should also know that you brought me into the climate change program, keeping and screaming. She didn't think climate was important. Oh, oh. That was a long time ago, Sheila. My story basically starts with four people in cities being invisible to planning and to data and to investment. And yesterday, when I heard in the sessions that I was there and in the other discussions, the whole discussion of linking transparency, good quality data, and democratically accessible resources, it really showed me that we were on the right track in terms of what we do as STI. But those of you who don't know us, we are a transnational alliance of social movements of the urban poor in 33 countries, more than 500 cities. And our most powerful instrument is poor women mapping informal settlements and creating their profiles at the city level so that they know who has evictions, who has tenure, who has toilets, who has drainage, and present it to the city. And you talk about pushback? Cities don't even have data on one-fourth of the settlements. And so initially it was to fight evictions. Then it was to get access to resources from the municipality for toilets and for water and for drainage. And now that we're coming into the discussion on vulnerability and resilience, new words, all of us are learning, we use the same data both in assessing vulnerability but also mapping the impact of no development on the city's SDGs. And we see a huge value in linking the two together because development investment that is critically essential fundamentally is not available. And I was surprised, and I think those of you who saw me in your group saw me championing for the rights of cities and the urban poor to come into this process and to develop a strategy where the urban rural continuum is seen in its natural progression rather than the way in which development looks at it today, which is urban versus rural. And so I want to challenge this group that next year I will bring from 10 cities, 10 countries, a team of women and their government officials who are negotiating these processes and bring them into this process so that you learn from them and they learn from you. Well, I certainly think that's a challenge. And I'm sure D&C organizers and my foundation has been part of the organization. Of this particular D&C, we'll really listen. I think we have a lot to learn. Maybe 10 might be a little bit tough on organizing, but certainly some. We'll meet some 30% of. OK, we'll negotiate. Diana, it's very important to have the perspective of the private sector at this conversation. And the private sector, and we mean business, have been very much engaged in the D&C days. You're the Chief Sustainability Officer at Kellogg's. And I think you do have important perspectives on our discussion. So tell me what the team of shared resilience means to you and what message you've taken. Thank you, Mary. Yes, thank you. As a global food company, if we aren't part of shared value at a community level, and if we aren't working on the resilience of the communities from whom we rely for our ingredients and where we operate, then we don't have a business either. So for us, it's absolutely a business imperative working within the SDGs, particularly SDG number two. And climate at this intersection of hunger and enough food for all to ensure that we are providing mechanisms that will support farmer livelihoods as much as they support our business. We don't own farms. We're not vertically integrated. So we very much are dependent on these resilient farming communities. So as a business, we have a number of commitments across the sustainability and climate spectrum. But the one that's most focused really into resilience is our commitment to support half a million farmers through the implementation of climate smart agricultural practices. And we were actually at the UN when the Climate Smart Agricultural Framework launched. And the reason that it was so important for us is that, yes, it looked at greenhouse gas emissions coming from agriculture. And agriculture does have a big footprint in this space. But far more importantly, it really looked at resilience and yields of farmers first and foremost ahead of getting to the mitigation factors. And that adaptation and resilient piece is what for the Kellogg Company really resonated. I'll share just two very quick stories. We've got work on the ground in many of the countries that are around the world where we source our primary ingredients of maize, wheat, rice, potatoes, et cetera. But let me just share two. The first story that I'll share with you is of rice farmers in Thailand. We were seeking medium grain rice. I don't know if you enjoy Rice Krispies and Cocoa Krispies. But they actually use medium grain rice. And traditionally, long grain rice is what has been grown throughout much of Asia. And that was what we were using. But we found an opportunity working together with the International Rice Research Center of the CGIR and the Thai Rice Research Institute and the communities to test medium grain rice that could be approved by the Thai government to be grown that would create new markets in the region, not just for Kellogg, although we committed to purchase it as well. And working together with local communities and millers, we were able to engage smallholder farmers, about 70% of whom were women, in understanding what were the crop cycles that they were experiencing through climate changing aspects within their specific environment, and how to have a medium grain rice variety, all that would be approved by the government, bring them successful crops. And what practices did they have already? And what practices might help to improve their yields? Which sort of was an offset to testing new grains. It's hard to test something new when your livelihood depends on one or two crops and harvest the season. It was actually recognized as the first successful private public sector partnership in Thailand by the government. But from our perspective, far more important, it improved yields by 30%. It's going to be awfully quick on the second example. It will be quick. Elevator version. One more. My second event, because I'm partnered here with South Africa, we are working in South Africa with women maize farmers as well to improve yields with partners like Technoserve. There, we're focused on the Eastern Cape, where drought has been a challenge. What we've been working on is how do we create opportunities with the government for transportation, logistics improvements, so that we can begin to incorporate that maize into our own operations, which we cannot yet do because of logistical challenges. So it's always a nuanced need of complex solutions for success. OK, thank you very much. Thank you. Mikaela, you're a rural green development implementer. And you have the last word at this stage, and then we'll open it to the floor. So what's impressed you? What do you take away? What's the message you'd like to convey? I think the first thing, Miss Mary, I think let me just say I was educated actually. It's my first call. I don't know what to expect. Coming from the rural area, I'm educated. And I think I will take some words from the former president, Mr. Nelson Mandela, when you said that education is the best thing that can give to a human kind. And you have empowered me. I've seen that with many progress actually. The panelist here, it's women. I think 80% is women. What we have resolved on in the Paris Agri-Main Dictionary, you are actually implementing, not just talking Turkey, but implementing. But let me say, you know, when I saw Kennox in a room yesterday and talking about empowerment and coming from rural area whereby we are not cut, but we don't have access to market, access to finance. We had jobs last year. And the farmers there, they could not survive even right now. Because there's no insurance for small-hold farmers. And I said, thank you. COP23 is giving us an opportunity to talk about sustainable partnership which is very key. Very key in the sense that we need to, we want to take inside the procurement of these companies and share the presentation that they must give to local communities where they're operating. It's very key to us. In South Africa, we talk about transformation. We know where we come from as a country. We talk about transformation every time. What you are saying, and which is the thing which I'll take home and say, Kennox, can we start the discussion and implementation to say we've got 1,000 farmers where I come from who are producing maize, who are producing grain? They need the support. Government is there, but government is very, there's procrastination within our government. They take long. But through partnership with different stakeholders, we can achieve. And lastly, incubation, you know, sometimes we come from a background whereby we do not understand business as well. We do not understand how it works in the international world in terms of market, in terms of market. If we are there, bring us in your enterprise development. Bring us in your supply development program. But does any of that happen at the moment? Do you have any technical assistance of that kind to understand? We don't have. We've got government that gives certain, they've given certain people, farmers some money to the capital farmers, but we do not have the support, the ticket support that needs you, that assists you to go forward as a business, so you're able to sustain your business. As a result, we've got people that are moving from the rural areas that are going to cities right now. That's why we've got a lot of shacks and former settlement because of the economy in the rural areas is not there. So I think that is a time whereby we build upon rural economic development. Thank you. Thank you very much. I think that's a tough story to talk about. Thank you very much. Well, I think the panel has done us proud so far. I really do. I think each story and each experience has been very, very worthwhile. But now, and we're pretty good to time, yes we are. But maybe a minute or two over, we have a best part of half an hour, 30 minutes. For your questions, comments, observations, challenges, we've had challenges from the panel. We can have challenges from the floor as well. The lighting is OK. The back of the room, I might have trouble seeing. But Mars is going to help me, OK? And that would be very helpful. Yes, please. You have a question, comment? No? Oh, come on. Wake up. Hey, come on. You're not exhausted. Come on. You've had a great panel now. And they've given you lots to think about. Oh, yes, there we are. Hand there. Good, good.  OK. I have a question for Ms. Patel. Good. Oh, yes, my name is Ulamila. I'm from the Pacific Islands, Fiji. And I'm here under Climate Voice Women, which is an advocacy group of women in leadership in grassroots society. I have a very specific question for Ms. Patel. As I heard you speak yesterday and also here today, and I'm quite impressed, because we do have slum and shack dwellers in the islands as well. But not as mobilized as how you're doing what you're doing. My question is, do you engage with your local government or do you engage with government at any level at all? I say this because I'm from grassroots. What we do, we try and engage via local government, and then they take it up from there. I'm just wondering, do you somehow engage with your government at any area at all? Thank you. OK, I'll let Sheila answer that. And I'm very glad that Climate Voice Women was the first to speak at that. Now, wake up, everyone. I want some more questions after this. Sheila. We start by fighting with our mayors, because they're evicting us. But then we make friends with them, and then we start working together. The community, especially the women, are very clear that they have nowhere else to go, except stay in the city. So collecting data, making a representation, and shaming the city about how little it knows about where a very distinct majority lives is a very good tactic. So if you want to explore this, we'd be very happy to show you how we do it, or maybe have you talk to some of the women who have been empowered. We were all like you when we started. Doesn't take long for women to take charge. Sheila, can I just ask you for another second?  I mean, taking Mumbai, where I know you're based yourself, I mean, how much of Mumbai some areas are now mapped and able to speak for themselves? First of all, there are 68% of the city, which is 12 million people living for the informal. And right now we do ward wise, because each of our wards is like your city. So when we do the ward, we go and talk to the ward officer, and now we become a little more aggressive. They say, what's your budget? How much of it are you spending on bringing toilets and getting drains? So the thing is that data is available with the city, but it is never disaggregated to the level of the informal setting. So it's very easy now. So usually we have this thing like a two page thing on each settlement profile. So they can go with that to their municipal representative and to their eminence. Now we're starting going to our politicians. We don't like them in the beginning at all. And most of them come for wards, because poor people always go to wards, but they never get the returns on their investment. Now we try to get it. Thank you, Sheila. OK, over here, I think we have a question there, please. My name is Domino Frank. I come from Liberia. I live in Switzerland. And I'm here on the platform of corridors of peace.  Liberia is 150 years old, or older. And for the past 150 years, Liberia remained the biggest robot producer in the whole world. Yet there is no plastic producing company or machine in Liberia. All the robots are exported to the USA. To produce an ordinary plastic spoon, we need to import from Nigeria or from any of the West African country.  We are here addressing climate change, talking about grass roots. My question is, is there any way the average local woman, rural woman in Latin America, in Asia, in Africa, can get benefit for good management in the home? We talk about grass roots. And a lot of us here are the elites, the class that are privileged to experience this. But take, for instance, all the money that is got from UN, from European Union. Who does it benefit? It goes back to the same elite in the class. And all what we say here will be nonsense if it does not affect the average rural woman. Who used the most plastics in the home from the shop, from the supermarket, from the market? It is a woman with the children. Is there any way we can get this money and get it back to the women? And you will get benefit for not throwing the plastic in the sea, on the road, in the forest. This is my question. Could there be a platform that some of these things can be addressed? Because the whole thing we talk about, grass root is just a privileged class, I'm sorry to say. So my question is directed to all of us who have had something to talk about. Grass root, can we create a platform where the rural woman will have benefit for home well managed, for not throwing plastic, for not throwing garbage into the sea, into the forest, or anywhere in the environment? OK, thank you. I'm going to hold that question for the moment and see if we can get some other comments. Because I'm going to give each of the panelists a chance at the end to respond. We have one here. Yeah, OK. Thank you. Anybona from the BRACE program. I have a question to the World Bank. There is a very big program to renovate the methodical services in African country called hand-commet renovation. What is the plan of the World Bank to involve civil society to give them a role and ensure that farmers will get the climate information they need? Well, rather than answer it just for the moment, if you just hold it, maybe we'll just get a couple of more questions. You're lightening up a bit, yes, at the back. I see two hands now at the back. Good. You know, wow. I am getting worried, but no, I'm not worried. I am by the name Scots and Socolate, from Toronto, deep in Uganda, very far from here. My question goes to World Bank. In Uganda, with the farmers, I'm a pizza farmer. I'm very happy that the European, the island government brought me here to be in the delegate. So I'm so happy. Thank you very much. Now, the question goes to the World Bank. The World Bank in Uganda, we don't even know where the World Bank is. We don't even understand the issue of the World Bank and how the World Bank works. We are not even allowed to move near. Maybe it is there. But I don't know how. These farmers of where he works, how did they access the World Bank and how are they working? The World Bank, how are they working with these people at the local level? Because we are the major producers. We produce food for the whole world. And yet, most people don't think about the grass root women. But I'm happy that the world is now beginning to recognize the small-scale farmers in communities. Thank you very much. Thank you, Constance. I'll make sure the World Bank answers your question. Now, I think there's another hand at the back. OK, hi. My name is Yvonne Biot. And I wanted to use the opportunity to say hello to Michelle, because I hadn't seen her yet in this environment. Hi, Michelle. But it's also relevant, because Michelle is the person who took me away from the city of the service and took me into the marvelous NGO Farm Africa, which taught me the importance of the private sector and markets. And I discovered that at this DNC days, and I've been to quite a few of those, that finally we are starting to acknowledge this. And finally, we are looking at the private sector and markets as our potential partners rather than the enemy. And I would kind of suggest and recommend to the DNC community and to the future, let's embrace the private market, the markets and the private sector, because at the end of the day, when farmers want to sell their produce or when they want to buy their inputs, they're not buying it from government, they're not buying it from NGOs, they're actually buying it from shops. Shops are linked to larger private sector companies, et cetera. So I would say, and I would hope, that the inclusion of the private sector and of the market kind of engagement element of our work that we've started here is only the kind of start of a much deeper engagement. Thank you. Thank you very much. I think Magali was making that point, but you can also reinforce it later when you have your minutes at the end. OK, and yes, here, please. My territory is Blando from Guatemala. I'm here, like, working with Wider Commission, that is a global network of grassroots organizations. This is for Agnes and Sheila as well. So can you please share with me about how do you see grassroots organizations to be scaling up and be considered key actors in the climate change arena? And how can we approach the donors and researchers to shift their roles to support these processes? Good question, and I will give them a chance to respond. I think we've time for one or two, yes, please. Thank you, Mary. I'm Noel Wootley from Editation Network in South Africa. My question is for Esther and for the Red Cross and for young people in low-lying tropical countries that are likely to be affected by hurricanes. Would it not be wise to, at a grassroots level, do an inventory of what materials might be likely to be most useful? Because we say the way to hell is paved with good intentions. And I'm sure the intentions of the donors were off the very best when they gave you the inappropriate materials. But we know that we're going to have more of these extreme events, more frequently, more with great intensity. So perhaps it would help the donor community and the relief community to know what it's likely that we need it. Maybe the donor community would need to fund that for Esther, for a letter answer. At the end, yes, back. Good. Hello, everyone. Thanks for the great insights. I'm from India. I'm a solar professional, and I'm pursuing my master's. So my question is to Agnes Leiner. I hope I spelled her name right. So she was saying that you need to bring the ancestor's wisdom, which is timeless wisdom, I believe. But what do you think? It's like the wisdom which the ancestors shared. It has to have a logical reasoning. Because in modern era, which we see, we need the logical reasoning for everything. So I think it would be great if whatever the knowledge which our ancestors shared, it has to be actually with a reasoning, like why it was done or else it doesn't go into the masses. So how do you think it has to be imparted in the education system? This is my question. Any more questions on the floor before I give the panel a chance to respond? Because I have quite a number of points made. One last question. OK? OK. Hi, my name is Thelmisa, and I'm from the Maldives. And today I'm here with Climate Wires Women as well. So I wanted to reiterate the importance of having a bottom-up approach in designing or implementing projects. Because I could very well relate to what the young lady from Kiddibas was saying. In the Maldives, we had a similar experience. And one would think that the donor community, with their best intention, might have learned from that experience. Because right after the tsunami in 2004, one of the islands, which is Kandoradu, was completely wiped off the map. And the people were in three different islands. And this was before we had a democratic government. And after the democratic government transition, I was in the government in charge of relocating people to the newly built island, which was Duafer. And what had happened was the new island that was built, that it was beautiful homes built for people to resettle in Duafer. But it was built in a modern style. And women in that island lost their livelihood because they dried fish in outer, open kitchens. And that was not taken into account. There was an open facility built to dry fish for these women. But they had to go away from their home in order to earn income and to dry fish, which they can't go because they have kids and they're doing it in their own backyard in their home.  So it is so important. And then I asked them, who designed this project? Why, what happened? And I was told that it was designed in consultation with the island chiefs who were in charge of the island. But there were men. And so none of the women were consulted. Not even the women's development community of the island was consulted. So there was a huge gap in the consultation process itself. Though you think the consultation process took place, it actually didn't take place in a manner in which it touched the grassroots women who needed to be a part of it. So I think it's very important to look at who we are consulting and at what level at grassroots we are consulting in order to make sure that the bottom up approach is being implemented. Thank you, that's a very good example. Now I'm going to turn to the panel and let them have an opportunity to respond. And I am actually very pleased with you. I was a bit shook at the beginning that you weren't putting up your hand. Actually, this has been a rich discussion. So I'm very happy. Thank you. Now, we started the World Bank since there were a couple of curve balls thrown in your direction. All right, is this also our final? Yes. OK, good. Thank you very much. Thanks for a series of very good questions. Let me start with the HydroMap program. This is indeed one of the larger undertakings that the World Bank is doing in partnership with WMO to make sure that we get better data, better projection when it comes to rainfall pattern, when it comes to weather changes, and so on. Because that is what's needed. We need to get these messages then, of course, to the farmers. And in this context, we have worked with grassroots organizations because just getting the information and not having a means to actually act on them, that doesn't mean anything. And we realize that if you look at Africa, 80% of the men listen to the weather report, but only 20% of the women. So the traditional channel of getting that information to the women farmers is not going to work if we rely on radio. And this is where we bring in the grassroots organizations to make sure that actually the information is being received and being acted upon. With regard to Uganda, I know we have a huge program in Uganda across several sectors, including agriculture. But I don't have the information where, what projects are. And after this, I would be happy to exchange cards with you and I'll provide you the necessary information, but also the contact to our World Bank office in Uganda in Kampala. And then you would actually be able to meet with the people on the ground there. So I would be very happy to do that. But I don't, I'm honest, I don't have the information of the details here. I see Constance nodding.  But let me close by saying one thing, Mary, you mentioned that the bank hasn't always been like this. Indeed, when I joined the bank 28 years ago, it was a totally different bank than what we have today. And what we have today is, and I call that the five piece, it's we have the policies, climate change, gender, protecting the people and the environment, central policies that govern how we support countries, how we design projects, and so on. So the policies are there. The policies have really changed over the last decades. We have the people. When I joined the bank, I was one of the few who was an economist and an agricultural engineer. Nowadays, the disciplines of who we hire is completely different than 15 or 20 years ago. We have all kinds of disciplines, anthropologists, social scientists, data scientists, to help us actually extract and exploit the huge data that is available. The people skills have totally changed to actually make sure that we are working much better on the ground. This is the third P, presence. We have large teams in countries. And if you are in the country, if you're in Kampala, you have a much better appreciation for the local context and what the local people want. It's hugely different from sitting at a desk in Washington. We work in partnerships. That's the fourth P. We work in partnerships. We realize that funding alone is not going to make it. And make it towards elevator version. OK. Partnerships is the fourth P. And the last P is passion. I think everybody who works in the bank shares the passion that is in this room to improve the likelihood of the people across the globe. Thank you. OK. Thank you. Agnes, I think there was a specific question to you, but you also might want to make a broader comment. Wow. There were three specific ones that I wanted to react to. But I know time will not allow. Indigenous women don't know how to speak for four minutes. They like to speak for four minutes. But I'll try. Let me start with the latest question from the young man behind about using. He calls it ancestral. I call it indigenous knowledge. And the fact that it's no longer more than, I can understand that coming from a young man because it's technology, Twitter, emails, telephone. And you know, traditional knowledge doesn't have all that. But it is so rich. And it's very shameful that we are actually ignoring it and rushing to the new. And it does not inform the old. Or rather, the old should be able to inform. It is OK to welcome all the modern technology. No problem with that. But we must document our own indigenous knowledge. It is what actually has brought us today to where we are. Remember all those small animals that you knew? For here, I think you talk about ladybars. I don't know. There's more little doodle that you call ladybars. It's disappearing in some places. Remember when you last saw a beautiful butterfly? All that is disappearing because of climate change. And we must ask ourselves, who has documented what we used to have? It's actually that knowledge you should never ignore it. I can tell you that in Kenya, we are actually documenting our indigenous knowledge, not just on climate change. We are actually now putting in our curriculum issues of, I don't know, many people may not resonate with that, but issues of early marriage and female genital cut, maybe you've heard about it, FGM. And now we are documenting it and we're putting it in the streamlined, streamlining it in our educational curriculum. Because there are so many children who don't even understand that all there's something known as genital mutilation cut because it's a traditional thing. And that's one which we do not like and we want to teach children that we do not like this. There are many that we like and we must document them. So I still believe that, especially where I come from, personalist communities as we are women also come from, we have survived because of our traditional knowledge, moving from one place to another informed by our elders. And we still respect the opinion of the elders, of our astrologers. We still respect, if it were not for that, you would be wiped out completely. If it were not for time, I would have given you a small story about... I understand, I understand. Just one minute, not for a while. But you had a couple of other things you wanted to say about. Can I please just mention those two? My friend from Guatemala, we have an indigenous people's caucus every morning at 9, at what it is called, what are the people who go to the indigenous caucus here? I've not gone yet, but I know it's there and I get all the information. It's there every day. Please connect to that. Then from where you come from, there's a whole movement called FEMA. Indigenous, yeah. So through FEMA, you'll be able to understand so many things that indigenous people are doing. So I'll talk to you later on about that. And then the young man about papers and plastic papers and saying that, oh, there are no indigenous people, rural women represented here, it's rubbish. It's not rubbish. I come from the community. From the, it's from Kajada town, Muminanos, I stay 10 kilometers away from the town, right inside the village. Where there's no electricity, no radio, no nothing. What? Did I see your hand up? I'm pointing at you too. Oh, at you too, yes. She's got to ask a question, I forgot. Yeah, so yes, and you too. So the idea of plastic and all that, let me tell you, every little changes that we have in this world was started by someone. The passion in which you spoke about the plastic bags is the same passion in which you will go back to your rural area and gather those women and say that we are going to protest against plastic bags. In Kenya, we have done it. We are such an example. For the last one week, no, no, sorry. I think a few months now, NEMA, you know, every country has a NEMA, National Environmental Management Authority. We have banned plastic bags. Plastic papers are no longer there and I'm so happy.  And now we don't have plastic bags in Kenya. So it just takes you, your own passion, to actually change that. That is how it works. That's how you begin. That's great, thank you. Wonderful. I also want to come back to my brother from Liberia and his challenge about grassroots women. And I had the privilege yesterday of spending some good time with Constance, who is part of the Irish delegation. And she said something yesterday that really, really struck me. The hungry child does not go to the father for food. The hungry child goes to the mother. And so when we think about the role of women in building resilience, we're not victims. We have a responsibility. And I think we have tons of examples of networks of grassroots women who can step up and who can find ways to organize and make a difference. We find, we, I'm using the broader we, we find our empowerment wherever we can. I think nobody expected that M. Pessa and Kenya would empower women, for example, to save money behind their husband's backs, frankly, to pay for school uniforms and whatever. So I think it is really important that we support those women, though. And sometimes it's not always about money, but money is also important. Now, I was reflecting on this and I was looking around the room and I was thinking, gosh, there's an awful lot of very senior people from agencies mobilizing a lot of money. And maybe we do owe it to ourselves to seriously look at how much of our money actually makes it to communities. I am quite pleased to say that the Irish government is at pain in the neck when it comes to that. And we will always be like, what's the difference for the community? What is happening with the community? What's happening with women? But really, maybe we should sign up to some voluntary code that a certain amount of our money always makes it to the grassroots level. Really? I think there was a comment directed sort of to you. Do you want to answer to it? But anything else that you want to say as well? Okay. If you want to repeat your... This is for you. I just want to write for parents. And Esteele was just asking if it would not be worth the investment of mobilizing the youth and mobilizing through the Red Cross society to be prepared for any future like you, extreme weather events, especially in the tropical region. So that people know, donors know what kind of materials will be needed. So you don't have a sort of Puerto Rico situation happening. Thank you. I'm really sorry for a young girl to be like a forgetful. I'm sorry. Yeah. Because back in Cuba, we are not the ones who make decisions. We are DMC, DMO. As volunteers, we just follow what they tell us. Like for the response, we just go to the response with the instructions and all. But I think that is a very good point. But maybe you can, you know, make more suggestions and say, this is what we want and we feel it's necessary. Yeah, okay. Good. Thank you. Sheila, sorry. You also had a question, but yeah. Yeah, I have two things to say. One is that usually when you have women's groups at the community level, they feel very disempowered when they are by themselves. But when they are part of a network and they begin to share their ideas and strategies, they become more powerful as they aggregate more and more. So one of the things that we do in SDI is give women an opportunity to make representation that strengthens their sister's hand.  But then her friend who lives in the next city says, you know, I did this with my mayor. You don't do it with your mayor? Oh, it makes a lot of difference. So over a period of time, we've developed a wide range of strategies by which we support each other in representation. We support each other with ideas that work and we network with different networks to sharpen and deepen what poor women's voices want to say. And I think the important thing here is to do that. The other very important thing is to help donors understand the things that they do that don't work. We spend a lot of time documenting things that come to us from top down in terms of accountability, in terms of things. And then we make fun of all the mistakes they make because you can't keep being punitive to poor communities and grassroots NGOs for the things they do and not be accountable yourself. And so we have many, many people who are long-term donors who now treat us entirely and sit with us when we do contractual agreements on who will do what. And I think the time has come for that kind of thing. And so if there is a way by which those of us from the ground and those who are donors help others develop this insight, there can be a partnership. And that's our attitude, you know? We are all trustees of the public resources that will pass up and down. And so we need to develop new ways of holding each other accountable. And I think it's very important to make sure that a large amount of money actually goes to communities. I am aghast at how much money spent in consultants, designing projects, and then the piddly amount of money that goes to actually what the project is. It's shocking to me. I have a change. Thank you. I didn't have any question directed to you, but I can say something about when it comes to climate information services, how indigenous knowledge is being integrated together with the scientific knowledge in sharing that. And of course also doing that increases the trust that people will have in the climate, scientific climate information that goes to them. Just to give an example of what we question once when the science people, the Kenya Meteorological Department came to share the climate information with the local people. And in agreement, they also gave what they observed, you know, the indigenous knowledge, what they observed in the environment. And they said, oh yes, actually there's drought coming because we observed camels are actually aborting naturally. And then we wondered, oh, how does it work? They say naturally the camels says that there's a bad drought coming. And to prepare themselves, they actually abort. So that is local knowledge, feeding into scientific knowledge. So it's good to appreciate both sides of knowledge. Thank you. One thing I would add is one thing the private sector is really good at is measuring outcomes and measuring results and performance. And what we do is the Kellogg company in the space with some of the examples I've shared and much more is not philanthropic. We're doing it because we know that it's good for our business to have healthy, resilient communities. But more importantly, with that, we're measuring the outcomes and the impacts and ensuring that it's actually having focused where we're sourcing from and with the communities who are benefiting from that. And together with us, learning and sharing that back up the chain as well so we can leverage it in other places. So for us, it is very focused on impact and outcomes that are shared. You have the last word as a panelist. I think outside by, I want to respond to a little bit there, but she has responded to it. But I think we are partners in our own development. I think that is very key that immediately you come from a growing area, you come from everywhere. You need to know that developers are with yourself and they're a partner within that development. Perhaps she probably taken also the donors and also the same society that at the level, at the initial level, I think it's about time that we also know this one to say that we need to involve everyone who's a stakeholder within climate change. Climate change doesn't affect you only, it affects all of us. Everyone has got the role to play and another person in the community has got the role to play. Even if he's old, he's aging, but he's not aging, he or she is ripening. You can see the lady here. If the young child in the school, if we communicate climate change issues, we need to start there also. We are building a future for ourselves. That's a lot for ourselves because we are getting old. But for them and for the direction you come. So if you can tell the young ones say, this is what must happen or this is climate change, they will tell their fathers. They will actually empower their fathers and their mothers and everyone in the community. And that becomes a powerful tool for all of us. That's it. I'm still saying that sustainable partnership with practices is very key because of bureaucracy within our government. You know very well. If we can, in this negotiation, push for a bigger partnership with local, local sustainable partnership, it's very key for us and block. I think I will stop there. Okay. Thank you so much for you. And I really think this has been a wonderful discussion. Excellent panelists. And they've responded very well to what they've heard from you from the floor and their own thoughts. And just to pick up on what Pagale was saying, it is true that we are all involved in our own development and we should all have a voice in that. Now I'm pretty ripe at this stage. I mean, I recognize the point you're making. The more we can involve young people, the more they will also, in their own families, have conversations with their parents who might not, so it is extraordinarily important that we also have very young people engaged in this as well as Esther and her generation and others. These developments in climate days are a wonderful opportunity to hear a diversity of voices, to listen to those who rightly feel they are not sufficiently listened to and not sufficiently supported and not sufficiently understood in being in the front line of the issues and the problems. And I love the way you spoke about the traditional knowledge and the role of elders, Agnes, and I very much take that point because we've seen the mistakes that have been made and we've heard a number of them even in this conversation here today. If we can only influence the form of discussions of climate, of COPs, I think the more we can do that, the more we can try and bring this energy and commitment and passion into the COP itself, the more it will be people-centered and that is what Fiji wants of this COP under their presidency. So let's just try and ensure that we bring some of the spirit of the development days into the formal climate talks as best we can. Some of us can hopefully have more access than others but I really do feel that if we can ensure, for example, a robust gender action plan that recognizes the importance of the participation of grassroots women, of local and traditional knowledge, of the experience that we've been sharing here and if we can value as we have the role of the private sector in partnership, in an appropriate partnership and the lessons that have been learned and need to be learned, the way that big institutions like the World Bank need to take their responsibility to really turn around the way of doing and listen bottom-up locally. And I like the fact that you've said you link with Constance and I know you'll go and talk to her afterwards because that's what it's about. It's about really trying to learn from each other in a way that will ensure that we have taken responsibility for our own development, all of us, and that we do it in solidarity and in an understanding that it's those who are closest to the problems who really understand them. And those tend to be people in vulnerable countries at grassroots, it's a very climate justice idea, it's what my foundation reminds ourselves every day that this is what we're trying to work to and make people more conscious of. And there is an injustice in climate change and that we also have to bring out and that is affecting those who are more vulnerable disproportionately and they need access to finance, they need access to decision making, they need access to the resources that will help to build resilience. And so it's been a great conversation and great comments from the floor and I've really enjoyed it and I feel energized for the COP. I'm gonna win there tomorrow and do my vest with my elbows. Thank you. Thank you.


In this section, I'll explain another important concept which is derived from the concept of capital asset pricing model CAPM and that is the security market line. So when you draw the equation which we have just discussed that explained the equilibrium level of the expected return on a certain security, you can get the value of you can get the security market line. So firstly, we need to understand what is meant by the security market line. So security market line basically is an investment evaluation tool which is derived from the concept of CAPM capital asset pricing model or capital asset pricing model. We have just discussed this in detail that this is a risk-return relationship for a specific security when we take a security or an overall market index as a benchmark from the market. We have decided to go for it if we have decided to go for it. So in this, we account for the expected return, we account for the excess market return, we account for excess return on that particular security and when we plot the equation, the line which you will get is called the security market line. Now, if we look at the factors on which the security market line depends, the first one is the time value of money.  So the utility or satisfaction I have to derive from spending right now, I am postponing it. Suppose if I am investing my money for one year or two years, I am separating my money, I am separating myself from the money which I have, if I am investing for one year, I am going away from it. I am not spending it immediately. The satisfaction which I will get from spending right now, to compensate that satisfaction, I need some return. And that return will be equated to the time value of money. We call that particular return time value money, and that is basically the concept of time value of money. We have to count the time value of money when we are discussing the security market line. We are trying to understand it. And the second important thing is the risk premium. You are taking risks again. First, you are spending money. You want to take advantage of that which we call time value money. And second, you are spending money and taking risks. So the risk premium. So these are the two things we account for to define the security market line. Now, if we look at this particular equation, this is the measure of risk. And this is the excess market return. And if we take different values of this particular thing, then when we plot the data from the market, that you took the information of excess market return, that you know the risk-free return, that you are expecting, that you will get expected return from an investment in a certain security. You will be able to estimate those values. Now, if you plot it, you will get the security market line. So this line explains the equilibrium in the capital allocation, capital asset pricing model. And if we plot it, then you get the security market line defined. Now, I'm going to show you the graphical demonstration. So this is the graph of the security market line. You took different values, like I just told you, you need a total of three values. You need data to understand the overall movement of the market. As a benchmark, you will take any standard or index for that. Like we will do an analysis in Pakistan right now. If we will use the capital asset pricing model, then we can take KSE 100 or index values. You took that, that would give you the value for RM. And similarly, we take the value of T-bill return, what will you get on that? 60 days, 30 days. The state bank quotes its data on a daily basis. You can open the website and see. So from there, you will get the value of RF. You have to calculate market returns, you have to calculate risk-free returns. We will show you the difference between the two. You will get an excess market return. You can take an excess market return, you can take a certain security. You can subtract the return from the return. You will get an excess return from that particular security. With the help of these values, you will estimate the line. You will come up with a security market line. I have just drawn it here. The slope of it, we have drawn it like this, with a certain data. The intercept is zero. You saw it here in the equation. You can see that in this equation, we do not have the intercept term. The slope value is defined via the excess market return. So it means that if you do not have the intercept term here, it means that our intercept value is zero. You can see that our SML is passing from zero. So this is our SML. Risk-free, risky asset will be more. Your beta, i.e. the slope value will be more. In that case, it will be something like this. It will pass from the origin. But the big slope means that it is more steep. The slope means that it is a more risky asset. So it could be something like this. It could be something like this. I am calling this A. I am calling this B. A is telling us that any security market line, suppose for A, but we can say that if we look at the slopes, they are different. B has a greater slope. A has a lesser slope, which means that B represents the security and the security market line is more risky. It means that its beta is higher. It means that its slope is steep as compared to this one. So the security market line is derived from the formula, the equilibrium, which we defined to represent the equilibrium to explain the capital asset pricing model to express it in terms of equation. Now, if any security is not on SML, what does it mean? Suppose we are talking about this J point, so if we take any security values, the risk, the risk premium, the beta values, and we have the value of J on this point, that is not optimal. This particular level of risk which J represents, the risk premium you should ask for is higher corresponding to point M, but the risk premium you are getting is at a certain level of risk, that is lower. That is not an optimal point. So if any combination, any point is lower than your security market line, then you will get that inefficient point. That is offering too low expected return. Now, similarly, this particular thing will be against the principle on which the CAPM is based. We will say there are rational investors who explain CAPM to them and they have a lot of information of the market. They decide on their basis and they always go for the efficient combinations. If they go for J, then that would be the corresponding expected return, that is too low, so they would not go for J. They will only go for the combinations that fall on the security market line, which we have discussed right away.


Hi, I'm Zor. Welcome to Unisor Education. I would like to talk about rotation, in particular uniform rotation, with constant angular speed. I think this particular theme is not paid a lot of attention during the regular courses of classical physics, so I would like to spend some time on concepts of this rotation, and especially rotation, which is relative to another rotation, which is kind of complicated, but nevertheless it needs to be addressed. Now this particular lecture, and many others actually, are part of the Physics 14 course presented on Unisor.com website. I suggest you to watch the lecture from this website, because it contains lots of notes. Every lecture has notes, basically like a textbook. The site is free, no advertisement, so feel free. Okay, so again, our ultimate purpose of this particular lecture is to learn something about rotation around some axis, whereas this axis itself is rotating around another axis, something like this. Well, these axes are considered to be parallel for simplicity, and obviously I basically consider the plane, which is perpendicular to these axes of rotation, and everything will be actually happening inside these planes, which I will use my white board, obviously, to represent. So z coordinate is always equal to zero. Now before going into complexity of this relative rotation, let's just again, maybe one more time, maybe it's a repetition, but still it's important, address a couple of concepts related to rotation. In particular, angular speed, velocity vector of rotation, and linear speed. Now, first of all, angular speed. If you are having an object which is rotating, let's say there is a radius r here, it rotates uniformly. Now what does it mean? It means that the lengths of the arc covered during the time t is always proportional to time t with the same coefficient of proportionality, and that coefficient is called angular velocity. Now, in other representation, if this angle is phi of t, which describes location of the point on the circle, on the trajectory, then I can say that this is position, basically, it defines the position of the object. Now, obviously, this function can be differentiated by time, and that means that I'm basically trying to find instantaneous average speed from moment from t to t plus delta t. During this time, my angle moved from phi of t to phi of t plus delta t, and if I will subtract one from another, that's the angle difference, and that's basically how much my angle has increased during this delta t moment, and if I divide it by the time, which is delta t, actually, I will have average speed from t to t plus delta t. And if I will use the infinitesimal delta t, I will basically get my first derivative of the phi function. Now, I assume in all the problems, which we will consider, I assume that this is equal to constant, in which case phi of t is equal to omega t, if at the moment t, I was at angle zero, which is here. So, this is our normal assumption, and this is basically what angular velocity is. We will measure it in regions per unit of time. So, in this particular case, for instance, if my full circle is accomplished in the time t, then my angular velocity is this. So, this is the time which it takes for objects to go one full circle, and one full circle is 2 pi regions. So, this is my... Now, if, on the other hand, object makes n rotations per unit of time, that means the angle would be 2 pi times n and per unit of time, so divided by t. So, if I know that I'm making, let's say, 25 rotations per second, then t is equal to 1 second, and 25 rotations would be 25 times 2 pi would be 50 pi, and that would be my speed in regions per second. Okay, so angular speed we got. Now, going from this picture, if this angle is phi of t, then from geometry, you know that the length of the arc is equal to r times phi of t, where phi is angle in regions, always regions, remember, not degrees or anything. Okay, so that's plane geometry, obviously, of the circle, that we have to know. Now, if this is true, then I can always find the average speed during which I have covered this particular distance, l, right? So, that's the distance divided by time. Now, again, as in case of angular speed, what I should actually do, I should take, what's my l of t plus delta t? This is the distance I covered by the time t plus delta t, subtract l of t and divide by delta t, which is t plus delta t minus t. So, my distance increment, I divide by time increment, and that's my average linear speed as I'm going along this curve, how much real distance I have covered along this curve, if I measure it during the time delta t. And if I will divide one by another, that's an average speed. And again, if delta t goes to zero, I will have my instantaneous speed along this trajectory. Now, obviously, since this is r omega t, and I have, this is my derivative of this function, so my linear speed would be equal to r times angular speed. So, this is my linear speed as I'm moving along the curve. Now, what is the real velocity vector in this particular case? Well, velocity vector is a vector which is directed towards my direction of the movement, and it has certain magnitude, and how do I obtain my velocity vector? Well, first of all, we are talking about the system of coordinates. So, let's say this is x, this is y, this is position. So, what's my position vector of time t? Well, if this is r, and this is phi, or phi is equal to omega t, then I can say that my x coordinate is equal to r times cosine of angle phi, which is omega t, and my y coordinate is equal to r sine omega t. So, that's the position vector. Now, we talked about many times, if I have a motion, this is basically a definition of the motion. This is how my motion occurs. I have a function of time for both coordinates. Now, if I want to know the velocity vector, well, that's the derivative of the position, right, which is minus r sine, and inside would be w sine of omega t. That's my derivative from r cosine omega t. Now, in inner function, outer function, so the derivative of the outer function is minus sine. This is just a coefficient r, and in the function, I have to have the derivative of omega t, and that would be omega. And here, similarly, I will have r, I will have omega and cosine of omega t. So, that's my velocity vector. Okay, first of all, what is the norm, what is the magnitude of the velocity vector? Well, that's x square plus y square, right? The velocity is a vector, and if I will have x and y coordinates of the vector, the square root of x square plus y square is the magnitude, right? We have a vector, this is x, this is y, the magnitude, the Pythagorean theorem. Okay, so r square, this square plus this square. Okay, obviously, it would be square root of r square omega square sine square of omega t plus cosine square of omega t. Now, this is one sine square plus cosine square, regardless of the angle, and the square root of this would be r omega. Now, look at this. So, the magnitude of the velocity vector is equal to linear speed of the vector as it moves along the curve. Well, that's not a surprise, obviously.  So, that will be zero. Now, what does it mean? It means that vector of velocity is perpendicular to vector of position. Position vector is here to the point. So, velocity is tangential. So, that's basically all we wanted to know about the rotation. Angular velocity, linear, sorry, angular speed is better. Linear speed, because these are scalars. They're not vectors. And finally, the velocity vector, which can be expressed in these coordinates, and we know that this vector is tangential to the circle because it's perpendicular to the radius. Now, let's talk about relative rotation I promised in the very beginning. So, here is the picture. So, this is a fixed center, fixed to the earth, let's say. Now, this is the road, which is rotating. It has radius r and constant angular speed omega. Now, let's call this point A. So, I will use omega A here. Now, I have a point B. Now, this is a point around which my disk can actually rotate. Now, it has a radius r, lowercase r, and the angular speed is also constant, but it's different. So, my task is basically find out the position and velocity of point B. Now, what I will do is just use exactly the same approach as I did with rotation of one particular object. But now, I will have to do basically the combined motion, which I can define one of them separately from another. And then, if you remember, if you have one, let's say, system of coordinate and another system of coordinate, which is moving relative to the first one, I can always find the position of the point in the original one if I will add this to this. Right? So, all I need is how my origin of the new system, of the moving system moves relative to this one as long as the axes are parallel. So, that's what I will use. Okay. So, as the time goes by, what is my position vector for A? It depends on time. Well, obviously, my system of coordinate is related to this O, right? And let's assume that in the very beginning, my A is on the x-axis. So, initial angle is 0, in which case it's equal to r cosine omega A t r sine omega A t. That's my coordinates. Okay. Now, let's talk about point B. Again, we will assume that point B in the very beginning as t is equal to 0 is here, horizontal. So, if I will have position of the point B relative to point A, point B relative to point A. So, I assume there is this system of coordinates. This is lowercase r because that's the radius of the lower cosine omega B t. Now, I'm using its own rotation and r sine omega B t. So, that's position of point B relative to system of coordinate related to center of the disk with axes parallel to these ones. So, all I have to do is, if I wanted to find coordinates of point B in original system, unconditional, it's basically coordinates of A plus coordinates of A, B. Because vector from here to here is equal to vector from here to here plus vector from here to here, right? Which basically gives me the expression of coordinates of the point B in original fixed system of coordinates. So, this basically represents my relative rotation. It's rotation over rotation. This rotation is relative to this rotation. Now, this combined motion gives me, well, obvious formulas.  That's my x coordinate and the y coordinate correspondingly with the sine. Now, I can find the velocity of this by just differentiating by the time t. And I will have the velocity. And let me try to explicitly do this. So, velocity would be velocity of point B relative to original system of coordinate. Obviously, it's, again, it's equal to the sum of velocities. But anyway, let me just differentiate this.  That's my x coordinate of the velocity. And my y coordinate would be, so I will have sines there, right? So, it would be r omega A cosine of omega A t plus lowercase r omega B cosine of omega B t. What is this at moment zero? So, whenever my disk is here, at moment t, my disk is here. That's what my A point and my B is here. So, what happens in this particular case? Well, my velocity vector of zero is equal to zero and zero sine of zero is zero.  That's the magnitude. Well, that's not just a magnitude. This is basically the vector itself. I have x and y coordinates. But what's interesting is what's the direction of this vector? The x coordinate is zero, right? So, the direction is obviously this. What's also interesting is that this is a sum of two things. This is the vector of this movement relative to zero. And this is this movement of B relative to A. So, whenever we start the motion at t is equal to zero. I never just started. My connection between O and A move almost vertically up, almost straight line, right? And connection from A to B also move straight up. So, basically it's like we have an old uniform motion. Let's say you have a platform and moving, let's say, straight. And then the person on that platform moving in exactly the same direction. You basically add the speeds, right? We were covering this before in relative motion material. So, this is exactly the same thing, but applied to rotation. Because whenever they are aligned this way, I can always say that these are directed along the same direction. And that's why it's just plain addition of their linear speeds. Because the linear speed is vertical. Direction is vertical and linear speeds are basically adding together because they are in the same direction. Well, that's all I wanted to talk about as far as the relative rotation is. This is maybe a little bit more involved than whenever you're considering the uniform motion along the straight line with constant velocity. But in many aspects, the uniform rotation, which means omega is constant as we are considering and probably all the problems which we will deal with, we will have rotation as a uniform motion, most likely. It's equivalent in some way, but instead of the regular velocity you have to use the angular velocity. And then the analogy would be quite obvious. All right. That's it for today. I suggest you to read the notes for this lecture. It's like a textbook. After you have listened to this lecture, that would be very easy reading for you. That's always helpful. And that's all on Unisor.com. The direction to this lecture, by the way, is from Unisor.com. You have physics 14, then mechanics, then part of the mechanics, which is called kinematics. And then you have frames of references. And that's one of the lectures in this particular section. All right. That's it. Thanks very much. Good luck.


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