Welcome all and thank you for attending tonight. So now is an introduced Jodi Raze, who is our Senior Consultant with Rural Solutions. She can give us some background on Sheet Connect and introduce, main presenter, Mike Avery. Apart from Jodi's obviously extensive qualification, she's also comes from a very practical background. Jodi grew up in the South East on a family farm and now lives and works a serial livestock property in Central Air Peninsula and is based in our Minnipur office. So I will hand over to Jodi who will give you a bit more of a rundown on Sheet Connect. Thanks, Philippa. As what I said, the program tonight is brought to you by Sheet Connect SA and I'm the Pastral Region Coordinator for that program. Philippa asked me to mention the beautiful photo you see there is actually from our wall on our property. So it's a photo I took in our recent shearing. So just a bit of background about what is Sheet Connect. So Sheet Connect is an extension project run by primary industries and region South Australia looking for opportunities for producers to do practical programs where they can make positive change to their farm production and management practices. And that's focused both in the pastoral area, but also in the agricultural areas of South Australia. If you want to know a bit more about Sheet Connect, we have a Sheet Connect website, so sheepconnectsa.com.au and you can also follow us on Twitter. We couldn't have this webinar tonight or part of the other programs that are presented by Sheet Connect SA without the support of numerous funding bodies. So we'd like to thank them, AWI, Perza, The Sheep Industry Fund and the NRM Board, South Australian Arid Lands and SA Murray, Darling Basin. Just a disclaimer, Perza, from Perza about liability or responsibility for any information that you may hear and is presented tonight. And it's my pleasure to introduce Mike Avery. Mike is the partner at Southern Aurora Wool and has been there for a number of years. He's got over two decades of experience in the wool industry and holds a number of industry positions and they have included being a director at the Australian Wool Exchange for six years. And so it's my pleasure to introduce Mike to present tonight's webinar on forward pricing of wool. Good day. Thanks a lot, Jody. Well, we'll get into it fairly quickly because we've got a number of slides to go through. I'll quickly just give you a rundown of our company. Who we are obviously is Southern Aurora and our job is to provide solutions in agricultural commodity markets. What we do, we offer brokerage in OTC products but also in physical commodities and futures options and foreign exchange. We also do development for Ryman on different OCC products and we have a advisory structure finance wing. We're currently looking at a few other new products. They include cotton, revamping the current cattle contract. Also lambs not on there but it should have said milk rather than cattle. Canola, we're looking at dairy and water at the moment. This is a view of the guys and girls that are involved. We'll move on quickly and get into what we want to talk about is wool and forward pricing. I always like to start with a mission statement or something and that is that the value of certainty is more important than the fear of lost opportunity. I think that's an important place to start because we are talking about forward pricing and certainty in a business that has a lot of volatility. I'll just quickly give you a definition on what is price risk management and the types of contracts and obviously that's key to what you want to hear tonight. Price risk management is all about margin management. It's not trying to pick the top of the market or anything that. If we can do that life would be very easy but it's about managing price and because price is not necessarily the most important factor to a successful business it's managing margin and historically wool like most agricultural commodities are very volatile and that volatility makes forecasting budgeting and cash flow management difficult and affects how business is perceived and also its long-term sustainability. Hedging is a price risk management strategy that's designed to minimize exposure to market risk that's associated with changes in supply and demand and price. Hedging products such as wool forwards they need to be simple and hopefully at the end of this you'll see that they are but they've got to be versatile in their application and it's intended just to reduce risk and increase stability. The types of forward contracts physical forwards you've obviously been accustomed to that come via the broker. We've got the OTC forwards that are based on the AWECS MPGs and that's what I'll be talking about tonight and also hopefully if we have time cover options which you've probably been presented as minimum price contracts. The physical forward contract is where the grower contracts through his broker or an individual exporter deliver their wool sometime in the future to agree specifications. Now as you know with wool those key parameters are micron length strength, vegetable matter yield style and all these present issues because of the relevant primes and discounts that are attached and assessed by the individual purchaser and that's where the downside in the physical forward because the buyer needs to consider all these parameters in factoring his own primes and discounts if wool falls outside those species and the buyer needs to consider those risks involved and formulate a premium discount schedule accordingly. That differs from the Ryman over the counter product is what we're talking about tonight because it's cash settled, it's independent, it's based against the AWECS exchange nominated price guides, it's the midpoint of the north and south MPGs. We do a few bespoke contracts based ex-west for some of our western Australian clients but the ones we're talking about tonight are the ones that are the screen traded so that the bids and offers are visible through an app or on your laptop. They're a wholesale product so therefore it's a business to business where the grower via their wool broker goes direct to the exporter and processor. There's no premium discount schedule attached because they're based against the MPG and the primes and discounts are ascertained at the time when you will sold not against that particular contract. So the grower sells at auction on the maturity date and receives the marketplace premium discount and the profit or loss is then applied to their total account sale whereas they may have hedged 20 bales of wool against the 200 bale clip that they've sold at that time and the profit or loss on that hedge of that 20 bales will be attributed to their account sale. There also is the ability obviously to buy that contract back should the occasion arise. Now we'll just talk about the market dynamics and how the exporter is pricing, the exporter and processor are looking at the drivers of the market and as a producer I think that's what you also need to do when you're formulating your strategies so you can regulate your returns just as the same as the exporter and processor do and they use those forward hedging to manage their margins rather than margin their margins as it says on the screen there are to reduce their risk exposure to adverse market movements. The exporter prices these bids based on their greasy sales or the expectation of those sales and the exporter tends to trade both sides of the market depending on the changes in the supply and demand dynamics. They use it a way to for to to increase their position whether it's a board or sole position based on on where they're going. Processors on the other hand tend to to be to come traditionally from just the buy side where they're looking at that that that pricing basis the sales of their tops yarns and and finish goods. Hopefully you're getting these screenshots in the same order that I'm seeing them that's just a cut of the AWICS daily price guide which comes out the evening after every auction which gives you the price for the spot market of that day and the movement so that's that's available through AWICS every sale day. What you will see on your app and your screen is is what that market the forward market looks at and that's just a screenshot that's up there now of what the major microns are. We do deal from 18 through to 30 microns not all the microns but 18 eight and a half, 19, 19 and a half, 21, 22, 23, 28 and 30 so a fairly wide coverage not always the best way to do things according to the purists because you tend to move liquidity away from from a standard. Those of you who have been in the business for a long time remember the original SFE or City Future Exchange contract. Wool was the first traded contract on the futures exchange going back to the 1960s. There was only one wool type that was traded and that was a 21 micron to everyone. All growers had to look at their own basis and we'll get on to what basis means against the 21 so if you were growing 19 microns you only had a 21 micron contract to hedge. When we developed these contracts the feedback from the grower side was that there needs to be more variety to reduce that basis and exporters have taken that on board and are bidding accordingly. That's just a shot of what the app screen looks like which obviously hasn't got the same detail. The one you're looking at is for 21 microns. Each micron has its own screen so it hasn't got quite the same capability or the same depth that that is applicable in the other screens. Now the other major contract that is that is dealt are options. Now this is usually a topic that has people glazing over because it can be presented as a very difficult concept. It really is fairly simple. It is very similar to an insurance product. What is this guaranteed minimum price contract and whether the price premium is determined according to time, a strike price volatility the current at the money price which is where the futures price is for that time and it is what is termed a put option and what you probably have seen as delivered by your brokers as a minimum price contract and that's what it is. It gives the grower the right but not the obligation to have a sole contract sometime in the future and for this right they pay a premium and just like an insurance premium. The grower chooses the date which is aligned to their projected auction date and he chooses a price level where he'd like to take protection. Now that price level is a big driver of what that strike price or premium would be. The seller of the contract which is usually an exporter will price the premium based on their view of the market, the relativity of the strike price to the current futures price which is the at the money price and the current spot and they'll use the implied volatility and the time to maturity. Now volatility is a complex thing. It is derived well actually the mathematicians that derived volatility guys called Black and Sholes got the Nobel Prize for mathematics so that will probably give you an idea of how complicated it is but it looks at the movement of price over time and has a complex mathematical formula behind it to imply volatility to that market. When I was first looking at futures probably 25 years ago I went to a seminar and was told asked what was the the most volatile commodity that was traded on the world soft commodities market at the time and fortunately wool wasn't the highest volatile market it was the second highest but most volatile was onions. I thought oh well at least I'm not working in onions. These models all incorporate these factors and they guide the buyer and the seller to ascertain where fair value is and where fair value is what the market is predicting the insurance premium should be and as you know is fairly evident the more time you put into a a minimum price contract the higher the strike sorry the the premium will be it's just like if you want to insure your car for six months it is less expensive than insuring it for for 12 months and the same thing about the volatility if you consider volatility like the incident of of accidents and that's why if you are fortunate like myself to have young drivers in the family your premium is much higher than if they're older drivers because the occurrence of something happening the volatility of the chance of an accident is higher for them so it's really not a complex concept if you break it down into into that that idea of it being an insurance product but the key in why some growers use a mixture of both options and forward pricing outright forward pricing is that the option has that upside for the grower where they're just looking to guarantee against an adverse event but are still in the market because they have the option and not the obligation to take up that sold contract whereas you know an outright you have you have sold a contract so you have the obligation to to deliver so it's deliver the wool but but to contract that price. Mike if I might just interrupt you there briefly with a couple of questions so we've got is there is there a general percentage that you find growers contract of the total clip? Yes I'll uh I was I was going to get to that but we'll get to that now usually in a hedging strategy and we'll talk about some of those strategies a little later growers will start off at at shearing looking at their next season and they'll either have price targets or they'll have time targets where they like to hedge forward let's say 12 months out they'll do their first percentage and that might be as low as 5% or 10% of their clip within the first two or three month window then another 10% in the three to six month window and then another 10% in the six months to up to closer to the shearing date and so they'll look at pricing two or three or four times along that curve to a total around about I'd say for those that are actively involved in the contract they're looking at doing no more than about 30% of of their clip you know they're just they're taking their getting that certainty around around some of it and whether that is to of course it's price driven and we'll look at some of those those drivers a little later but if the prices are very very high and well above their cost of production they may choose to have that percentage a little bit higher and where that sits in history but in sort of an average market you're looking around about 30% and Mike you mentioned earlier with the no obligation situation so if something horrendous were to happen in regards to some sort of natural disaster fire etc and you're not obligated to fill those contracts that for an option yes for an outright no you need you're going to be cash settled against that you have a contract that says I've sold for next December 20 bales just like if you had a physical forward contract you've got to meet that obligation an option is you have the option they're the diff the main difference between the two so let's say you you bought a 21 microns are currently say 18 87 so a 1700 option for December 30 cents then you would pay a premium of 30 cents and you have the the option of if the market was to fall below 1700 of of triggering that option and taking that sold futures because it's going to finish in the money if if it doesn't then nothing happens it's out of the money you've paid you 30 cents premium or whatever it was and you've paid your insurance nothing happens a little bit like yeah being happy that you ensured the car but you didn't have an accident but you've got the insurance behind you if you do have an accident you've got there in this case the accident is that the market fell to $10 and you have a sole contract at $17 and so yeah but the the bonus for the option is that should say the price stay at 1880 where it is today for 21 microns then you will have not the if you'd taken a an outright forward contract at $17 then yes you would get for 100% of your clip 1880 if the price stayed stable till December but you would pay out 180 cents against that forward price so you in that case you would have been far better taking a 1700 put option and paying away 30 cents so the option gives you the opportunity to get the upside of the market should stay there and get the upside not just on your total clip the 70 or 80% that you've that's unhedged but also on the 20% or 30% that you did hedge with an option you also can can be involved in that having paid away 30 cents so you're getting no deduction from your from your outright hopefully that explains it yeah that's great thanks Mike it's it's a very you know it isn't an easier easy concept to understand where as you know when you're looking at pricing your your clip with a an outright forward sale what you're doing is is locking in some of your clip at that price and and and saying okay fine and we'll look at some some numbers that are on there later on where where prices are forward and so you you're looking at at basically hedging some of your cost of production against against the forward market should there be there something happen and I guess the next statement really sums up how I would say difficult the process is but of of wading through or navigating the the future and that's Donald Rumsfeld the American Secretary of State once made a quote and said there are no knowns there are things that we know and there are known unknowns that is to say the things we know we don't know but there are also unknown knowns and there are things that we don't know we don't know now that might seem incredibly confusing at the time poor Mr Rumsfeld was was very much derided for saying something until people actually looked at it and thought about it and if you relate that to the wool market then we do have a lot of known knowns we have current and historical prices of wool and competing fibres we have current historical supply and demand we have via the forwards of forward curve and growers know their cost of production so there's a lot of things we actually know or we can get our hands on knowing what we don't what the unknowns that we know are here's a bit of a tongue twister Mr Rumsfeld but they're the future supply and demand and that's going to be impacted by weather price currency global macroeconomics government policy these things that we know happen but we're not so sure about and that's what risk management is all about by trying to wade through those things we we we know that we need to try and get out and one Mr Rumsfeld unknowns unknowns which was about I think probably what was it weapons of mass destruction we we had our own fortunately didn't in impact Australia when the black swan events which are these known unknowns in 2010 we had rift valley fever in South Africa and all of South African wool was quarantined by China so all the demand for wool or the supply that was possible for out of South Africa was there was a moratorium and the outcome we saw in Australia was quite advantageous to us through September of 2010 through to July where you'll see a chart where the market went at that time now not all of that was was on that but that was really something it was a black swan event that pushed the price of wool up because supply globally although Australia is by and far the largest supplier of of marina wool um South Africa is was at that stage a significant supplier into into Europe particularly and entered into into China and Mike we've got a question here that's probably on a bit we were just discussing prior to but it says should the options be used closer to sale of wool or as a tool to use throughout risk management strategy and this growers just said that it has been some advice that they've received from brokers if if the volatility is not so high and prices are low and the projection is prices may go high then then options can be a very good value option again choice for a grower to make because of that fact that they can be involved in the upside of the market at the moment and and there's the question leading to the question the closer you get to maturity uh affects uh the impacts on the on the premium quite significantly so they'll probably look more attractive closer to uh the shearing date then then well into the future because the unlike uh an outright where the the the seller of the option which is usually the the exporter he's he can't put that directly into his export book not the full value of it he can only put a percentage of it and that percentage is actually quite is quite significantly tied to the time factor and the the time is one of the big drivers of the cost of the premium just as as I said if you compare it to um ensuring a car if you're only ensuring for six months it's half as cheap as 12 months in options that's pretty much the same it's not exactly linear but it's it's close to it and uh and so it may it may prove from a price point of view uh better uh to do it close we did one very close to shearing uh uh the other day when the premium was was very low and the strike was was close close to the market but the grower was just here he was he was only six weeks out from shearing we were at 1900 cents but the market very volatile for 21 microns and he was looking just to to take some cheap insurance you know if you look at 20 cents on 1900 cents it's fairly cheap as a percentage uh just in case one of these black swan events uh or uh something impacted whether it be uh currency or something yeah government policy you know there's a fair bit of risk out there in the world of government maybe not just our government but you know if we give an example of of mr trump you know talking about uh trade trade embargoes or a trade war you know that could impact uh us significantly even even though uh we're not directly involved the the kick on from something like that so he was looking at a a very short term option just so uh he he was happy to pay away 20 cents because uh you know if the price of wool fell a dollar he uh he wanted to make sure that uh he had some some cover over some some big event highly unlikely and when something's highly unlikely just like in any insurance business it is the the cost of it is quite cheap so uh it's I think for a grower uh if the price is right options are are a good strategy it's it's just liquidity an issue and and uh and getting close to that fair value model if it if uh if you know the volatility and uh and the time then it's it's easy to calculate using a model to say what is a fair premium and um you assess you know what um and that that premium is driven obviously by price and you might want to just say okay um I'll take a well out of the money option so so a strike price well below where the current level is but I just want insurance in case something uh outrageous happened to the market but I would think on a on a ratio we're probably doing 90 forward prices against uh about 10 of options um when the market was was moving in an upward scale 12 months ago that percentage was probably higher on the options um exporters had a view that the market was was going to continue up and were quite happy to write options at these current historically high levels you know the rider of the option is is really on a hiding hiding to nothing if you know they're aggressive with their premiums because uh you know we had a couple of instances in the last uh week or two if we're talking on say 19 microns where we saw the price decline over six selling days well over a hundred cents now if um if an exporter had priced an option with a premium of of even 50 cents uh he's lost his uh he's lost most of his premium um lost his premium but the strike price had fallen below he um he's he's got very little reward in that he captures the premium just like any insurance you pay it up front he's captured say 50 cents premium and you've seen the price start to fall back down to the strike level or past the strike level so it's it's quite a risky proposition writing options at the top of the market and and they're they're currently priced accordingly hopefully that uh covers that question yes thank you Mike no worries and what we're talking about in this all this data it's out there and available through your local broker or through the National Council AWEX AWI and and ad consultants it's just you know the job of the of the grower to uh to press his his brokers to make sure he's he's well informed and you know I get a lot of that data through from the brokers and they're they're pretty good at doing that uh and and making growers aware of it but if there's any particular stuff that that that growers need it can it can be sourced this might be a good time to even tell our our attendees about the handouts that we've got there in reference to elders and landmark and quality wool but they can download at any time they choose and have a look at it later um just to refer back to uh yeah what you were just saying right yeah and those those um that data I'm talking about I do now are available on all three of those uh company's websites that you've uh that you've said those those daily and weekly reports uh they're they're all there and and yeah not not uh on a daily basis some of the other historicals uh I'll just go through a few examples of of why uh you know a visual really of why risk management is uh is a necessary or not necessary tool but I think an advantageous tool for looking at at managing margins um this is the longest dated chart that I could get which is I'm not not well this is not in microns but that dates back um longer than Jody uh happily informed everyone I've been in the wool industry um so that's that's almost uh oh it's 42 years of data and you can see the peaks and troughs that we've had over time um we'll go through a few others um if we look at a shorter timeframe this last decade then you can see 18 microns has gone through the best part of a thousand cents in that time um that's just a chart on connects all those those finer microns and you can see the movement is is in a pattern which which we spoke about earlier where there was only one uh micron that was uh uh hedgeable from the SFE and the reason behind that is you'll see that that that the price movements are uh for wool in in uh concert with each other until you break them down so you actually it all looks quite regular but if you break it down what we've discussed in a few minutes uh because we haven't got a lot of time about basis between the microns and how that can be used but that's why there's hedging the underlying product is more important than getting the basis absolutely right uh having said that we now have a variety of products which can which can eliminate some of that uh that basis the data we're talking about is is from a historical point of view how to look at it this is what's called a percentile chart um and it just gives you a reflection over the last i've cut it back to two years because i think if we go back further some of these numbers uh this is the move the upward movement so even in this short time frame you'll see that we're currently sitting on some of these these uh microns or all of them except for 30 microns in the 85 percentile or higher which means that for 85 percent of the time prices have been lower than this over these the last two years and if we will look at this uh over a decade period then you find that the majority of the of the marinos are now sitting still in their 95 percentile band for the last decade but i think that's that we need to reflect on you know the last two years more importantly because that's where we've set things but it goes to show that even in that period that there is considerable downside from here to get even the average price of the last two years for 18 microns it's it's 250 sets under here and when we get to a basis chart uh you can see that's over or just over 400 sets from the from the average on 21 microns which is really very significant and if we look at uh just some prices without the the visuals the 21 microns the average over the uh the last eight years is 1270 cents with the low of of just under 900 and a high of uh 19 that's actually not correct the high was 1938 oh that's uh yeah so that didn't change that last six months it broke that previous high so we are talking about a volatile commodity and something that that we need to address uh as uh as growers if in principle we're happy to accept the pricing of the work that we do for 12 months for one single day on that sale day or now i know there's multiple occasions people sell across the year with with uh with more than yearly shearing but the the principle is that we should be looking at pricing uh you know the work done over the year on more than one occasion that's just a clip of the of the uh indicative forward grid you'll notice that's still in quite severe backwardation and a lot of that's been on the back of of where where we've travelled especially on the finer microns uh where it's come back over the last uh few weeks so now if we just talk about what are the the key i think are the key drivers in trying to to develop a strategy and they're different for every enterprise and but they need to relate to the cost of production risk appetite and the impact if any on the cost of financing because that's what the banks we're talking to are now looking at at that volatility especially at these levels and you know uh they want to move risk around and are happy to price financing based on some strategy of risk minimization we're actually getting close to time so i'll run through these fairly fairly quickly they're just the type of strategies and this is really just textbook examples of of what happens in other commodities and what what strategies are about whether they're survival adaptive control or hedging strategies um i spoke about basis and i'd just like to explain that it refers to the difference in the product that's being hedged to the underlying contract so when we had the sfv contract if you were 19 micron wool grower you're hedging 21 uh the basis was a difference between those two and that chart we showed before that they do move in line but they actually do shift out when you break them apart in the case of wool it's the difference between your clip and the underlying mpg that you're going to hedge with and for the export of the type they're delivering against that mpg so the you don't they the export doesn't live to china on 21 micron the mpg delivers a type 55 and for a grower the clip will might be around 21 microns it won't be exact but it'll be a relative or basis to that and in most cases it's best to minimize that basis and therefore hedge to that nearest mpg but sometimes important to look at at basis uh to see if you might get some strategic advantage now this will give you an idea of what that that basis can can look like this is just between two of the finer microns and you'll see in 2011 that basis got to near enough 500 cents and we almost got back that again so that means the difference between an 18 micron wool and a 19 micron wool is 500 cents so it was fairly important at that stage to be uh hedging your closer up to your production as you could whereas down in the lower section over a couple of years especially in in sort of 2014 when that basis got very very low then an 18 micron wool grower would be far better off hedging 19 microns when the basis is is almost nothing if that basis is out there in the forward market then it's better to to hedge the broader micron because more likely than not it will shift up from that basis not not down uh it did get close to zero but never touched zero um and we'll see that in also in 21 microns where yeah that basis again got down to sort of 20 or 30 cents against 21 so at that stage it would have been best to do 21 against 18 instead of that whereas at a peak in 2011 it got to a thousand cents so uh and again 21s you 19 to 21s you'll see that it has moved violently but it is now heading back in in the other direction close to concluding so i could have a few questions um the ongoing key of course and all of this is is education and uh just to to sort of put it in in broad terms um from the selling side wool breakers that are participating in the rhyman market represent around 90 of the volume that goes through auction so that they are very active but probably only half of those brokers are are a very active participants on the exporting side the same thing around 75 percent exporters represent about 75 percent of the wool shift but the majority is only probably traded by about 25 percent so we need education on both sides of that and the real killer for for wool unlike grains cotton is that only about two percent of the underlying clip is is hedged and i think jd asked the the i've asked the question about you know what is a normal strategy well that's probably closer to 30 for an individual grower so if you look at that uh then individual growers we're probably looking at at only about one percent of of individual growers or less using the contract because the guys they're using are hedging around about 20 to 30 percent of their clip and liquidity for everyone is the key to delivering accurate and and fair forward pricing and i always like to finish with uh the same mission statement um we need to look at valuing certainty uh which is more important than than the fear of lost opportunity because none of us can predict what the future is going to be thanks right well thanks very much mike is there any uh any further questions while we have mike's valuable time if you want to yet just drop them down that in that question box and i can certainly pass on to him um also worth mentioning that the we invited the brokers to provide the informations in that handout section so absolutely download them and have a look and i suggest if you want any further information to to contact your broker directly but yes if there's any other questions if they would like to come in fairly quickly um we're we're reaching the end of our our session time and we're always very conscious of of not going over people's time again just a reminder that we will be sending out a recording of this a link to the recording that you can listen to it at your leisure so we yes we highly recommend that you do that especially if there are items or bits that you missed or um if like me your line speed tops out in and out a bit you can at least then go back and reflect on all the great advice that mike gave us i will on on finishing up just firstly thank mike for his very precious time especially seeing we've called him back from easter at barren bay to do this which is very kind of him to to give us his time um and along with with mark and jody of course we would like to on behalf of persia and awr sheet connect and natural resources say our lands like to thank you all for attending we hope you've really enjoyed it at the end of the session there will be a a couple of questions that we'd love you to answer just makes it easier for us to know what type of topics you're looking at next time and we found that these webinars are just getting more and more popular so we find it an excellent tool for for passing on information to a wide audience and so if there's nothing more and we've got a couple of comments coming in mike about the fact that it's a yep been a great session and most most valued so that's fantastic so anyway so thank you very much again for for logging on and attending and we look forward to having you again at our next webinar thanks very much


We're gonna be squinting on photos like And I'm so pumped that our mall has a next door now tonight I'm going to do a 5k my first 5k ever. I just wanted to show you my new favorite combo It's an always first one Hey guys, hey everyone. It is what day is it? We are going to the top of our apartment because we love to just like take pictures there even though it's like not golden hour, but It'll have to do because I'm going somewhere later And I just wanted to start vlogging again because I feel like blogging is really fun And I love to like watch my vlogs back. Maybe I'll do a weekend in my life Ever so often so if you want to see those let me know in the comments down below today I went to my orientation for my major which is arts help radio television generalist official so Somali and I came up to the rooftop to like get good pictures and it's really bright We can't even like open our eyes all the way We're gonna be squinting our photos like this like Update 15 minutes into our photo shoot my hair looks so flat But we're trying to get that good good Instagram like always but this wall is like kind of cute It literally looks like Arizona because like if you just get this wall and this one little like weed It looks like you're in Arizona. It's weird, but yeah, that's humble weed So I decided to pop some popcorn and my secret trick is to add garlic salt and your popcorn to so so good Kylie Jenner popcorn recipe, okay, I'm Kylie Jenner They're from forever 21 There's spandex like I love hot Cheetos. You too. I like these those are like fries like I don't really like buy them, but like When I do eat them They're so good. So these are my favorite so far. Okay, so that one that one this one. I like this one. Yeah, this one Yeah, oh Well them. Thank you. You did a good job These vlogs are gonna be so fun This is literally what we do on the weekends have slumber parties during the day And day naps. That's what we do right now sleepy time It is 6 21 right now And I was supposed to pick up Kaylin to go to the mall because we wanted to like return and buy stuff at the mall really quickly before the birthday dinner I don't think I even told you but It's Rachel's birthday today. So we're going to cafe to to tango or something like that I think it's a tapas restaurant and I haven't been doing tapas restaurant in so long and I Love tapas food. So I'm really excited about that But yeah, we're gonna go to the mall and I Bought like a medium in Hollister bralette and I wanted a large So I'm gonna return that and she's gonna buy one of those because she lost her bralette So she was gonna buy one but she like already had one and then I have to return some forever 21 clothes that I bought online Just didn't really fit the way I wanted it to think that's about it in the mall And then we're just gonna go head over to the dinner. So hopefully we have enough time to go shopping She's like running late from the grocery store. I think she's stuck in traffic But I think we'll have time so I'm on my way to pick up Kaylin and we're gonna head to mall of millennia I live for Orlando Sunsets like look at this It's always so pretty Sunsets here picked up Kaylin on the side of the road So we went into the next door and I'm so pumped that our mall has a next door now because we don't have to worry about Target getting sold out of stuff or all just getting sold out of stuff. It's right over here Cuz like the next door is always gonna be in stock of like their products obviously So it's like crazy to see everything in stock because I'm so used to seeing everything on stock It's like really interesting there was like a painter We'll show you guys I really got ready so fast this morning Because I was going to go to it's in Winter Park, and I didn't think that they had a line I thought it was just like a kind of Chipotle like a subway kind of line like you just get it and go but I don't know for some reason like my friend just called and they said they had a line at the door and Kiki's has a line and first watch has a line We just need more brunch options over here. I usually eat out on the weekends I don't have a meal plan at my sorority house on the weekends and a lot of my friends eat out anyways So I think it's a waste to like buy groceries and then like eat out So I got this new app called no weight and obviously this is not sponsored Basically, it has like a lot of restaurants to like pick from you can click on like the restaurant And then it'll say like how many parties are ahead of you like for me My first watch place in line is 12 parties are ahead of me which are a lot Oh, it just turned to 11 but They said the weight would be like 15 to 20 minutes, which isn't bad because at first it was saying like 26 to 36 So I was just like mmm. That's why I like called all the other places So I'm probably just gonna meet Maya at first watch wherever we go I always get the elevated egg sandwich because it's so good And I feel like I need to like try different things there because Obviously, I bet everything on their menu is really good tonight. I'm going to do a 5k my first 5k ever I'm really scared because I'm not a runner and I just signed up because it's like FTK, which is for the kids UCF has a dance marathon called an Ithon and I participated in it last year and it was really fun I'm gonna do it again this year and it's like a zombie 5k. So I don't know like what's going down But basically I don't know what I'm gonna do because I can't run I think I'm just gonna walk with my friend Hannah So that'll be interesting. I feel like a lot of people walk 5k though So maybe it's not that weird, but I've never even been like at a 5k before But I also need to buy a new micro SD card for my GoPro because I have no clue where it went Which is really annoying because that is not very cheap It's like not in my GoPro not in like my little SD card case So I don't really know where it is really quick. I just wanted to show you my new faith lip combo So I actually got these two products yesterday at the mall I got this lip liner in toast and it's from NYX and I showed you guys the next store It's so cool. And then my newest favorite I think it's called the lip-tensity and it's from Mac and it's in this really nice brown shade and So obsessed guys. I'm so obsessed. I'll do a swatch for you really quick toast first So it's like a pretty dark brown. This is the lip-tensity lipstick toast and butter Let me swatch that. I think it's a really pretty combo. So these are the two colors I think they go so well together when you like smack your lips and like mix them up I honestly wish every Mac lipstick looked like this like I think the packaging on this is so beautiful And sometimes like the outside packaging doesn't really match the lipstick color, but this does like perfectly We're at first watch and we decided to both get the The next sandwich I got the kale tonic. It has kale, Fuji apples, cucumber and lemon in it Let's try this Yeah, it's pretty good. It has like grass taste. I like it Dude has arrived Just got my brows done at Venus brow bar She wiped off a little bit of my eyebrow pencil So she filled it in with like a really dark one But it doesn't look that bad on camera. It just like looks kind of weird in person So probably just have to go at home and fill them But right now I think I'm gonna go to CVS and get like a micro SD card for my GoPro So I'm home now and I just put my SD card in my GoPro and I was gonna test it out But the batteries actually like dead so I'm charging all my extra batteries right here I actually want to get like More batteries and more charging ports because GoPro batteries literally last like maybe a second If you're lucky just getting that's exaggeration But still I feel like especially if you have like the screen on the back the battery goes down so fast I always have to have my extra batteries around because I Never know like how much I'm gonna use my GoPro. So I'm just charging that up for the run tonight I don't know how much I'm gonna film But might as well just put in my fanny pack and have it with me I really have nothing to do today except for that 5k later So I think I'm gonna take it out because why not like whenever you have a time to sleep in college you take it That's what I'm gonna do. So I'll talk to you guys later when I'm getting ready for the 5k Just took a nap and now I'm like super groggy. Of course like this always happens, but this is my outfit Got these like forever 21 leggings my Nike euro shruns My fanny pack. I don't know where I got this like Walmart or something forever 21 top And it's open in the back and then this sports spot is a Nike So I'm scared.  So I think I'm gonna start vlogging with my GoPro So I don't know how great of quality this is gonna be on this GoPro. The Sun is setting right now We are gonna do the zombie 5k hell yeah, and like as civilians in an hour ish Check and start at 7 at 645 But yeah, Hannah well, we were gonna meet here at 645 and like walk at 7 But apparently Rebecca Kelly is like picking up people She just said like you don't need to be there right at 7 But I didn't know that so I got in my car and then she told me and I was like, oh whatever So I'll just chill in the PBR I Only have one more mile to go And I just realized I didn't even eat dinner the only thing I had was first watch So I should probably eat something maybe a little sooth high celebration afterwards. I don't know We'll see first five get is this your first 5k. No Yes, yes, maybe okay. I did a color my first 5k finish it We were like literally jogged like the first half Not even first half.  We'll just walk but my shins started hurting like really bad I think I have like shin splits when I run because I I had a fad where I like actually ran like Oh, you know on the treadmill or whatever a mile a day, which isn't bad But like I started getting like really bad shins ones especially from like cheer and stuff So I think it's cuz I didn't stretch which obviously I Super because I thought I was walking but now We are well, I am getting suit high


Alright, we're, we had a reintroduction on, last week, I think both days we took a reintroduction looking at rotational motion. Now we're going to go to general motion, which is a step beyond the stuff we did in physics one. We're going to look at not just translational motion, that we started the class with, and started physics one with. We're not going to look just at the rigid body rotational motion. That's where we ended up in physics one. Actually we did the kinetics of rotational motion. But now we're going to look at the kinematics of general motion, which is the two of those together. The fact that things can rotate and translate at the same time, of course is a little more realistic than just one or the other in terms of getting a big picture of the things that are going on. We're going to do this in two flavors. The first is as an absolute motion analysis, that's what we're going to do here for the first part of today. In that, we define the constraints, which means come to understand just where and where cannot this object move. For example, we're looking at a common car tire rolling down the road, which is clearly an example of translation and rotation at the same time. One of the constraints is that the tire has to follow the roadway. It can't go into the roadway, and as long as we're not looking at any kind of major bounce of any kind, it won't leave the roadway. So the constraint is that it would follow the roadway. Then we'll look right after that at relative motion analysis. This is where we use the fact that any points on these objects are an equidistant apart, so that if we know the motion of one point on the object, we can use that to find the motion of some other part point on the object because of the relative motion between the two. We might get to that today, depends on how things go today. We have lots of detailed drawings to do, so as we start getting into these, the first couple sketches aren't going to be a big deal. After that, we're going to have some pretty good detailed drawings that make them kind of big when they get started. For the absolute motion analysis that we'll start with, we want to do a couple things with it. Generally, what we do is establish the known path of a point. This is one of the critical pieces of putting the absolute motion together. For example, if we take the very simple idea of the wheel rolling on a road, it's fairly clear, I hope, that the center must follow a straight line. That's due to the constraint of the wheel maintaining its size. Remember, this is rigid body studies, so the wheel is not going to change size. This is due to the constraint that the center of the wheel must follow a path that's parallel to the roadway itself. Once we've established something about the position, we'll find S as a function of either angular position of the wheel or a function of time, and then from that we're going to establish then the velocity and acceleration of the wheel and of any of the points on the wheel that we might need to find, depending on whatever the problem is. That's our general picture, a little bit more specific of how we're going to do this. Then we'll start in on the real picture of just what this is going to involve. Imagine we have a wheel here. We'll label that initial point of the center as G. It's in contact with the ground a distance r, o, a. We'll label that initial contact point A, and then some little bit of time later, and I'm kind of exaggerating because I've got to fit everything in here. The wheel's rolled to that spot, so G has moved here to some place. We can call G prime. A will have moved to some other place. I don't know where I could, depending on what the distance is, maybe A prime up there. That will mean that our radius marker went through an angle of theta. Because of the arc length we can identify how far it rolled because it rolled a distance that was represented by this much of the track and that's a distance r, theta, when theta is in radians. That's the kind of thing we're going to do. Only we'll be a little bit more specific with it. That's just a general idea. So our first step will be to identify the position as a function of theta and that's going to involve this idea of arc length, S equals r theta. Now with just saying that, there's a very, very important idea that's here, but it follows through the other parts that we're going to do because then we'll take the derivative of that to find the velocity, which will also be a function of theta, but because of the time varying nature of theta, that will also be a function of time or theta dot, which is omega. So we'll relate S with theta, S dot with omega, and then of course we'll find acceleration, S double dot, and that will be a function of alpha and all the other little parts that will come into a theta. So we'll have these three concurrent ideas as well. Those three simple little things there are absolutely crucial to everything we're going to do, but they're also so simple that I could probably not even mention them and things would still work okay. What these three things together are called is the no slip condition. Those do not apply if there's any slippage at all between the wheel and the road. So we've got to maintain those. For the most part it's nothing more than us saying, well it's nothing more than us using these relations at any time. That immediately establishes the no slip condition. But they also are inherently defined if we happen to have a gear running along a toothed rack, a gear rack opinion type system, because gears by definition don't slip. We use that the other day. So we had that belt running around the pulleys. We had to assume that those pulleys, those belts were not slipping on the pulleys. If they were slipping, then there's velocities between the two and we can't establish all the pieces to that with at least our first steps through that. You have to take a more complex analysis with it. Alright, so we're going to start this picture over again and make it quite a bit larger. Alright, so there's our initial position. We're going to establish a couple things. One of the things we need to do here is when we identify the constraints. In this case it's the constraint that the center has to follow a horizontal line parallel to the roadway itself. That's an easier condition than using the roadway itself as the constraint because no one point is always on the roadway as the wheel rolls. There's a different point on the roadway at all times. But that center of that circle, the center of the tire does indeed have to follow a path parallel to the roadway. So that's a good constraint for us to use and we'll lay our coordinate system in line with that because then it makes things very easy. So our coordinate system will be that in the x direction and then that in the y direction and it's got to remain on the roadway there. So our initial position is such that, let's see, we'll name a couple points here. Just for reference, there's point A. Point B is the current contact point. That will be our angular reference line. We want to see how that line changes as the wheel moves a little bit. We'll have a secondary reference line that we'll put at some, a little bit of an angle here to it just because we're not going to go through even parts of a revolution. We want to look at some general condition where we roll to any other possible position or angle. Not forgetting that there's no slip of the wheel as we go along here. So that's our original setup. The other thing we just need to label for the sake of being obvious is the wheel has radius r and is rolling with angular speed omega. So that's our set up there. We've got that at least. Some little bit of time later the wheel has moved to some point there. That's not bad. Those look to pretty much the same side circles. You guys, you must be in subdued state of awe. I can tell subdued because you're not standing clapping right now. Usually when you use your head as a template. What? What are you saying? Use my head as a template. You're not understanding what you're saying. We'll watch the tape. Alright, so it rolls to some other place where point A is now moved down to somewhere here. I'll call that A prime and of course B since it's a rigid body is still perfectly opposite that. So A went about, what's that, about three eighths of a turn and so D, that'll put D at the top. Not for any particular reason just so we always have some point we're looking at at the bottom of the top and we can see how things have moved. So it went through that much of an angle. So A was straight up. There's the angle of rotated theta. Remember it's rotating with some angular speed omega and that causes it to move some velocity V which is part of what we're trying to establish. What is the velocity based upon the angular velocity and those kind of things. So we've got all those parts there. So it moved, don't forget this is our origin, the original center. So it moved that far. It's moved now to point X where that some distance X along there. But more than that point A has moved from up there is now located somewhere like that. So that's the position vector of point A. And A is just some general point so we'll be able to establish that as a general condition. So let's see. The position of point A is made up of two parts. One part is this component all the way out to here. So that'll be rAX. From the origin it's the horizontal distance that point A has traveled.  The center traveled the distance X but point A traveled this little bit of distance farther. And that little bit of distance is r sine theta. No r cosine theta. No r sine theta. Let's see. It's a little hard because it's a little bit over an angle but if it was only that far. Yeah that's the angle. The side opposite the angle. So plus r sine theta. See remember what we're trying to do is establish the position of any point as a function of theta and then we can deliver it that as we need. And that's in the I direction. So that's the I component of this position vector rA. And the X component is that little piece there. How much it's dropped below the original origin. And all these apply even if it was over that. Plus minus r that's just simply cosine theta j. So that's the position of point A at any rotational distance theta. We can fix things up a little bit. We still have an X in there and that's a little bit problematic. It would be nice if everything was a function of theta. But X is the very same distance as this arc length here. Those are one and the same. That arc length is the same as the distance X because it's the amount of distance that was rolled out here as the piece rolled. And B went from down here to up there along that arc length. So that's r theta. So we have sine theta. Put the minus there. We can pull the r all the way out I guess. Doesn't matter. It's a constant. So it's not going to be too big a deal as we go through the pieces there. Okay. So that's the position of any point A. Well not any point A. I guess the point is started there. Well I guess it couldn't be generalized at any point. What we want to find out next is what's the velocity of that point. The wheel as a whole is moving sideways with some velocity. But because of the rotational nature there's another component to the velocity of the point A itself. And that's going to be the time derivative of that position vector because that locates point A. So that's d r d t. But we don't have that position vector as a function of time. We have it as a function of theta. So we're going to have to do d r a d theta d theta d t. That we can do. This last little piece. That's no trouble because that's the angular velocity of the wheel d theta d t or theta dot or omega. Alright so let's take the derivative of this r a. See if we can get all the pieces together. Alright so we have r times d theta or that which would be this part with derivative with respect to theta which would be 1. Gotta get the minus signs alright as well. Yeah that'd be just cosine theta. That's the d r d theta of the first piece. But times d theta d t which is simply omega. So that's d r a x d theta times d theta d t. And then that's in the i direction. Little pieces right? Yeah. And then the second one it's a little bit easier because it's not a compound in any way. It's an r's a constant. So this becomes the derivative of this with respect to theta is minus sign becomes plus because of the minus sign already there r sine theta d theta d t which is omega. So put that in and then that's in the i direction.  That's just pulling the r omega out. The r omega sort of a familiar term which I was nice to have it out there. So there's v as a function of theta because everything else is well if it varies with time. We can take care of it in a second. Now let's see. Here's another very important point in all of this. It goes with the no slip condition. It pulls 180 which means the wheel has simply done half a rotation. A is now from the top all the way down to the bottom. That's the one rotation of 180. What do we get as the velocity for point A? Theta 180. What's cosine of 180 degrees? Not one. Negative one. So this is zero because we have one plus a negative one. So there's no i component to the velocity and the sine of 180 degrees is zero. So the velocity for point A is zero. At any instance the contact point, because that's what A is after a rotation of 180 degrees, the contact point has an instantaneous velocity of zero. Any time there's no slipping of the wheel. The contact point has an instantaneous velocity of zero. That's why I don't guess I want an A on there. I guess I could put Cp for contact point. That's going to be very useful to us a little bit later and actually several times here but be very, very useful in a couple days here of weeks or two. Also though it's one of those things that's very easy to forget. It just seems a little counterintuitive. You feel like every point on this wheel should be moving because in an instant later it's somewhere else. But if you also look at it in terms of the roadway itself if we have the no slip condition this point is in contact with the road. The road's not moving and this point's not moving either at that instant. So as the wheel moves the contact point moves but this is not the velocity of the wheel and the point that just happens to be in contact with the road has zero velocity. An instant later it doesn't. It starts changing velocity. I didn't say it's not accelerating. I just said it has no velocity. And as you can see it's sine and nature as we go with that. Alright so let's let's clean up the board a little bit. Let me put our position vector there r times theta plus sine. They all do it for rewriting this so I clear some board minus cosine theta j. So they're pulled r out. Now we'll rewrite the velocity up there because then I'll have a little bit of rule of mind that we can do the acceleration.  Alright that's just a little bit of housekeeping for me up here at the board because now we need to deliver that again to get the acceleration of point A which is the time derivative of the velocity but we don't have it as a function of time. We have it as a function of theta. So we're going to have to do the same thing we just did. Do dv d theta d theta dt and remember d theta dt is omega. The angular velocity. Okay so once let's not belabor the taking the derivative of this too much we can get down to r times alpha plus quantity 1 plus cosine theta. Remember we've got to do a couple of chain rules in here and they're like minus omega squared sine theta and that is the i component. When you have a little time and those of you who love taking derivative of trig functions and compound functions can sit down and do this.  Let me make sure I get all the minus times right. That's the only one. Alright that doesn't really clean up very much so I'll just leave that as it is. But we can now figure out what the acceleration is at 180 degrees. The 1 plus cosine theta drops out again as does the sine theta so the entire i component disappears at theta equals 180. Looking at the j component the sine component drops out. The cosine at 180 is just one so we have r omega squared j omega squared j which should look somewhat familiar. This is using our no slip condition also b squared over r which doesn't matter if it's point a or point c it's whatever the contact point is at that instant it's got a centripetal acceleration component. So there I did it for point a here it just happens to be for point c so I'll call that a c prime and that's the only component of the acceleration at that instant. Which kind of makes sense if this wheel rolls just a skosh farther than that wheel that contact point there'll be a new contact point down here but that contact point will have risen up a little bit as that edge of the wheel starts to rise up as the wheel turns so you can kind of see a piece to that. This is the one we're going to need a little more often but this other piece is also important in its own right. So now we have the whole general motion for a wheel rolling along a level surface and we did what we planned we get r as a function of theta and then take the derivative of that to get the velocity and the acceleration. Alright any questions of delight for that? Get all the pieces? Okay so we'll look at a couple a little bit more specific problems. That's a pretty general problem just wheel rolling around a level surface but it did give us that notion that the contact point is not moving at any instant in time. Okay so let's do another problem. Imagine a circular can it's essentially a disc however it's mounted off center it's center of rotation will put right there that way you get an eccentric path by each of the pieces and there's a follower arm that rides against that at one point level with that so there's a follower arm there that's you know runs in some kind of rollers just to keep it from flopping around and it's spring loaded so it remains in contact with that with that wheel. So as this wheel goes around this arm's going to move in and out following the edge of it as that wheel as that can turns. Alright we'll give it a particular angular velocity and acceleration and remember it's about that point O so this wheel is not rotating about its own center it's rotating about a point attached to the edge and then that arm is meant to follow that for whatever reason so let's label a couple points for reference oh what we want to do is find the velocity and the acceleration of the rod itself so in this case our general motion is we know that wheel is or that rod is constrained and move horizontally we're just not sure how fast it's going to move at any one second. Okay so that's yeah that's the picture. The end of the rod follows a straight path we just have to figure out what it is it's this point is of some interest as we're going so we'll label that point B point A is the center and so R is the distance A0 and okay so we need to establish how the position of this bar as a function of the angular position of the wheel so that's the angular position of the wheel and the position of the end of the bar at any instant is that distance x and how that changes will give us the velocity and the acceleration alright so that's that's our picture so x we need to relate to theta and then take the derivative of that to get the velocity and the acceleration so let's x is twice this distance which is our cosine theta and then the velocity of the rod will be the derivative of that and we don't need to do this a vector because it can only move horizontally due to the rollers but we have x as a function of theta not t so this will be x d theta d theta dt but that's omega so we're going to relate it's the horizontal velocity of the bar to the angular velocity of the wheel itself by doing this derivative now so without belaboring it either we get minus 2r sine theta d theta dt this first part that's just dx d theta so this is minus 2r omega sine theta so that's the velocity of the bar related to the angular velocity and the size of the wheel itself so we can figure out something about the velocity of the bar and the acceleration is dv dt but we don't have v as a function of t we have this function of theta we have to do that with the same kind of thing we did before and that's a little bit more involved because I have both omega and theta in the equation there but we can finish up with oh we can pull out r as well it's constant that's the size of the wheel not the distance from the center of rotation to the contact point of the bar alpha sine theta plus or minus square cosine pull the minus 2r out and so that's all we're looking for on this piece we established the position of the point of interest which is that contact point but that defines where the entire bar is as a function of theta then take the derivative of that once and then twice to find a velocity and the acceleration so that's just sort of calculus one stuff it's setting it up that always takes a little bit more of a step a little bit more of an intuitive step through it but we're not going to deal with this one as much we'll be getting to relative motion analysis a little bit quicker enjoy that when you took the derivative of this you ended up with one part that's d omega dt and d omega dt is out there so if you step through the derivative of this you've got these two parts that are both time variant we're not assuming this is a constant velocity rotation we're allowing the fact that there could be acceleration okay but that's all we're looking for on that point well occasionally in the problems they'll say at a particular angle what is the velocity and the acceleration so you just put the angle in what would change in this if that it wasn't a wheel it was a regular shape like a lot of cams aren't perfect then r wouldn't be a constant r would change the theta as well I guess if we could make it more simply though it's always going to be simpler it's a circle but with any cam analysis you need to know the equation of the cam itself and so that would become a part of that that would then be also our function of theta if you don't think these problems are hard enough Alan you feel free to make them harder you usually do too okay I do I don't know at some point these are gonna get harder no we're we're gonna do another one or two of these and then we'll get on to the relative motion analysis which generally is more useful and students find a little easier I do this this kind of well they're taking the derivative trig functions is always confusing I think you've got minus signs and and trig changes and all kinds of stuff going on but just setting up getting that first part you get the first step and you're fine it's just sometimes that's the hardest part of these problems it's been my experience for the students and was my experience going through these classes so we'll do another one garage door opener type problem so we have a door hinged at one point and supported by an actuator of some kind a piston if you wish it goes up to the midpoint so that's a maybe a hydraulic piston of some kind that opens and closes the door and it's attached at the midpoint of the door which is a meter on either side and the cylinder extends at a rate of a meter per second so that's actually been the speed of the middle of the door not the velocity because as the door opens these angles change that's the speed of the middle of the door and then we can figure out then what the rest of the door is doing we want to find actually the angular velocity and acceleration of the door at 30 degrees where theta is the amount of the angle at which the door is open so the one point that's traveling along a prescribed path is the center of the door and it's going to go along a circular path like that a radius one meter as the as the pneumatic cylinder extends and so we can set up a triangle based on that that be the origin of that point a and this point B so we have the speed of point B that's the point five meters per second so remember we've got to establish that where that point is as a function of theta and then take the derivative of that to get omega and alpha and as they follow so let's do this as well we'll call the the length of the actuator that distance AB which is variable by the point five meters per second we'll just call that s for abbreviation sake because now we have a triangle whose sides and angles we can relate with the law of cosines so that's a oh a is the is the side of yeah I already have that so the distance a oh or oh a where well that's that's just two meters this where the door is when it's closed yes I should show that as well so this these distances here are also one meter so we know that a oh and then the law of cosines a oh squared plus b oh squared minus 2 a 2 a oh b oh cosine theta does that look like the law of cosines for that triangle make sure I don't mind yeah okay and this is two meters squared because that's a fixed distance a oh and the oh is also a fixed distance that's one meter so those two together is two meters squared because those are fixed distances so we just have this theta we now have s as a function of theta which is the first step we needed in all these the position of the door which is this distance s a d the position of the door the position of that prescribed point that establishes where the door is and is following a circular path and then we can now take the derivative of that to find the velocity and the acceleration of the door and do it at particular point there so we can we can do these easier said than done of course with those values put in and taking the square root because we want s not s squared it simplifies to 5 minus 4 cosine theta that's putting in the values 1 meter 2 meters as as the simplifying okay so we need to take the derivative of these so the velocity of that point is ds dt which is ds d theta d theta d t there's our omega so we take the derivative of that I know you guys want to be doing all these trig derivatives yourself I'm kind of stealing a great fun of this particular class let's see it's square root so the power comes down get the same quantity the power reduced by one it was to the one half power we take the derivative that reduces the power by one and then times the derivative of the quantity inside which is the 5 minus 4 cosine theta 5 is a constant so we get the derivative of the cosine which is minus the sine that becomes plus times d theta dt which is omega that look great I think that's all the parts we've got we can simplify this even more or see this is omega what is it as obvious is that little piece there is 1 over s because that was s there and that's to the minus one half coefficient so we can simplify that even a little bit more it comes to sine theta remember we're going to take the derivative of this so the simpler we get it the simpler we can make it and so that all reduces I believe to 2 sine theta yeah because the one half one half times the four leaves us the sine theta omega so that's pretty simple and we can evaluate that at 30 degrees if we wanted to leave it in general terms we'd leave it like that oh we already know what this is because this is the velocity of that the speed of that point b so at 30 degrees actually at any time let's put it this way that equals the point five meters per second that that bit of moving remember that being this s is all set up on where that point b is and how fast it's moving so now we can find what omega equals at 30 degrees by dissolving that and it's point six two gradients per second just putting in 30 degrees and solving for omega nothing magical about the 30 degrees just a chance for us to put some numbers in and see what the values are but based on the speed of that point b we now have the angular speed of the entire door so we've got s we've got B we now need the acceleration so we'll take the derivative again we don't have v as a function of t we have it as function of theta but we we've been doing that whole thing along as we go along here factor omega is going to come back into this one again as it has before alright so we're now taking the derivative of this piece here two sine theta over s times that's just this quantity times river that quantity which is omega dot which is d omega d t or alpha so there's our acceleration component in there two omega s cosine theta dot no that's not right theta times theta dot d sorry d theta d t that's just this piece on there again so this is what we're doing is of course the the chain rule business the thing is we have theta omega and s are all time variants so that's why this one's getting kind of strung out a little bit we've got these three parts going into it omega sine theta minus s square that's not minus s quantity squared that's s squared minus so that minus stays with her and then d s d t which is v which we already have so that's the whole smear of that piece the whole derivative of that it's multi part because remember we've got three parts in here that are all time varying s theta and omega are all changing with time so we can then put all these pieces together this is s double dot if you'd rather oh we can we can we can simplify this a little bit that may help so this is 2 alpha sine theta s because alpha is d omega d t the second part here that d theta d t is omega so we have an omega squared this becomes 2 omega squared over s cosine theta and then the last piece the little piece on the end that gets really easy that's minus v square because notice we have 2 omega sine theta s 2 oh no not v square d over s square it will be that's v squared over s that takes care of the extra s there that's a little simpler and we've got all the pieces then so then we can evaluate it at 30 degrees then the acceleration is minus 415 radians per second oh wait that's got to be alpha no that's that's a oh dear s dot in radians per second square so some of you can check it your eyes haven't lost over yet Anthony your brother miss which part yeah that's that's right here yeah that's what that's what this is that's v okay so I don't know if this is a I think this I think this is supposed to be meters per second not radians per second but you can double check it when you pull the pieces together when you sit down and go through this two hard parts one is just establishing the original position equation I've raised it was the one over s of that part then the hard part you gotta derivative it with respect to time and get all the pieces right you can't can't lose any minus signs or squares and that just gets to be complicated so we're not going to make a big deal about this one this is this is a much more of an academic exercise than is the relative motion which students generally tend to gather better and enjoy more because of that so was that question I was just looking at the derivative the same that if it's the derivative of the velocity with respect to time is the same exact thing this velocity with respect to theta times theta with respect to time and data with respect to time is omega then you should be able to replace this step here no or the acceleration right here if you erase d theta of dt and put omega in the tallys then the answer you get is a lot simpler it's only like the second term of that whole thing just this down down one more right there but these these terms drop out well if you have to do it wrong if you just if that's the velocity of their two sine theta over s omega then you take the derivative of that and then multiply it when you're done multiply times omega and you get two omega squared cosine theta over s well it can't be right because you've lost these two terms because don't forget even though you have omega here it is time bearing it as well and you have that on that d theta dt on each of the terms no I think well oh we're looking for alpha so yeah but that is alpha so I had the units right symbol yeah that makes more sense oh yeah you don't do this in and you don't well when you're doing on your calculator you can do sine of 30 degrees okay you know you set your calculator appropriately if you're putting in degrees or if you're putting in radians it's just most people I don't know about you guys I can picture what degrees are angles and degrees are much better than I can in radians so that was just you know not return of chosen value for that all right so hopefully that scared you off absolute motion analysis well enough couple homework problems do your best with them but we'll do most of what we do with the relative motion analysis so we'll establish that next you'll find that a lot easier I think which means so do I so this stuff kind of makes my points I like the real stuff a little bit better which the relative motion analysis seems to be a bit more and there are some problems it can be done either way so if you're not specifically given a way to do it then then don't worry about it so first a little bit of a reminder on relative motion we've already talked about it before but if we have two points a and B and some arbitrary origin then we can locate the two vectors or those two points with their position vectors r a and r b and the relative position vector this is just a reminder that we've done this before the relative position vector b relative to a if you're sitting at point a where do you have to look and how far away do you have to look to find point b in this with this vector describes the direction you look and the distance you'd have to look to find point b is defined as the difference of the two position vectors remember my my offering that it's with those subscripts in the same order b a b a and then you can always get the vector in the right position with that and then the relative velocity vector is the derivative of that which just becomes the difference in the velocities of the two and the subscripts keep the same order as they before so if we know something about the motion of one point on a rigid body we can keep we can get an idea of the motion of another point don't forget on a rigid body the distance between any two points is a constant so we'll use that doesn't matter which but it's the fact that the distance between the two is a constant now what that means if we've got some rigid body and it's got these two points a and b on it and we know something about how point a is moving let's just for example say point a moves along that path then we can figure out more about how point b is moving using this relative motion here's the idea don't forget we're looking at generalized motion so there's translation as well as rotation so not only is this object moving along here because point a is moving along that path but it's turning as well so some little bit of time later just because of the way egg where a is so some little bit of time later point a having followed along that path but because of the rotation point b is now down here and we can figure out the position of point b and particularly the velocity and the acceleration of point b if we know something about the motion of point a and the relative motion of the two between them so if we're looking for the velocity of b that means solve for this that's going to be the velocity of a plus the velocity of b relative to a that's just solving this velocity equation for bb I'm trying to figure out something about the velocity of point b the whole object is moving along and it's rotating so there's some complex more complex notion of velocity of b at this one point than there there is to point a point a's just falling along that line that constrained line of some kind so this is the piece that we need to figure out how that business works and here's the simple idea that'll give it to us that's the velocity of b relative to a if you're sitting at point a what does it look like b is doing that's what this question is that's what this term is b relative to a you're sitting at a you're looking out at b what does it look like b is doing if you're just looking out at b you're not looking at anything else you're looking out at b you see b is off in that direction at first that way it be a little bit later you're looking that way and be and then sometime later maybe point a is moved to here point b is over here you notice as you sit at point a that point b never gets any farther away from you is that true yeah it's a rigid body that's our definition of a rigid body but none of the distances between any arbitrary points will change so you're sitting at point a you look out at point b and notice it's not getting any farther away but it is moving always to the side it looks as a matter of fact like it's orbiting you doesn't it no matter what that object does if you're sitting at point a it looks like point b is orbiting around you you happen to be moving as well but when you're sitting at point a you don't sense that moment or you don't pay attention to it you're just looking at point b it looks like b is just orbiting around you of course you are young enough you think the world over or if it's around you anyway it's not the whole of universe but here's a here's actual justification for that are we taking a to not be turning them a is just a point a is on the body it's right there the body later turns now a is right there now a is right there the thing that we're saying is that we we know something about that velocity of the velocity of point a that tells us what the whole body is moving when we are doing particle analysis we only look at part a and say the whole object is doing that but now we know the object is turning around it I don't know which particular direction looks like maybe it's that direction but you can't say point a is or isn't turning because point a is just a point it has no dimension points to have no dimension so point a is going along a known path the rigid body is also rotating around it in some way we're trying to figure out what the velocity of point b is due to the motion of a and the fact that the object itself is turning that'll get risk no the the only time you're worried about the reference frame on the body is when you're trying to figure out what this is because this is relative motion bees relative motion to a so in this case your reference frame is point a but no we don't consider that reference frame to be turned the the reason this is good is we already know that that's as far as point a is concerned this is pure rotation and so if we know the velocity of point a we can add to it the fact that relatively speaking the object is rotating about point a and we've already looked at that we looked at that last Friday that's omega cross omega a b which is the angular velocity of the body times the relative position vector and that we've already looked at we looked at that back in the earlier parts so we want to know how b b is moving we look at how a is moving because that determines where the whole object is going but we also look how the object is turning around point a as point a moves itself and so we can figure out now the velocity of being with the relative motion analysis here's another point that students often forget notice I I didn't bother to put a slash between this when we have any rigid body with any number of points on it that we can connect so if I had an a a b and a c and this object has some angular speed that angular speed is the same for any of these lines they all have the same angular speed students sometimes forget this this angular velocity is for the entire body and any reference line we can scribe on it so all of these pieces are also rotating with angular velocity omega where the center of rotation is we don't know it doesn't matter if that body has that angular velocity any part of that body also has that angular velocity so this is a much easier number to come up with than students a lot of times think they think this often is something different they have to determine if you're told the angular velocity of one part of the body you know the angular velocity of the entire part of the body okay so we'll draw it to a close there and we'll put this to work on Friday given the velocity of a and how the object is turning we'll be able to find the velocity of any other point and then of course the acceleration as well boy that's not interesting enough to get you back on Friday what


Alrighty here let's watch the whole thing. It's a long sequence, bam-ba-ba. Alright cool cool so I think my main reaction is some of the staging in the camera and some of the actions. Let me see that sounds very broad. So you're gonna have to have this character out of frame so that we don't see him. This guy opens the door comes out.  So that let's go fancy here with the extra drawing tool. It'll be more like this. This continues on. We see this and then you know whatever whatever is down there to continue that thing so that we are in my crappily drawn thirds. Oof, someone's right. So that the the one character comes out and is here and then the other character comes out you know here-ish so that we still have that much room to refocus. Hold on let me take this out because right now what's happening we have this character center like we're center frames composition is a bit it's usually not that center unless it's for a specific reason and go a bit more traditional like I said in my crappily drawn thirds. So somewhere around here the other thing that happens now because we're so center and low is that when he comes out hey they're kind of moving at the same time I know he opens the door first but just give the characters enough time to register to the audience because the moment he comes in right door opens okay wait what and then this character comes in so it's there's not enough time to me but also he's way too long and then he gets goes out of frame pretty much I mean kind of stays put there but we we never really get to see it so it's either you do this and you don't show this character and you keep it centered and I would technically still be there just to kind of give us a bit more room there even if the other guy doesn't show up but having that solo and coming out almost at the same time it's just I don't think confusing but we still know where to look so if you take this guy out and you just have him comes out here and then looks down even then you might even argue that you can do something let me see can I my hockey is for some reason not working so it will be almost something like this let me bring down framing to something like that so now you have character comes out and it ends up in those you know thirds and then you can have him look over because now he's not a small now we can register what's going on facially a bit better and he can he can look over and then do a big sharp turn with his head to look down and then as an audience we look down as well and then maybe you can have the door open so we see movement so we're ready to go oh something is down there that I want to see and then let me frame slowly painfully then you cut to the second shot and now we are here and the door continues to open and he comes out but the thing is again it's so small like what are you showing off in this like it's we barely see anything in terms of you go back here you got a silhouette with that arm which is a nice I like the framing but so technically we don't really see what's going on I don't think we needed to need to have it that wide this might work as a first shot where we see something I wish it's an establishing shot we understand the geography okay then the door opens and we see movement then we cut to this like I said where it's the close-up and then we cut back to a third shot but then that third shot let me do wait slowly here go into that I mean that would even go to be honest something like that whoops I'm trying to drag my frame something like that because again we've had the establishing shot and then you can do really big broad moves because again that's something I care to that size it's going to be all about big gestures which could work here but then this would be more of a story shot of maybe showing you know how far away they are that this guy goes back in like there's not much you would show off animation wise in terms of putting this on a reel so that's something just for you to think about if you do this whole sequence and you want to put the whole thing on a reel I still be careful to have every shot show something that's substantial in terms of showing off your skills versus this being more of a story sequence if that makes sense then you have this here and then I be careful with this is a big it looks like a translate down versus a rotation I don't know if you need it you could cut but if you do something like that I would again have him more here in the thirds and then as the character moves over you gradually pan with the character and tilt down to land here but the character would be leading the action a bit more as in it could cut off here like you could break frame and then the camera catches up and just but lands a bit slower with a bit more overlap not saying you have to do a lot of handheldy stuff but I would make the camera moves less sharp because this is borderline a cut right you move a bit but you stop really sharply and then you might as well just cut from shot to shot same thing here this goes down one two three frames like this is might as well do a cut but you can do this all in one long shot coming down by now maybe the camera has settled and again it would be reframing and not be so far to the left there because now I'm expecting someone to come through that window or jump into frame but we never have that then you go down to this I don't mind that I will probably have that character here at least at the beginning so it's a bit more you're not that much of an overlap there and potential tangents but I don't this is where I have slight questions about the character choices so the character comes down here and this guy's just kind of waiting looks at the feet doesn't really look up and it kind of waits right going left and right and what is he doing why is he not already grabbing the feet and what is this is this like come at me bro this is a taunt is it going for a hug I'm not understanding what this is then we have that and then generally animation is just really really fast I'm not quite buying the what's it called to the wait and then this is tricky was now you're crossing the line as in we're looking to his his right side he goes left to right cut to a 180 break we're now we're looking at his left side and he's got he goes right to left so I will keep that a bit more again tilt down or cut into a wide that's technically this and then the character can just continue because there's no other shot after that so you might as well have something like this you might have to change this here but that's the exit so the character comes out and then jumps out here and again this is in terms of animation a bit wonky in terms of that much momentum going forward comes to a sudden stop then goes out to a sharp right and keep that a bit more fluid with a wider arc and if he if he goes like this to me it's more like well you're gonna put this arm here and not go like that I mean unless he wants to push off that's what I think it looks like because it's not really sticking through the wall is he supposed to jump and then push off here or is he just gonna vault the other side you know like this arm down flip him over he just kind of jumps over that and then again momentum wise if he does this and actually uses this wall and pushes off that momentum will carry him way to the left and this feels like he hits a wall right here and goes boom right throw that line here so he just goes here it's that wall and just falls down so that exit would be out this way and not like this if that makes sense so that's kind of that if I played a whole thing what are we out here 70 like 25 percent slower comes out hey huh what's over there you over there it's a bit slow places and in places it's okay like actually I really prefer that 25 percent slower but then this feels like the jump feels good to me better this feels slow and the rest feels a bit slow so to me it's it's a mix between 25 percent slower and then regular speed and then slower again and that's kind of that so I know those those are bigger changes in terms of well do you want to change the camera do you want to change the whole beginning and make it an establishing shot and you know and it's it's not to say that you can't do an establishing shot afterwards but I would probably still go closer here now I would still probably play with the idea of character frames this way and then at least when the other guy comes in we see more of it that's probably the biggest thing for that and you could still cut to that and make that the biggest establishing shot and do this right where you have here with the big big move I think either way would work doing this first or not so whatever version I have before I think they both can work I would just definitely rework this and then after that it's mostly camera movement if you want to go just cut and cut and cut or make this one longer shot but then really work on the camera moves it's it's less over three frames and just sharp and then camera the character interaction feels a bit weird like I said why what is he doing here don't quite get this and I don't know what the red light is here I don't see anything in your email like why why is it constantly getting having that that layer of red on and off and that's it all right thanks all right there's an email you can sign up you can start whenever you want you can submit whatever you want you get 16 submissions either way like and subscribe would be awesome all right thank you