While actress Sandra Bullock maintains a huge real estate portfolio, she has a tendency to sell quite a few of her properties too. At the end of 2022, she had sold one of her California homes, a stunning 6,000-square-foot ranch in San Diego County for $5.6 million. Tucked away from busy Los Angeles, this sprawling property sat on a 91-acre law surrounded by mountains and palm trees. The spacious and private estate was built in a Hacienda style, a main home boasts four beds and six baths. While else on the property, there's a guest house ideal for when your family or friends stay over. Out back, the grounds offered an Oasis-style saltwater pool and hot tub, located near the dining and lounging areas. No wonder.


Well, my dear students, the course is Labour Policy of Pakistan and the topic is Marxism. Marx is of the view that the consciousness of those who earn a wage or salary would be modeled by their conditions of wage slavery, leading to a tendency to seek their freedom or emancipation by overthrowing ownership of the means of production by capitalists and consequently overthrowing the state that upheld this economic order. My dear students, for Marx, conditions determine consciousness and ending the role of the capitalist class leads eventually to a classless society in which the state would wither away. Now let us move on to discuss the point of view of Marx that the Marxist conception of socialism is that of a specific historical phase that would displace capitalism and precede communism. Dear students, the major characteristics of socialism are that the proletariat would control the means of production through a worker's state erected by the workers in their interests. Economic activity would still be organised through the use of incentive systems and social classes would still exist, but to a lesser and diminishing extent than under capitalism. My dear students, for Orthodox Marxist socialism is the lower stage of communism based on the principle of from each according to his ability to each according to his contribution while upper stage communism is based on the principle of from each according to his ability to each according to his need. The upper stage becoming possible only after the socialist stage further develops economic efficiency and the automation of production has led to a super abundance of goods and services. Marx also argues that the material productive forces brought into existence by capitalism predicted a cooperative society since production had become a mass social collective activity of the working class to create commodities but with private ownership production or property creates little bit relatively lesser value. This conflict between collective effort in large factory and private ownership would lead to a revolution. Hope you have understood the topic. Thank you very much.


So, I'm going to talk about the study with colleagues here at ICTP, Ricardo Parnaty and Fred Kukarski and Tim Stockwell at TCMWF. It's a bit strange for a talk on decadal variability given by a person from an institution that doesn't do decadal studies by mandate, but of course we do a number of things which are related. And so my idea was to see whether we could say something about the decadal variability from basically what we do at TCMWF, we do reanalysis and we do seasonal predictions and longer sets of reforecasts. So just a few slides to start just to summarize where we started from and of course these things have already been discussed, some of them just in the past couple of talks so there's no need to spend too much time. So we have discussed the hiatus in global mean temperature and so, first of all, we can look at it in terms of the decline in the trend of annual mean, global mean temperature. And for example, if you use the Hadley Center, the Hard Crew T4 data set from the IPCC report, you can quote a trend of about 0.26 degrees per decade from 84 to 98 and almost flattening in the following 15 years. However, it's also been reported that this hiatus has a seasonality. You see much stronger if you actually look at the northern hemisphere winter. For example, if you look at the picture on the left hand side from Trenembert et al in nature climate change, you can actually see that actually if you look at the basically cold season in the northern hemisphere, you actually have a slightly negative trend in surface temperature. And even more so, if you concentrate on what happens in the northern extra tropics, then the decrease is even stronger. Now, we have heard a lot of discussions about the role of the PDO or IPO and in particular, we have heard from Dr. Kozaka about this very nice pacemaker experiments, which have actually shown a very good reproduction of the strands and one thing that perhaps she didn't mention was the fact that not only in this period they managed to reproduce a lot of the pattern and the overall amplitude, but also they managed to reproduce at least part of this seasonality with, again, the strongest hiatus being during the northern winter. However, if you actually look at the observations, you can actually see that the seasonality is even stronger than what is actually simulated in this particular experiment. And if you look, for example, at regional levels, you can actually see some discrepancies, which, of course, you may expect because of the chaotic nature of the response in the extra tropics. So one question is, is there a missing ingredient in simulating the seasonality and if you actually think about the global energy budget at the surface, and you do an annual mean, for example, this is a result from era interim, then, of course, what is very noticeable is that the regions where the ocean loses heat to the atmosphere are mainly concentrated in the regions of the western side of the ocean, the regions of the western boundary currents and this actually loses heat mainly, of course, during the northern winter. So a related question is, what is the role of the variability in this region in actually modulating the changes in near surface temperature? So as I said, we don't do the KDAL simulation at tcm.gov, but we produce the analysis. So I looked at some data from the era interim, reanalysis that now covers from 1979 onwards and then I looked at the set of reforecast that we use to calibrate our seasonal forecast system. The latest version is called System 4 and to calibrate this seasonal forecast, we have done reforecasts every month, starting from January 1981 and you can then add the operational forecast and every sort of continuous set. In particular, for if you consider the December, January and February season, we have runs from the 1. of November. In this case, the DJF season will correspond to forecast months 2 to 4 and for this we have 51 member ensembles in the reforecast. So it's quite a large set and basically we used it to estimate the internal variability arising from basically the internal spread within these ensembles. We have sufficiently long records so we can cover basically the latest transition to the hiatus. So we computed trends and we tried, since of course there's the issue of where actually you put the limits of your trend and the issue is that if you put it in 98, as many people do, then it's really the year of a very strong El Nino. So you may really get very large numbers or very small numbers simply because you start from an El Nino year. You get a more consistent estimate of trends if you actually run a 5-year running mean over the temperature first, which is roughly the main period of an answer cycle. So you get something which is more related to the Kedal modes. So we computed these trends from various quantities that you will see from 84 to 98 and then from 98 to 2011 in various areas. Basically an area just excluding the polar cap south to 70 north, the tropical belt to 20 and the northern extra tropics in various regions. And the first thing I wanted to check is this. If we make the hypothesis that the main contribution to the IATOS comes from this natural internal variability of the climate system including the PDO, including other possible, then a main contribution will come basically from a reduction in the heat transfer from the ocean to the atmosphere. So let's now take the, basically, the air entering fluxes and you actually plot, basically, the net heat flux into the atmosphere, which would be basically some of latent and sensible heat, the upwelling, long wave radiation from the surface and the absorption of solar radiation, which actually doesn't play a very big role in winter, then can we see IATOS? And the answer is yes, we can see it. These are plots starting from 1980. The red dots are individual yearly means and the blue dots are five year running means. So you can clearly see that the much stronger positive trend in the fluxes correspond about three watts per meter square per decade and after 1998 this flattens to about 0.6 watts per square meter per decade. And if you convert these numbers into some temperature trends using a simple, basically radiative equilibrium hypothesis, then you get numbers which are not very far from these estimates from the hot-coated data. So there's a consistency between the fluxes and the observed surface temperature. Now these are yearly means if you look at what happens during the northern winter, DJF, this again is 17.0 to 17.0 south and then you can actually see that consistently with the temperature record the trend in the fluxes is actually becoming slightly negative in the last 15 years. Okay, then you can ask where is this signal coming from and you can actually compare these two regions which have roughly the equal geographical size the tropics 20.0 to 20.0 south and the northern extra tropics 20.0 to 17.0. And again you can look at the total heat into the atmosphere from the tropics and again you see the Ayatos, you see it's the effect of dedicated variability in the tropical Pacific. But if you actually look in the northern extra tropics then you see a much stronger signal and a complete flattening of the heating into the atmosphere. In order to cut the story short you can actually find out that most of these signal come from the latent and sensible heat. And what we know is that latent and sensible heat are strongly modulated by the circulation by the intensity of the winds and by the capacity of the northern circulation to what we call there over warm ocean during winter. We wanted to explore this particular aspect and a few years ago we tried to link basically the observational definition that Mike Wallace and collaborators gave of the so-called cold ocean warm land pattern which is basically wave number two pattern that brings warm air over the continents during winter with the prediction of thermal equilibration theory which has been discussed by a number of authors. And basically what this theory says is that you can have basically two states of this wave number two pattern in one phase you actually have the highs over the ocean and therefore you reduce the heat exchanges and you have basically the atmosphere equilibrating to the surface temperature contrast or a force mode which is actually this one where you actually have a strong advection of cold air over the warm ocean you extract a lot of heat from the ocean and then this heat is actually advected over the continent. So we define this cold pattern actually using the wave number two component of the net surface heat flux in this way basically is the net flux out of the ocean in this region minus the flux into the land over the continents and if you actually look at the time series of this particular index over this last 35 years you actually see that in the last 10-15 years there has been a downward trend so we wanted to see whether this was actually related to the hiatus so we first look at how this pattern was simulated in the system four model and so we computed covariances of this index with the number of variables and in particular you can see for example in other intensification of near surface winds over the northern ocean this extracts more latent and sensible heat flux and then this actually turns into warm anomalies over the northern continents. So then what we said is okay probably worry too much about the details now we have this index we can compute it from each ensemble member every year we are 51 ensemble member and then we can somehow composite in this case is actually a weighted average basically those members which have very good representation of the variability of this particular index and those who actually have a very poor representation of this particular index in particular ensemble members do not simulate the variability of the car pattern and then we can construct ensemble means from these weighted averages and we compare what comes out in terms of for example surface temperature and this is what happens so you see here in red dots the time series of the observed car index that you have seen and in green is the time series of the index from the ensemble that reproduces the analysis is called NSA and you see that it fits quite well with the red dots and then we have this N0 which is basically an ensemble that doesn't reproduce almost at all the variability in this now since these are seasonal forecasts that are actually initialized with the same SSD in the first few months the SSD don't change very much so if you actually look at for example the most identical between the two ensembles so these two ensembles have basically the same SSD in the tropics so what they differ is simply the response in the extra tropics in one case you get the response similar to what has happened in the other case you have near zero response now let's look now at the two meter temperature over the northern hemisphere in this two ensemble we plot the two curves so you can see that the strong increase before 98 is well reproduced in both ensemble and then you see a decrease again in both ensemble but if you actually look at the black curve where there is no extra tropical variability you actually have I would say a flattening of the temperature if you actually compute a trend from the one that has the right variability it actually has a decreasing trend and in fact if you plot the difference you can see that just the difference in the extra tropical response accounts for a decrease basically a negative temperature trend over the northern extra tropics of about 0.1 degree per decade so we have talked about this missing 0.2 degrees overall on a global scale if you actually concentrate on the northern hemisphere in winter about 0.1 so half of that can be explained by the extra tropical signal and in fact this estimate it is quite well with the recent estimate by Sapfioti et al and he is here in the audience so I think he will talk about this probably tomorrow now the interesting thing is that well it is interesting to look at these integrated quantities but what about the regional effects and the regional effects are in fact quite strong over the land so this is the change between basically the beginning and the end of the last 15 year period this is the change in geopotential height from the reanalysis this is the difference in the trend between let's say the good ensemble and the bad ensemble again remember this is almost the same SST they only change in terms of extra tropical variability this is the difference in 2 meter temperature in global level you see this very strong warming actually over the Arctic but in general quite a strong cooling over the northern continents in fact if you just average for example over Europe you get actually a cooling of 0.34 degrees now if you look at the basically the pattern which is attributable to the change in this wave number 2 component then you see that this continental cooling is pretty well simulated and in fact for example if you concentrate here over Europe you see that the ensemble with the correct variability reproduces the cooling of 0.49 centigrade the ensemble with no variability in this wave number 2 actually gives a slight warming of 0.21 so at the regional level there is a very strong difference now but another interesting feedback maybe in terms of the feedback on the ocean circulation and we've actually seen that the ensemble with the correct tropical variability actually simulates a response in terms of near surface winds over the Pacific that tend to actually slow down the direct circulation and therefore the subtropical circulation so this may actually be relevant for the mechanism that Ricardo described in his earlier talk about the possibility of a feedback of the isotropical response on to the PDO itself ok? so coming to conclusions so although the recent reduction in global warming trends can be detected in both the tropics and the extra tropics the seasonality is which is strongest in the DJF season if you actually trust in the winter in fluxes you come to the conclusion that it's mostly originated in the northern extra tropics there is still a component from the tropics but the fact that it's so strong during winter to explain it you have to take into account what happens in the extra tropics so we've seen that changes in the phase of this wave number 2 kaul pattern and the associated heat flux anomaly gave a significant contribution to the slowdown in northern hemisphere warming trends during the winter of the last 15 years in many overland and basically by subsampling the different members in the ECM that we have system 40 forecast which have basically the same tropical sst anomaly and very very similar also extra tropical sst but by construction different terms of strong or weak variability then we can account for about 0.1 degree per decade in the IATO so it's about half of what you actually need to be explained and we have also seen this possible feedback on the wind circulation that we are going to explore in the future thank you


Maybe if you're seeing this on YouTube and if you haven't checked out the first three parts Please go check those out if you're watching this on YouTube. It's very cut-up version We can only three four five ten minutes of very cut-up footage So if you'd like to see full-on cut versions you can head over to patreon link description below and the pinned comment And at the end of this part we will go into a review and talk about the movie as a whole So please wait to the end and talk about your mom as a whole.  What can we do? I did it too. So I killed him. And they're like, whoa, wait, we didn't want that. Without any ambition, without any ambition, I feel like I'm the only one who can do it. I'm hungry. I'm hungry. I'm hungry. What? I'm hungry. I'm hungry. I'm hungry. I'm hungry. I'm hungry. I'm hungry. I'm hungry.     We're all one along with the small effort. We're united together. And yet, we are united. We have seen the change. But I don't believe it. No matter who is next to us, they are the same kind of criminal. Yes.  The size of the money is wrong. Small and medium large. The size of the house is big. Everything is extra large.  Who is going to kill them for this? We are doing the wrong thing. You can rule the law. I shouldn't take the law in my hands. Why are there police officers in the court? There are. It's been 57 years. These mistakes are happening. We can finally get rid of them. We can get rid of them and come out. We need to protect them. We are worried about them. What we have seen now is the crime of being given to me by the first company. Or else, I will kill all the criminals in my website. This is the picture. He has removed it from the traffic. He's reformed to India. That's right. Everyone's afraid. If they break the law, he's going to kill them. Sir, the whole thing. Look at the way he opens the phone line. That truly boggles my mind. It's very, very common. Pissing on the side of the street. Oh yeah.  IP address which is a dial-up connection phone. We found it, sir. Where is it? It's in Thiruvalli. You know Tholjingapuramal Coventry, sir. Look at this, sir. It's the same person who complained about five murders, sir. This is his phone number, sir. What? It's the same person who called and called the complaint. Look at the number on the phone. I hope all of you in leadership are taking note of this. The best way to get what you want is to threaten people with death. It's a good deterrent for sure. It is, yeah. That's how I raise my kids. Distract. So subtle. More fully. Just to remind you. It's right. That's his stuff. The hair spray for Rambo. This is the one, sir. Help me. I'm fine. P.Ramanujan. What's your father's name? Parthasarathi. How many people have killed him? None of them. This is the scene we've seen. They're gonna put him in the thing. That's good. Pretty amazing. He had that contraption ready. I'm there for him. He must use it quite often.  Yeah. It's like Han Solo getting froze. Nice. We loved this. We can't kill him. Objection, your honor. He's trying to get a new name for himself. He's trying to get a new case. No, no, no, no. He's in the scene of the scenes where the MPD's gun was shot. It's a big scene. I'm so sorry. This is the scene where the shooting of Rambo's shooting of the Rambo. You've seen this scene. I'm sorry. This is the scene where the Rambo's shooting of Rambo's shooting of Rambo's shooting of Rambo's shooting of Rambo's shooting of Rambo's shooting of Rambo's shooting of Rambo's shooting of Rambo's he's in the scene of the shooting of Rambo's somebody shooting Rambo's they're while they're Hey, how are you? I'm fine, I'm fine. What are you doing? Ambi is the only one who likes it. I'm going to the honeymoon. Don't torture me like I'm going to the movie theater. Everything is happy. Excuse me. All the ladies are sitting here. Don't keep them somewhere else. Do you have any customers? Go and sit here. Is there any problem? No, doctor. Then there is an important matter. I don't want Anni to come after that. Ambi should be here. Yes, doctor. Even now, he was drinking with me. He came with me to the next seat. He's completely alright, doctor. No, he's not. Wish you a happy married life. Thank you, doctor. That was as-built fun. You can't expect anything else. No. I'm glad he actually didn't get fully tattooed. I'm glad he wasn't actually healed or anything. Yeah, no. That would have been disappointing. He was like the Anyan or whatever the character was hiding. Absolutely. I much prefer that. It's ridiculous, but it's fun. At least they kept the theme of that going throughout the entire- Yeah, it would have sucked if it had tried to be really serious and then went back to the other. It just, the whole thing worked the way it is. I don't know if they scrapped it or not, but this could do with a remake. Absolutely. It doesn't even have to be in another language. No, just do it with Vikram again. Absolutely. They didn't have the technology that they needed to. Yeah. They could have better fight choreography, the technology. So this is one that's like, it was made probably before it should have because of the concept. Yeah, the concept was ahead of its time. But then they didn't have the technology or the other stuff. Even though I thought they did a good job, it's just, they could have done even better fights and cooler fights. Yeah, and I do like there is a moral to the story in there. There is the moral compass in there. Obviously going to the far extreme of everybody do right and be right or you're dead. Well, they've done that with a lot of stuff, like in terms of somebody who takes absolutely the Quran too seriously or the Bible too seriously and goes by old biblical law. You could do that. You could do this with the Bible. All over the place. It's in V for Vendetta. Yeah, it's all over the place. Yeah. And then making the perfect, he reformed India. There's more taxes today than there's ever been. Everyone has stopped smoking. Yeah. It's fantastic. Yeah. It was fun. I enjoyed it. I'm glad too. He did a great job. She did a very good job too. He does a great job carrying the film. Especially his breaks in between of like going from onion, and Ramo. Like the transitions from onion and when he has to go from one and like you have to see the switch in his face. Yeah. I thought he did a very good job. Like I said, I think he like if he even did like you could do a sequel or whatever just like we're remaking the same film. With him again. Yeah. Just with better technology, better. You could choreography. And you could absolutely sequel this. You could point out that he stayed married and he kept it under wraps for a long time because he didn't want to be found out. But injustice became too much. Yes. And he had to release himself again and hold everyone accountable now. Yes. Yeah, you really could. Ramo was fantastic. He's got the best song. He's got the best song and man is he just the quintessential cheese. I need to go do some yo-yo later. Absolutely. Loved it. R-E-M-O. Yeah. So it seems like this to right this is like this director's M-O in terms of like one his songs are big and extravagant. Yeah. The music, Harris's music was great. We've seen that a lot. He likes these big extravagant like in all the songs. Yeah. Even though we haven't seen it yet. We've seen all the songs. I'm expecting this style of film. Absolutely. And Vikram's the lead in that. I can't wait to see it. I mean, we've been seeing that a long time. I don't even know where I can find it. But yeah, same director. So that's kind of what I expect is that he does these big masala over the top films. Entertainers. Hopefully will entertain you. Yeah. Don't look for the logic really in it. Just look for going in and try to have a good time. Yeah. Laugh. And entertain. I don't know who that one guy is. Yeah. His sidekick, his wingman. Is it Prakash Raj? No. Prakash Raj played the cop. That's why we know him. Yeah. We've seen Prakash Raj a lot. Yes, we have. We've seen him quite a bit. Not based on those thumbnails. Yeah. I don't know who it is. That was him. Yeah. We've seen him in a ton of things. I think like if this was like a remake, you could make it really scary. Yeah. You could turn this into a horror film. Yeah. Or it would work as a masala, right? It would. Because like you have the nice romantic part going over the edge. Yeah. And you could do really good fights. I thought they were good, but they weren't entertaining. But no. They weren't entertaining. I wanted a lot more like the last fight scene in the other fight scenes in terms of like bone breaking and really good. I did love the cables though. He loved the cable fights. Yeah. Cable fights were, there was a lot of cable fighting. A lot of cable fights in this. And obviously like some of the bad CGI or the whatever. It's kind of endearing though. It could just, I mean you'd know when it came out. Yeah. And you know like it was probably good for its time. Right. But seeing in 2023 you're like, oh this could be really good if you gave it a sequel. Yeah. And if you made Anian an absolutely terrifying character. Well I mean maybe they will do, because like I said I'm pretty sure they scrapped the idea. You guys can tell me if that's wrong of, because it was announced but then all the remakes did terribly. Yeah. Vikram Vada or whatever. They just all, I bet a lot of them got shelved. And so I think it got shelved. Yeah. But he's also the director of Indian which is Kamahasan which the sequel is coming out next year, later this year. They've made a sequel and that film came out in the early 90s. I mean the late 90s. So maybe they'll do a sequel to Anian. I would love it. Which I think could do with a sequel. Sure. And I think it could. It absolutely could. I'd rather see that than a remake. I really would. I'd rather see a sequel. Yeah. And make Anian absolutely terrifying. And I thought he was scary, like a lot of it like the jump scare. But you could just do it with today's technology and today's editing. Yeah. Obviously Vikram, you could keep Vikram there because I think he did a very good job.  Yeah, I love that. Every time he appears. Harris of music was great as always. Cinematography was really impressive in a lot of spots. Yeah. Really impressive in a lot of spots. For the time I thought. Nearly 20 years ago. Really good. I'm glad it was entertaining. Yep. Because you know sometimes you could watch films that a lot of people like what we ran into with Debong. You know a lot of people love that movie and like just like it's a big masala and we just didn't work for us. There's times you've sat through movies and you're just it's excruciating and it's like you're walking through molasses and you just please God let it end. Yeah. Not even really. I was enjoying every minute of this. Yeah. A lot of those still have like the illogical stuff that this one had. The illogical stuff. But as long as you keep me involved and interested and there's also other stuff. Because there was some obviously Vikram gave good performances and I actually think a lot of the supporting cast actually was like pretty grounded. Yeah. I was going to say they did a very good job of making it silly when they needed it to be silly and making it grounded when they wanted it to be grounded. Yeah. And that helps a great deal. I think a lot of the issues with this film is that it's actually just dated. Yeah. Now. That's all. Like because you could. But that actually adds an endearing quality to it. It does. It'd be interesting to see like if they did a sequel. Can they bring Remo back now? Right. Because like he's extravagant and that was like very early 2000s cool guy. I know. The stereotypical. Very of the time. Stereotypical. Cool guy. Very of the time. They gave him cornrows and his. Which is. You can and you could make it, you know, comment on the fact that he's dated. Yeah. Yeah. I don't know how they do that. I don't either. But also does he have more personalities as well? You could explore like. You could. So many different personalities with whatever is an umby. Yeah. But I enjoyed it. I thought it was a good time. I'm glad I had a good time. Because it could be really bad if it's not and you sit for three. Three hours. It didn't feel like a three hour film so that's good. It didn't. I enjoyed it. I enjoyed every minute of it. Sometimes a lot of fun. Two hour. 20 minute of film. Yeah. It says a lot that we could sit for three hours. And I never was looking at the clock hoping it was going to be over. I was really enjoying every minute of the film. Yeah. So it was a lot of fun. I would love to see more from Vikram. I think he's a very real talented actor. I do too. So you guys can let us know for Vikram, for the director, what should be the next Damol film that we do a watch along of. So please let us know all that. And whenever the sound went bad we're sorry. I'm sorry. And I hope it caught it on the camera.


Welcome to the journey. Today, we're going to talk about how to include webinars in your content strategy. With the COVID-19 pandemic started, it wreaked havoc on small business owners and you've likely even think a lot about how to increase your revenue in your online businesses too. And with the continuing uncertainty of the times, it's more important than ever to offer maximum value to your clients while improving your bottom line. And with that in mind, adding webinars to your content strategy might be the next logical addition to your online business. And we want to share with you everything that we've learned about how to successfully integrate webinars into your sales funnel. Yeah, I mean, for me, webinars has been part of my life for five years. And I got to say, when the pandemic happened, I didn't know if that interest would maintain the same or increase and definitely have seen it to be very valuable to educate entrepreneurs during this time because small businesses just like yours still need the information and the education that we were providing. So I encourage you to take this time while people are online now more than ever to reach them with this channel, the webinar channel, and definitely record them too. Because that way, if people can't join in live, one thing we do is we send them a copy of that recording if they registered. I love that. And one thing we always like to do with these videos is start off with the why. So why webinars? Well, to start users love video content. And I'm a huge statistics guy. So let's let's do a stat. According to word stream, 51% of marketing professionals worldwide name video as the type of content with the best return on investment. These also said viewers retain 95% of a message when they watch it in a video compared to 10% when reading it in text. And that is incredibly powerful. And it's a lot more entertaining to take in a video than it is to read a long blog post pitching a product. And this is especially true when your audience is getting the chance to learn something new. Absolutely. And another thing, webinars provide value to your customers. People want to solve their problems and good webinars help them achieve some pretty quick wins. And while you don't have to give away all of your secrets, don't do that. Helping your customers with something for free makes them wonder what they would receive by paying you. Yeah, absolutely. And it helps you prove your expertise, prove your chops. Let's let them know that you have what it takes. Imagine having a captive audience to share your knowledge with.  You have 15 to 45 minutes to dazzle them with how much of a professional you are. And this is critical if you want to turn a prospect into a customer. Why should they give you all of their hard earned cash? Well, a webinar gives them a chance to get to know you, see if they like what you have to offer and hopefully trust you enough to pay you. Another great thing about webinars, high conversion rates for sales of the people who sign up for webinars, 46% actually tend according to 99 firms. And Neil Patel says the best webinars can generate conversion rate averages of 19% from the people who watch. So when you're just starting, you might need to host multiple webinars and tweak your message to achieve rockstar income. But once you nail your presentation and have a recorded webinar, you could set it up to run on autopilot resulting in your own personal ATM of continuous income. I'm all about that. But say you're doing webinars, you're about to do webinars. How do you take your webinar from good to great? And I think it starts off with not assuming you know what your customers want or need. And this one is critical. You need to get in the minds of the people you are serving and determine what they want and need. And the fastest way to do this is ask them, then deliver what they ask for. Now a super popular way to do this is by creating what's called an ask campaign. And all it is is sending out a question and a single question.  And that way you can start to determine what's on their mind, what questions they have, what are some of the questions that you can start to answer. Let's also talk about the importance of using intriguing headlines and titles. So after picking a topic to present your webinar on, come up with a title for your presentation that tells your audience why they should care. And keep in mind that punchy headlines capture attention. Yeah. And with with webinars, it's really easy to make it overly complicated, but you really want to keep it simple. It's tempting to create that complicated webinar offering, offering all of your bells and whistles, but resist the urge and focus on just one thing. Stell seminar recommends one topic and three supporting topics or sub topics for the best result. So I can do a webinar and teach someone how to build a website from start to finish. That's a lot of content to kind of focus on, but I can do a webinar on how to create the perfect about page and really focus on that. And the people that watch that webinar will walk away with way more than if I just info dumped a bunch of stuff at them. Yeah. So definitely keep it simple. Also be unique and bring something interesting to the table. Don't just find a similar webinar and recreate what a competitor did. You need to offer something unique to your audience. Remember, these are your potential customers, right? And so what would set you apart and compel them to register for your webinar?  Yes, I absolutely love that. But now let's talk about what a good webinar sales funnel looks like. So once you have your recorded masterpiece, this is what your next steps should look like for the best chances of making sales for your efforts. Starting off with promoting the webinar with blog posts and podcasts on social media, even on YouTube, anywhere you could promote it, you want to get as many eyes on it as possible. All your promotions should lead to a webinar registration page that explains what the viewer will get out of the presentation and bonus. When they register, they will give you their contact information, which you can use an email marketing later on in your customer nurturing journey. Yeah. Once someone registers, they should be redirected to a thank you page that includes the date and time of the webinar. And if you're using an automated webinar program, your thank you page could redirect to your website or your webinar link to play the presentation automatically. And this is the part of the webinar sales funnel where you present the webinar. It's the moment you've been waiting for. Now you're the star, your opportunity to wow your audience and give them so much value that they feel compelled to pay you for more. And while presenting your webinar, you'll hit your audience with your offer and you'll address the frequently asked questions as well as any objections to making a purchase. And after the presentation ends, send a follow up email reminding your attendees of the offer and give them a chance to watch that recording. Again, in case they missed it or they want to see it one more times. And you'll also want to send everyone to your offer page that makes it incredibly clear why your audience needs whatever you're selling for anyone that buys, deliver on your promise. For everyone else, start retargeting strategies and attempt to get more sales that could be emails that you sent out or targeted ads or just extra tips and tricks to get them into your funnel that much further, but then go back one step to step one, rinse and repeat. All right, that's a wrap. I know we covered a lot, but hopefully it showed you that there is potential with using webinars to make more money in your business. So leave us a comment below and don't forget to subscribe to our channel. While you're there, ring that bell to get these episodes first. This is the journey. Good luck and happy sales.


For more videos and people's struggles, please subscribe to our YouTube channel. One year ago, on June 6th, five activists and human rights defenders were arrested in India in a highly publicized media charade and slapped with serious charges of inciting violence and sedition. These arrests mark a growing trend in India of state-sponsored repression and witch hunts against activists and dissidents. Keys of suppression and arrests have witnessed a notable rise in the present regime of the far-right Hindu-conservative government led by the Bharatya Janata Party. The BJP came to power in 2014 and was recently re-elected in May this year. Apart from activists, this government has been cracking down on minorities, indigenous people and oppressed Dalit communities. In this environment of repression, the police action around the Elgar Parishad, also known as the Bhima Kuregao incident, was a new low. On January 1st, 2018, the Central Indian State of Maharashtra witnessed massive violence by far-right forces against the Elgar Parishad Conference. The conference, which began a day earlier, was organized to commemorate 200 years of the 1818 battle of Kuregao. This battle is considered to be a victory of the oppressed over the oppressors. The ruling upper caste Peshwas who belonged to the Brahmin caste, which is the highest caste in the Indian caste system, were challenged by Dalit Mahars, who was serving in the British Indian Army. Dalits belonged to the lowest-rung in India's caste hierarchy and continued to face oppression in modern-day India. Post this violence, instead of arresting Samaji Bhide and Millind Ekbote, the far-right leaders behind the incident, the local police began hatching a conspiracy. The first victims of this conspiracy were union activists and workers of Reliance Industries. These workers were arrested under the Unlawful Activities Prevention Act for alleged links to the armed Maoist movement in India. Shankar Gundey, Ravi Marappale, Baba Shankar Banguri, Satya Narayana, were arrested on 12th January and were members of the Mumbai Electricity Employees Union. They were active participants of the wage-hike struggle in Reliance Industries. The union office was sealed off on 19th January, which made it clear that this was a planned attempt by the state to decimate this union. As the fabricated police story against his migrant contract workers began to crumble and get exposed, the police took the conspiracy a step further and framed it as a Maoist attempt to kill Indian Prime Minister Narendra Modi and overthrow the ruling government. The police began targeting prominent activists who were active in various peoples' movements and struggles against state repression and corporate exploitation. On June 6th, Sudhir Dhabli, Rona Wilson, Suryendra Gaddling, Shoma Sen and Mahesh Rao were arrested by the police in connection to the Elgar Parishad Conference. On August 25th, 2018, in another Pan-India police crackdown, Suda Bhardwaj, Arun Farera, Vernon Gonzalez, Gautam Navlaka and Varavara Raur were arrested. All were accused of being part of a Maoist conspiracy to overthrow the government and they were all charged with the Unlawful Activities Prevention Act, which is a colonial era law often used by the state to silence dissent. Now let's take a look at the activists who were arrested on June 6th and their role in people's struggles. Sudhir Dhabli has been active in the struggle for the effective implementation of the Scheduled Caste and Scheduled Tribe Prevention of Atrocities Act and has also been active in struggles against the caste system and caste-based discrimination in India. After the 2002 anti-Muslim riots in Gujarat, he launched a bi-monthly Marathi magazine called Vidrohi. He is also the founder of the Dalit Liberation Organization called Republican Panthers. Dhabli was previously arrested in 2011 on the same charges of belonging to a Maoist organization, but he was acquitted after 40 months in prison. Shoma Sen is a former English professor at Nagpur University in Maharashtra and she has also been affiliated to several women's rights organizations in India. She is also a member of the Committee for the Protection of Domestic Rights and Women's Organization in Nagpur called Sthri Chetna which campaigns against issues such as violence against women and dowry debts. Mahesh Raut is an indigenous rights activist from Maharashtra's Gaciroli district. He is part of struggles demanding forest land rights for indigenous communities, particularly in areas affected by mining projects. He was also a fellow in the Prime Minister's Rural Development Program. Surendra Gadling is a human rights lawyer and activist who had been campaigning for the rights of political prisoners in India. He had fought the case of Arun Farera who was charged of being a Maoist. Gadling was also handling the case of the disabled political prisoner Jeehan Sai Baba who is also currently in prison. Rona Wilson is a political activist and was the public relations secretary of the Committee for the Release of Political Prisoners in Delhi at the time of his arrest. He has worked in the cases of various political prisoners including Essayar Gilani who was arrested in the case of the 2001 attack on the Indian Parliament and he was also later acquitted. Rona Wilson is a PhD scholar from New Delhi's prestigious Jawaharlal Nehru University. All the five activists continue to remain in prison. The comrades, family members and the members of various people's movements in India continue to stand behind these activists in their fight against the state conspiracy.


into some cases of linear momentum conservation where the system that we are considering is of a very special type where the mass that is there in the control volume may change with time. So, we will see that how we may take care of that. So, let us take an example of something which is quite common say motion of a rocket. We will have a simplified picture of what it is, the whole idea is to get the essential feel of how you can use the Reynolds transport theorem to analyze the motion. Let us say that you have a rocket shell of some shape, products of combustion, they leave the rocket with a velocity say v e relative to the rocket and let us say that m dot e is the rate of mass flow of this one. So, essentially what happens the rocket has a structure plus there is some fuel inside which undergoes a combustion process, the products of combustion come out and these create a so called thrust on the rocket which takes it to a great height. So, the basic understanding is well rocket motion has been studied from may be junior high school level and you see the level of explanation changes. So, when you talk about that how a rocket moves may be when the Newton's laws of motion were introduced the question if it was asked to you your answer was by Newton's third law of motion. Now, after that may be if you when you went to a bit of a higher level school studies if it was asked may be you could have said by conservation of linear momentum. And now we will see that precisely what it is about and well it involves conservation of linear momentum it involves the Newton's third law of motion but those are very qualitative statements. We will see that quantitatively how you can describe that what should be the parameters which would dictate the velocity or acceleration of the rocket. Now, what we are assuming is that whatever the mass flow rate that is coming out that is coming out at a constant rate. So, this is a constant that is what we are assuming it is not difficult to maintain it as a constant because if the reactions are occurring at a constant rate it is possible that the products also come out at a constant rate. Now, what about the mass of the rocket? The mass of the rocket is like when you have an initial mass say m0 is the initial mass it is the mass of the structure plus fuel plus whatever was there initially. Now this would decrease with time because some mass is leaving the rocket. So if you consider a control volume which includes the rocket then that control volume has mass which is variable which is not a constant. Now let us try to write the expression for integral form of the linear momentum conservation for this rocket. So we identify a control volume let us say we identify a control volume something like this and we try to identify all the forces which are acting on this control volume. So what are the forces which are acting? Let us say that at any instant m is the mass which is there inside the control volume. So m is a function of time and gravity is acting in this direction. So what are the forces which are acting on this? So you have the weight it includes the weight of the structure and the weight of the other materials fuel etc whatever is inside then there is nothing called as thrust force. See even in the free body diagram what forces you show? What are the external forces which are acting on it? So thrust force is something which is like which is something as a consequence of this ejection. So when you show this ejection you cannot show a duplicated thrust force. So it is basically there is nothing called such a thrust force. So what is the external force which is there? There is air resistance or whatever atmospheric resistance. So we call it a drag force. So there is a drag force. So if the rocket is moving in this direction let us say that the rocket is moving in this direction and let us call it vcv that is the velocity of the control volume because we will assume our control volume to be this moving control volume and which may be accelerating that is the velocity may change with time. So if this is the direction of the velocity then what should be the direction of the resistance or the drag force? It should be downwards. Let us say that capital D is the drag force. So when you have such forces the rocket seems to have some sort of resistance one is this weight another is the drag force and it has to overcome that resistance in moving upwards. The reaction provided by this flux, momentum flux that comes out that should be the prime driving force for moving it upwards against these resistance forces. Now let us write the linear momentum conservation for this moving control volume. So the linear momentum conservation. So what we have is resultant force-integral of say rho dv is like dm into a relative that is over the entire mass which is there inside is equal to that is the unsteady term and the finally the flux term. So if we write the scalar form of this we may write it in a scalar form because here everything is occurring in the y direction that is the y direction say. Then we can write the y components to have the corresponding scalar forms. When we do that let us try to see that what are the different contributions of different terms, forces we have identified what should be this one. So what is a relative, a relative was acv plus there is one a small xyz plus the terms which are related to the rotation. So let us write those so these are the terms which are there. So we have to see that here since there is no rotation the last 3 terms are not important. What does the second term represent a small xyz it is the acceleration of the fluid with respect to the small xyz reference frame which is the rocket here. So what will be that see the products of combustion whatever these are coming out at a constant velocity. So there is no rate of change of that velocity time rate of change of that velocity as viewed from small xyz reference frame that means this is 0 okay. So only acceleration of the control volume linear acceleration of the control volume that is there in this term and because it is assumed to be like a rigid body. So all points are having the same linear acceleration and that acceleration is nothing but dvcv dt. So this becomes as good as so a relative is a constant which is equal to dvcv dt that comes out of the integral. So the integral of dm becomes m so this becomes m dvcv dt. We are writing it in a scalar form as in the y direction so I am not writing it in a vector sense only plus and minus will indicate whether it is upwards or downwards. So keeping that in mind we have this m into dvcv dt now this m into dvcv dt the important thing is this m is not a constant it is a function of time that we have to keep in mind. Coming to the right hand side you see that there are 3 different things which could potentially be function of time but here rho is we are assuming rho is not a function of time. In reality because of some compressibility effects rho could be function of time v small xyz this is definitely this is what this is velocity of the fuel or the products of combustion with respect to the control volume and that is we are assuming to be some constant. So that means that is not changing with time and v is the volume of the control volume that also we are assuming to be the fixed one that is also not changing with time. With those assumptions this term will be 0 then the last term so the last term again it depends on how this velocity is distributed over the area through which it is coming out. Let us assume that it is a uniform velocity distribution if it is a uniform velocity distribution then v small xyz is uniform over this da so then how this may be simplified so you may take out v small xyz out of the integral first and that is minus ve because it is in the negative y direction then integral of v small xyz dot eta da into rho that is the mass flow rate so that is m dot, m dot e okay. So we have isolated this one first out of the integral the remaining is the mass flow rate and the proper dot product is positive because it is a outflow. So if you now write what are the forces for the force contribution you have minus d minus mg right these are the forces which are acting. So keeping that in mind we may write the equation of motion for the rocket as minus d e minus mg minus m dv cv dt is equal to minus m dot e ve. Of course m dot e may be written in terms of ve if you know the area of the cross section through which this jet is coming out so if that is a e then rho e rho into a e into ve is the m dot e okay. Now this equation is allowed not sufficient to solve for the velocity of the control volume as a function of time. The reason is that you do not know the mass as a function of time so which fundamental principle should give you the mass as a function of time the conservation of mass. So let us write the integral form of the conservation of mass. So conservation of mass again left hand side is dm dt of the system right hand side is the partial derivative this is basically this is nothing but what this is rho dv rho dv is like dm. And because of writing convenience we are writing in place of rho dv dm that is all the same that is elemental volume expressed in terms of elemental mass nothing very special about that then plus integral rho v so what is this let us write the first term that is what is this first term let us call it partial derivative with respect to time of the mass of the control volume right that is what it is mass within the control volume. And the next term is what is this so how many flow boundaries are there only one flow boundary is there through which fluid is flowing and what does it become this is nothing but m dot e this outflow rate of outflow. So we can say that mcv at time so if you just integrate it like this say like dmcv from say at time equal to 0 m equal to m0 to a given time when it is m is equal to minus integral of m dot e dt from time equal to 0 to time equal to t like that this is just like ordinary differentiation because this could be function of time and nothing else because the spatial effect has already been integrated average doubt. So only the effect that is remaining is the time effect so what do we get from this equation we get m minus m0 is equal to what now it all depends on whether m dot e is a constant or is a variable. So here in the problem it is given that it is a constant so if this is a constant it comes out of the integral so it becomes minus m dot e into t. So now we have 2 equations one for the mass conservation another for the linear momentum conservation and these 2 equations may be together solved. So you have one equation for the mass conservation which is at the bottom and the one for the linear momentum at the top. So many times for just for solution convenience let us say if you neglect the drag force if you neglect the drag force it becomes a little bit simpler differential equation to solve but even if you do not neglect it it is something which you may easily write only thing is that one has to keep in mind that drag force is not a constant drag force in reality is a function of the relative velocity between the rocket and its surroundings.  Now when you have the drag force so we should keep in mind that in reality this is a function of vcv at least that we should keep in mind this in reality is function of vcv that function may be quite complicated because it really undergoes a wide range of variation of speeds. So the air resistance is something which also varies quite significantly but at least we know that what are the parameters on which it should depend mostly. Now if you as an example if you neglect the drag force not that neglecting the drag force is something very realistic but it just tends to give you a first hand feel of what it is. So if you neglect the drag force if d is neglected then what do you get at the end? You get dvcv dt is equal to m dot e ve we have divided both the sides by m0-m dot e into t. So this gives a sort of clear picture that what are the driving parameters. So if dvcv dt is positive that means the rocket is accelerating upwards and what is helping it to accelerate upwards is basically the rate of ejection of the products of combustion. So if that is at a very high rate you can see that it becomes a helping term and more and more the products of combustion come out the denominator becomes what? The denominator as time increases the denominator becomes smaller and smaller and you would have the rocket itself not like existing as if this becomes 0 but this will not become 0. This will this I mean when you are considering this you are thinking that products of combustion are leaving but the structure has some weight which is there. So but in a limit it is lot of weight is there because of the product because of the fuel which is inside and once that is combusted and that is leaving it is actually a lot of weight leaving from the system because it requires a huge amount of or huge rate of momentum that requires to be generated to give it a force. So misnomerally this is sometimes known as a thrust force keep in mind this is not an external force this is just because of the action of the fuel the products of combustion which come out. So you may give it a name thrust again like just like there is nothing called as a centrifugal force when you consider it to be an externally applied force this is also like that. So it is an action because of some motion of the system so it is not just like you have applied this external force. So this external force tends to become more important as the products of combustion come out with higher and higher velocities and the mass inside gets decreased. So this combination is quite good because that is what it is helping and weight is of course not helping it and if drag force was there it would have also not helped it that would also be against the motion. So now if you want to find out that how this velocity changes with time you may simply integrate it. So integral of dv Cv is equal to m dot e ve integral of dt by we are integrating it from time equal to 0 to time equal to t. You can complete the integration quite easily this is very simple integration let us just substitute may be m0-m dot e t equal to x. So minus m dot e dt is equal to dx so this integral becomes the limits of integration. So this becomes ve ln of m0 divided by m0-m dot e t-gt this is say the velocity of the control volume at time t assuming that it is 0 at time equal to 0. So it is possible to see that how this velocity is changing with time like it is useful to get some physical picture of what it is. So I will advise you that you please try to make a plot of this as a function of time and see the behavior at different times. You will see that the behavior at different times will be interestingly quite different. So at least this analysis gives us a picture of like if you want to find out the velocity of the rocket what should be the methodology. Now if you have a complicated drag force say the drag force is given as some k into v Cv square say as an example that the drag force is there and it is equal to k into v Cv square. So you just substitute in place of that k v Cv square only thing in the analysis will be that there will be another complication in the integration. So it will may be bit more difficult for integrating but the principle remains the same. So the important thing is what is the differential equation of motion and we could realize that what are the basic principles on which we can write the differential equation of motion. So this illustrates an example of a case when the mass inside the control volume is a variable. Let us take another example to where we may encounter such a case. Let us say that you have a tank filled with water or maybe partially filled with water whatever say filled with water up to this much and there are some wheels which are there with the tank. Water comes out of the tank like this say with velocity v e relative to the tank this is the relative velocity just like the rocket case this is also a relative velocity. The initial mass inside it is M0 this includes the mass of the water plus the mass of the tank and again it is the water is assumed to come out at a rate of M dot E. I am trying to draw an analogy between this problem and the rocket problem that we have done. So the some mass is coming out let us say that it is mounted on a frictionless surface not that that is a necessity. If there is some friction you have to figure out that how the friction is influencing its motion. So now you realize that because of the water coming out of this there is some sort of force or thrust so to say but it is not an external thing it is just a effect of this water coming out. There will be a force in the towards the right on the tank which will try to make it move and it is basically a fundamental principle of a propulsion system. So it will try to make a system propel with a particular velocity that itself might change with time. Let us say that you have this height of water at the instant that you are considering is H. The question is that how far this situation is similar to the example of the rocket that we have considered and how far it could be different. Let us try to find the analogy and try to address a simplified picture such that it matches with the simplified picture of the rocket. So what is the simplified picture again let us say we have considered the control volume like this one which is a moving control volume. So we have the velocity of the control volume let us say it is positive towards the right and it changes it is a function of time. The similarity is clear that the mass in the control volume is a function of time. So if you intend to write the equation of motion what you see? You see that the left hand side resultant force acting on it along let us say now we write it for the x direction because x direction is or the horizontal direction is the direction of motion that will give us a picture of how vcv changes with time. And since this is a control volume which in general may be accelerating. So we have to write in terms of the relative velocities just in the general form of the moving reference frame. So what is the resultant force along x on this control volume 0 right. So you have 0 appears to be even more simple than the rocket then there is no rotational motion and let us say that this fluid is coming out with the velocity ve. So if you just consider it like a case of a rocket then it is like you write –m into acv or acv is dv cv dt. Let us first write it like a equation of a rocket and see that how it should be different from that. So for the rocket whatever we wrote let us just write it the right hand side is like what? It will become –m dot e into v square right sorry v not v square. The assumptions are that you have a uniform velocity profile at the exit. So that like you do not consider the variation of v small x, y, z over the area through which the water is coming out. And this m we know is a function of time and what equation tells us that is the conservation of mass. So you have so this should dictate that what should be m as a function of time which you need to substitute here get the velocity of the control volume as a function of time right. So in that way it should not be greatly different from that of the analysis of the rocket that we have presented. Now can you tell that like other than considering the frictionless what are the flaws in this? First here v small x, y, z that is ve this is not a constant right. In reality this is not a constant. When can you assume this to be a constant? Actually there are certain things which many times we do which is not exact but we sometimes make an approximation and say that although it is not exact we are following that. And that approximation sometimes is justified sometimes it is not always approximations are not bad. There are situations when approximations may be justified. So in general you are very correct that this ve is not a constant but when can we assume that this ve is roughly a constant? Area of the tank is so large as compared to the area of this one. So that the rate at which this drops is very small maybe at a very high velocity this is coming out but the area is small. So area into velocity whatever that is same as area of the tank times the rate at which it is coming down. If you consider it to be approximately described by that from a1 v1 equal to a2 v2. So then this v1 is very very small. So the rate at which this drops is so small let us say we are considering a time range which is not very large. So if you consider a time range which is not very large and the area of cross section of the tank is quite large as compared to the area of the nozzle through which or the orifice through which the jet is coming out then it is not a very bad approximation that ve is a constant because if this height is a constant clearly ve will be a constant. If this height is a variable it will be a variable but in general we know that ve is not a constant. So if ve is not a constant how will you treat that? See it becomes a quite a complicated problem then because now if you say that this area is somehow not is not somehow very very small as compared to the area of cross section of the tank. And let us say that if you take a streamline which connects this connects any 2 points between these 2 and write the Bernoulli's equation for say ve that ve you may write in terms of an unsteady Bernoulli's equation but again it will not be a straightforward as the unsteady form of Bernoulli's equation that we have discussed earlier because now the reference frame is accelerating okay. So I am just trying to give you the complication of the problem not that you have to just solve the full the complication of the problem with full rigor but at least we have to appreciate that what are the rigors which are involved in even such a simple case like this may be so simple you can have a tank and you have water like we have seen many times that like if you go if you go to a city where the road is being somehow washed by water you will see that there are big tanks like which are maintained by the municipality or corporation and they just have some mechanisms by which water is coming out and so it is it is it is like a primitive way of like cleaning the road and it is not so advanced in terms of technology but see the science is very advanced actually if they want to precisely get a feel of how the velocity of the tank will change with time and you know if the if the person who is driving that cart is very optimistic will say that no I will shut off my motor because with this thrust I hope that that the tank will go on moving but you know the road has lot of friction and we live in a country where optimism is not very strong so I mean he will be in full gear and trying to drive drive that but the reality is that it is it is it is quite a complicated scenario it is it is not as simple as even like unsteady Bernoulli's equation use itself will give a complication because of the variation of V with time and variation of V with time will give the variation of m dot e with time let us say somehow that approximately the unsteady Bernoulli's equation is valid if it were valid then what would have happened if it were valid then this m dot e we would have been able to find out as a function of time because m dot e is a function of V and V as a function of time we could write in a differential form by writing the unsteady Bernoulli's equation between 1 and 2 but that will involve what are the parameters that that will involve that will involve V e and d h d t these are the parameters that it will it will involve so then V e as a function of time will be a function of d h d t so V e will be an implicit function of time because V e is a function of d h d t and h is a function of time and that function of time will appear in this m dot e because m dot e is rho e A e into V e so this will become a complicated function of time but not a constant that we have assumed just now so then in principle same equation but when you integrate it it is not a constant that is going to be there so it will be again a complicated function of time that function of time you have to substitute here the other thing is that what is the other like if you still do that say by doing it correctly then what is the other approximation which is there which is not being taken care of here so one approximation which may be properly taken care of is by properly describing what should be the rate of rate at which the mass comes out as a function of time by whatever analysis now if you substitute here that as correctly say somehow is it complete or still there is some approximation that is already inbuilt here yes which integral this one forget about the other things we are not considering that the tank is rotating with respect to certain axis and all I mean if you want that complications one may add you may have a rotating reference frame in which a rocket is moving or something like that those are very good for academic purpose problem solving you will see that in in some books like in exercise those types of problems are given it is not bad if you practice it at least you will have a skill of using all the terms in this equation but it is not very common to have a rocket rotating in a reference frame and not trying to move up in some way or when it is trying to move up it is always rotating with respect to some axis it is it is not very common so for that is that is just like a hypothetical way of like treating the complexity of a problem but even in what I am trying to convey is even in the simple form it is so complex forget about a complicated form when like it is it is mounted on say a rotating platform or whatever but even like in this case when you have this a small x y z that was not considered in the a relative only this term was considered so a small x y z is something which is the rate time rate of change of the velocity of the fluid relative to small x y z and that is basically related to so it will be like v dot e so that will be a function of time and that will come along with this one so with this plus there will be some term from a small x y z with proper vector sign plus minus whatever so because you are writing along x so the vector sign will be given by the scalar with a plus or minus so that is so we have seen that that is a complicated scenario where you treat all the rigor now again like engineers may not be so happy in dealing with such a complicated scenario but such over simplification also one might not like so if you want to make a compromise now which is like which is not as as good as the reality but it is not as bad as the as the worst assumptions so then what what could give you a guideline of that see if you neglect the unsteady type of the Bernoulli's equation then what is this v then this v roughly is root 2 g h again the assumption is the velocity at one is very small 0 so even if the tank area is very large still here you will have this as root 2 g h there are other assumptions but we will not go into the detailing that we have already discussed that that root 2 g h formula whatever the what are the assumptions which are involved so when you have this as root 2 g h so you can put that in the calculations approximately v is equal to root 2 g h and h is a function of time is like a tank emptying problem that we have discussed in the context of Bernoulli's equations use of Bernoulli's equations that how do you find out that how the height of the tank changes with time so if you have v equal to root 2 g h and if you with an approximate analysis know that how h is changing with time then that can like simplify some of the expression that we are looking for here okay so I would encourage you to set up the proper differential equations for at least taking such an approximation you need not solve it because you will not be able to solve it but at least you set up the proper equation see when we solve a problem there are 2 parts associated with a problem one is a problem formulation that means whenever you are you are being described of a physical problem how can you convert it into a equivalent model problem model mathematical problem this is known as mathematical modeling so when you go for a mathematical modeling of a physical problem you clearly should be having a picture of the assumptions that you are making justifications of the assumptions and if the assumptions are partially justified then how certain things are approximated with that approximation you should be able to come up with some set of equations governing the physical behavior and those set of equations should be in principle closed that means if now if you were a champion in solving a differential equation you could have been able to solve it so these problems are like called as initial value problem that time equal to 0 you know that what is the picture now there is a differential equation which gives the variation as a function of time where everything else in principle is known as a function of time now you have to integrate just it to get the variable as function of time so that is the problem formulation now how will you integrate to get it as a function of time how will you solve the differential equation that is the problem solution part so formulation and solution need not be treated together I mean for analysis formulation is what is very important because these days even if you are not very good in solving differential equations you have many software tools which will do it for you but no software tool will formulate the problem for you because it requires an effort of understanding of the physics of the problem to formulate it so getting the answer is very important but you will invariably come up with a wrong answer if you do not formulate the problem correctly so problem formulation is the heart of the problem solution in these cases so the examples that we have seen we have seen that if there is a variable mass then the variable mass system is something which may be treated in the same framework as that of like as if like a constant mass but what is the problem the problem is that you are basically putting an instantaneous mass within the control volume which is changing with time and many times the complication arises because you are not confident about how this mass changes with time so that complication arises because of the variable relative velocity of the fluid which is coming out which may not be in the control of the designer because whatever here the height is changing with time in certain cases it might be something else now next what we will do we will try to see some other examples where we do not consider the linear momentum conservation but the angular momentum conservation but before that let us write the statement of angular momentum conservation so angular momentum if it was a point mass of say mass m and let us consider a picture like this where you have the origin of the coordinate system you have a point mass m it has a velocity v and position vector is r then the angular momentum is given by r cross m v that is the point mass or particle picture and see if you recall the basic classical mechanics that you have learnt see always when we when you have learnt rigid body mechanics the natural way to learn it is that you have a particle from that you extend to a system of particles and then from system of particles to rigid body because rigid body is a special case of system of particles so up to system of particles before you consider it to be a rigid body it is as good as a unified concept for a fluid and a solid when you come to a rigid body then obviously you cannot have a fluid except for a very special case we have seen that there are certain cases when fluid moves like a rigid body but that is not very common. So up to the system of particles view point like if you consider one mass like this and if you have a system of particles which with a continuous mass then this will be just replaced by r cross v r cross dm v basically integrated over the entire mass. So as if you have a elemental mass dm at so this now is replaced by an elemental mass dm which is moving with a particular velocity at a certain position vector and that is integrated over the entire mass which is there which is a collection of particles if it is a continuous distribution then it is an integration if these are discrete particles these are replaced by summation that is the obvious thing but in principle understanding is same. Now how do you write the angular momentum conservation here so let us say that we are interested to write the angular momentum conservation in this arbitrarily moving reference frame it is better to do that because of what because many times when you are talking about angular momentum there is something which might be a rotating component in the entire arrangement and when there is a rotating component and if you look into the phenomena by sitting on the rotating component you are yourself located on a non-inertial reference frame. So therefore non-inertial reference frame becomes or may become a natural choice for analyzing angular momentum conservation cases but what we will do is we will write the 2 forms separately one for the case which is with respect to a inertial reference frame and another with respect to a non-inertial reference frame to see that what are the distinctive forms in the 2. So if you consider the Reynolds transport theorem again dndt of the system let us say that we first want to do it for a inertial frame first is inertial frame objective is angular momentum conservation. So what should we replace capital N with yes so it capital N is something like r cross mv. Now you have to keep in mind one thing see loosely we write it as r cross mv or whenever we wrote linear momentum mv but you have to keep in mind that the velocity of different particles in the system is different. So when we wrote the linear momentum conservation actually it was an integrated effect so that v was the velocity of the center of mass. So here also it is an equivalent v of the system for which it may be represented by an equivalent r cross mv. If you do not want to do that then simply you can think about it as like dndt of integral of r cross dmv of the system then you do not care that whether v varies from one point to the other. But like this so this is the left hand side so what is this equal to this is basically like so these are elemental angular momentum this is the rate of change of elemental angular momentum and that is summed up over the entire mass. So that is the sum of the rate of change of angular momentum of individual elements so that is the sum of the resultant moment of all forces which are acting on the system maybe couple moment or force moment but resultant moment. So this is like the resultant moment of whatever forces couples whatever acting on the system the right hand side small n what should you replace with r cross v. So you have integral of rho r cross v dv plus integral of rho r cross v v relative dot eta dA and since the left hand side is equal to the right hand side this is the resultant moment of all external forces remember this is all external forces the action reaction does not come here. So the resultant moment of all external forces which is there for a moving reference frame so this we have written for inertial frame when we say moving again moving may be inertial but general moving reference frame. So for general moving reference frame we must have a correction term with this what should be the correction term see what was done for the linear momentum conservation in the linear momentum conservation capital N was substituted as v small xyz m into v small xyz for the moving reference frame. Now we will replace that with r cross m v small xyz so all the terms are basically crossed with another r nothing more than that. So when you have that see the first term is like it becomes the resultant r cross m v capital xyz ddt of that. So that is the resultant moment of all forces because in that inertial frame you can write the equivalent rotational form of the Newton's second law minus a correction integral of dm r cross a relative this is for the mass of the control volume which is instantaneously there and the right hand side you replace v with v small xyz with another r cross sorry r cross we have already taken dv plus integral of rho r cross v small xyz into v small xyz dot eta dA control surface. So you can see clearly the form is same as the linear momentum as if only thing is that every term has been now made r cross pre r cross that is r cross is there before all the terms because it is r cross mv type. Linear momentum had mv now it is r cross with that that is the only change so this is the general moving reference frame. We will stop here and in the next lecture we will see some examples illustrating this thank you.


At Mycroft, we've always been really focused on community. The company was started with a Kickstarter for our first Mark I smart speaker. And then we've now got another Reg CF going on where we're offering shares in the company to the general public. And there's a couple of reasons for that. You know, one of the big reasons is that we have a developer community of north of 65,000 developers out there who are using Mycroft on Raspberry Pi or in our Mark I device or on their laptops or robots or cars or wherever they've installed it. And we want to give those developers an opportunity to invest in the company that they're developing software for and with. And then the other one is just simply egalitarian. You know, the idea that only people who have the inside track in Silicon Valley have an opportunity to invest in early stage tech is really anathema to a company that's based on open principles and privacy in our case. And so we want to make the investment in the company available to anybody who feels that the future of voice includes a privacy component. Visit Mycroft.ai and invest in an early stage winner today.


Why does the government have a target to reduce prison populations by 30% but not a target to reduce violent crime? Mr Speaker, as the member will know, having worked across corrections that if you are seeking to reduce a prison population, that is often the equivalent of reducing recidivism. Many of the people in our prison population are circulating back through, so, if you focus on rehabilitation programmes, that makes a difference. if you focus on having as prisoners exit work to ensure that they are in employment and those things that prevent re-offending then you ultimately also reduce victimisation. That if you are seeking to reduce the prison population that is often the equivalent of reducing recidivism.


Welcome back to Tennis Talk, my name's Cam Williams and I wanted to go through the three things that I learnt during this Australian Open for 2022. A lot of happened over the last couple of weeks and I just want to have a chat about the three things that I learnt. First thing I learnt was that the next generation are closing the gap on the goats. We saw at the end of last year with Medvedev beating Djokovic in the Grand Samp Final, the US Open. Of course Vera beating Djokovic last year as well at the Olympics. The gap is closing and of course Medvedev this year nearly beating Raffer in the final of the Australian Open. Shapa Valov almost nearly beating Raffer as well. The gap is closing very very quickly between the goats and the next generation. They're getting a lot closer. The second thing I learnt at this Australian Open was that Ash Barty is very underrated. Not as just the greatest player at the moment but one of the greatest of all time. She is racking up the records. She's got three slams now, three out of the four. One on clay, one on grass, one on a hard court. One of the only players to be able to do that in the last couple of years. And she could definitely win the US Open, complete the set. Not to mention that. She also won the Australian Open without dropping a set which is a big big deal. She's going to be more weeks at number one than Justine Enon in a couple of months time as well. So she is racking up the records. Now I'm not comparing her to Serena Williams or Margaret Cord or Chris Evert or Navratilova. One of those players who have you know 15 plus slams. I'm comparing her to the players that have won you know five to ten slams in the modern era and have done really really well over their careers and who we consider as some of the legends of the game. And the final thing I learnt at the Australian Open in 2022 was that Rafa is the goat. I mean it's hard to deny that he is the goat right now. Now can Djokovic and Federo catch up to Nadal and take the status of goat away from him? Yes they can but as of right now it's very hard to deny Rafa as the greatest player of all time. He's got more slams than anybody else of course. Weeks at number one all of those other conversations can be had but at the end of the day whoever has the most big trophies is the goat and Rafa is standing on top of the tree at the moment with 21. So it's very hard to see him getting knocked off unless Djokovic comes back with a vengeance over the next couple of months. Let me know down in the comments below what are some of the things that you learnt over the last couple of weeks at the Australian Open? Is there players that you learnt maybe you didn't expect to do well and they've come out of nowhere? Maybe some players that you forgot about that have you know Madison Keyes and Simona Halep who have come out of nowhere or some players that maybe disappointed you? Maybe you thought the players were better than they were? Let me know down in the comments below some of the things that you learnt at this year's Australian Open.