 Alright, we're changing things, we're changing things a little bit, we've done two things so far, basically two big categories of things. We started with kinematics of particles. That's how we started the course a long time ago. Remember what kinematics is? Constant acceleration. Yeah, just not constant acceleration, that's one small part of it, but it's just the business of where something is, what it's doing while it's there, what it's going to do next, that type of thing, and then all of those things were tied together with time. So that's all we looked at the first couple of weeks of the term. Then we went to the kinetics of particles. Remember what that was? That was three things, and in fact a third we got, I believe just Monday, maybe a week though I forget exactly when we got it, but that was the third of the pieces of kinetics of particles that we did. This is how do we get these things? How do we get something to accelerate, or how do we get it to not accelerate, depending on which it is we need, but it was the involvement of the forces, how the forces are what affect the acceleration. Once you set the acceleration then the velocity and the position can all fall from that. We looked at three different ways to solve kinetics of particle problems. What was the second? We had a work energy equation. It wasn't something that works, it's not that these two don't work together, it was just another way to look at everything, but pieces of it came directly from F equals M a, so these aren't exclusive, it was just a little bit better way to look at some things. The last one we just got, impulse momentum, and each one of them solved a particular type of problem in a little bit better way, but they all came from F equals M a, so it's not like they're exclusive, it was sort of a prepackaged form of F equals M a that allowed us to solve different types of problems that might have been a little bit more difficult if we just approached them in the F equals M a way, but remember what type of problems this was real good for? Yeah, constant force problems, which we did a lot of, constant force and constant acceleration, assuming the mass is constant. Work energy worked well for position dependent problems because the work is very much dependent upon how much distance has it gone by and how much distance has it gone by, depends upon where the object was, and then certainly the gravitational potential energy term and the elastic potential energy term very much had to do with position, almost exclusively those were based upon position, but just some other little parts of it put in like the strength of the spring and the strength of the gravitational field, and then impulse momentum, haven't had too much chance to test drive it probably, there's a couple of problems there with it though, but we've been working with it in class a lot, just didn't get it in its impulse momentum form until Monday, works well for what type of problems? Time dependent problems, because the impulse is the integration of the force time curve, so forces change with time, then it is almost a no brainer to calculate the impulse, you just integrate the curve because they're real good at integrating, so now we're going to put that behind us, sort of, accept that we're going to start over, start over from the very first day, so, well I'm going to skip introducing myself, you know, we're going to kind of start over, we're not going to start, we're going to do all this stuff again, but not with particles, now we're going to do all this stuff again and we'll start with the kinematics, we're going to start with the kinematics now of rigid bodies, your day, last Saturday night, that's not what I mean, what you're all thinking, a man to slash some man that wasn't here, so, talk like, oh, I need to edit, I need to edit myself, but I can prove it over the years, I can't do that, in order to do it in real time, that's true, so, we're going to look at the kinematics of rigid bodies, never before did it matter to us how something was oriented, where it was facing, how it was turned, remember the kinematics of particles, we even talked about the fact that if we're talking about position and velocity and acceleration and if we were even doing it of a person or a car, I didn't care which way the car or the person was facing, I just said, it's here, then later it's here, what it doing between to get there, that's all we ever looked at, we took a single point to represent what could be a very complicated object in some very complicated motion, we used just a single point, in the last couple weeks we kind of came to understand, without ever having said so before, that the center of mass would do very well as that point, but I never even bothered with that in the first couple weeks of the class, if I was talking about the space station orbiting the earth, we just took the space station to be a single little point, and that little point represented the space station, and it was that point that we got to orbit the earth and we looked at how it would do so and what the forces on it, all those kind of things we looked at, that's not going to be the case anymore, now we're going to worry about how things are facing and how do we get them to face some other way, if I need to move a car from one place to another, it's not just as simple as getting one little point on that car to go somewhere else, I've got tires to turn and wheels to turn and I've got pistons to turn, all kinds of things that are in very different orientations, each split second of time that goes behind the travel of that single car that we took as a single point in space for all the weeks coming up to here, so now we're going to take our first step into how do we get these things to change their orientation, not just change their position, so first a real quick real simple definition of a rigid body, well obviously it's any object whose shape does not change, but we're going to be a little bit more formal with it in our understanding, any object could be a potato, I hate to make you guys hungry, I know you like potatoes, you're a tater tots, probably, anyway moving onward, a rigid body is anything that we could describe with three points that aren't in a straight line with each other, any three points, so by saying any three points I mean that we're essentially, at least in our minds, checking the entire object everywhere because those points could be anywhere, as long as they're not all on the straight line, three points not in a straight line make a triangle and a rigid body is an object that can go through any type of motion, I don't care if it accelerates or it skids with friction or it rotates or it rotates and accelerates and tumbles and rolls and all the possible type of things real objects can do, no matter what it does that triangle will never change, not in its angles, not in its sides, it'll always be exactly that same triangle and if you think about it, well that's exactly what you'd expect of a rigid body, it's not going to change any size or shape in any way and what better way, more simple way to describe a shape than a triangle, so any triangle we could associate with that object no matter what we do to it, no matter what forces we push on it, no matter what impulse or work we do on it, that triangle itself even if it's not a real one, just a virtual one will never change shape, that sounds like a fair definition of a rigid body that is about as simple as we could do and we're done with it, Alan are you okay, you look like you're frowning, like you don't believe that's rigid enough, yeah that's a rigid definition of a rigid body, beautiful, oh a triangular tater tots, yeah alright so here we go, alright so let's let's say kinematics a rigid body let's well let's start kind of like we did before, what we started with with kinematics of particles we started with position and then we looked at what happens as position changes and then we looked at what happens when the change in position changes and so on we built up from there so so here's here's some rigid body we'll just keep it nice and simple, make it circular, you're all as good at drawing circles as I am, go and on, so I have to call Professor Hampton out here and scold you, the terrible thing is that's not too bad a circle but but on the screen up here it gets distorted because the camera is up there shooting down and it's really pitiful, I have to actually if I want it to look good on camera I have to draw in such a way it doesn't look good for you but you're the paying customer so you get my best circle, alright so there's a circle and positions, all we're going to worry about for position right now is orientation we're not going to let its its general bulk linear position change in other words this object is right here and for the most part it's going to stay right here but its orientation is going to change only, well the simplest way that kind of thing happens is if we pin it at one point and let it turn about that point then its orientation is changing but its linear position isn't so it's not going to be quite like a car tire because those rotate and they translate we're just going to it's going to be much more like up like a clock or a gear in a big machine that can turn but that's all it does and it can turn left and it can turn right and it can speed up and it can slow down and all the other things our particles did we're going to let our rigid body do now so we'll pin it at one point as convenient as any is that center point for the picture word kind of pictures we're doing but this this again could be a potato or a peanut butter jelly sandwich or anything else that we could pin and then let it turn so position well what was the first thing we needed when we were talking about determining the position of a particle weeks ago not just an origin but an arbitrary origin because we can pick it anywhere as long as we all understand what it is it's good enough to keep going so as useful as anything for our origin is a line that we'll use for reference so why not a horizontal line like that and then we let it undergo some kind of simple rigid body motion that does not include linear motion does not include translation we'll just let it undergo some simple rotation about that one point where we pinned it so position then is going to be a very some kind of variance from that reference point the things just going to turn through a bit of an angle so that will be our position so this is this is our reference position our origin we'll use the letter theta to represent angle so for any purpose that we're talking about we might if we need an origin we'll call that origin theta equals zero and then we'll turn through some angle so that I'm being theta one this might be theta two equals something else and your volume protractors before you could throw one down there and measure that maybe it's about 40 degrees something like that we can see what that is and so so now we've already got then change in position and and so we're already catching up with the places where we've been talking about the kinematics of particles pulling out kinematics of riddy-byes the only thing though that's not going to work for us here that we've got a change is it's it's not too great a change it's kind of like changing in your mind from talking about our position and inches and feet which we're all very used to to talking about position and centimeters and meters which is we're not as used to but we're okay with we can handle just have to get we have to do the same thing with angle degrees is not going to work for us because we've got a lot of calculations coming up just like we did here we've got a lot of things to figure out to calculate and degrees don't work in those equations we need something that does so we're going to measure our angles in radians we can talk about them in degrees but our angle measurement will be what's called a radiant in an entire circumference once all the way around well here's probably the easiest way to talk about I guess imagine a circle just like you did when you were first taking trigonometry everything there was built upon the unit circle wasn't it a circle of radius one and they didn't say one foot they didn't say one meter they just said a unit circle we're gonna look at a circle with radius one so that's what we'll do here because this this really is directly a part of the trigonometry anyway so radius of circle one has a circumference of 2 pi not 2 pi r because r equals 1 so very simply 2 pi so we're going to let some amount of the distance around that circumference represent our angle and it's just what you did in trigonometry for example 90 degrees as we might refer to it in easy discussion is one quarter of the way around the circle so that's one quarter of 2 pi or what pi over 2 remember talking in trigonometry about angles especially the the regular nice regular angles 45 90 180 270 3 we just talk about that's that's all a radian that's all the radians are it's that trigonometry angle measurement that you used when you first picked up trigonometry you guys probably started a couple years ago that's when you first hit it so that's that's this very same thing we're going to use we can talk in terms of degrees because I don't know about you after all these years of doing this kind of stuff I don't think in ratings you tell me the angles 3 pi over 4 you're gonna have to give me about 15 minutes to work out what that means in my head on a good day 12 minutes but you tell me 118 degrees I got that I know what that means so so we'll talk in degrees but we've got to do our calculating in radians so that's going to be our base unit for these these for the for the position of a rigid body in rotational motion of some kind and we'll abbreviate it RAD because we're just too dang lazy to write out the entire word so RAD will suffice alright so we've already got change we've already got position we've already got change in position set just like we do with particle particle motion a long time ago but then of course the question comes up we're not just interested in the change in position but we're interested in how quickly that change in position occurs so we're going to take a look at what the changes position is per unit time how many radians per second is that position changing yeah went from from this orientation to this orientation or it could even be an object that went from here to here we could we could look at it in that same way I guess that's no real difference because the point on the edge of that thing did exactly that so we're interested in in what was its rate of change of position in radians per second let's see let's see let's even make ourselves a little chart we started with linear motion we started with position then we had change in position then we had change in position with time remember what I called that that's velocity that's all even even more generally though or maybe more specifically that's what kind of velocity that I've got right here yeah vector has to do with the fact that we're only looking at a bulk change of position not the change of position any of the things in between is what average this was average velocity and then we went to instantaneous velocity so this looks like well if theta is an angle which it is whether measured in radians or degrees it's an angle this must be angular velocity and it is this is angular velocity so it needs a nice symbol it's average angular velocity we use the symbol omega kind of a fat round w omega and it's it's available in if you go on word you go to insert and then symbols it you can find it on there as one of the original Greek letters and the type of things we like to use now so we have this definition of angular velocity the rate at which the angular position is changing on average and shouldn't be too much of a stretch for you to figure well I've got average angular velocity I'll bet you we've got instantaneous average sorry instantaneous angular velocity which is the average velocity as the time step goes down to incident time and we've got that as well so we've got this this linear business and we've got this rotational business that's going along hand in hand for position we have now angle we then had change in position we then had average angular speed we got instantaneous the omega dg there's we're not really even learning anything new it's all the same thing it's just instead of position along the number line type idea it's positioned as an angle but nothing's really changing everything looks everything looks very very similar we do need one other thing though right now it was a good time to bring it in how do we know if if uh if we have all this right now how do we know this object is turning counterclockwise or clockwise and that make any difference in the problem yeah I don't think you'd want to get in your car and have some of the wheels going one way and some of the wheels going the other way it'll bet it matters which way things turn so we need some way to designate for us the direction things are turning because in fact this is just like this was this is a vector quantity it's got magnitude a 40 degree angle is very different than a 50 degree angle it's also got direction 40 degrees that way is very different than 40 degrees that way so these are vector quantities just like the position wonderful so so we really are duplicating what we did here now we'll have to think about that a little bit more how we're going to actually designate that I was going to write that but that's the that's the deal these are all really vector quantities but it's going to be pretty straightforward for us because in this class every rigid body we're talking about is going to lay in a single plane during all its motion these things aren't going to turn and wobble like they could do you know if I took a frisbee put it on the table and gave it that kind of funny spin they do and then they wobble as they rotate well it's not it's not going through any linear motion because it's still right there but it's going through a very complex type of motion when it does that we're we're going to make ours even simpler than that in that whatever we have that's turning is going to stay in a single plane whether it's a vertical plane like that circle if I could actually have something up there spinning or whether it was be on the table and it would just turn in one place it's it's really a 2d motion in fact it's kind of like the circular motion if you look at just a point on the edge of this it's just going in circular motion type thing the way we've looked at before except now it's a whole object doing there so there's two ways we can handle three ways we can handle this direction business that we've got to handle one we could say let's do what we did here and say one direction is positive and the other direction is negative so we could say well let's call that direction positive the other direction negative that would work that would work just fine nothing up here would have to change that would work just great we could say any kind of angular change in the opposite direction we could call negative that would work and that would work in the equations too which is good that's nice when things work in the equations without messing up it means you got to keep an eye on your negative signs but it works works just fine we could also say well for direction I'll just say counterclockwise or clockwise that would work too but it wouldn't work in the equations because how do equations work with cw in them for clockwise and ccw for counterclockwise so it would work for our understanding and our verbal discussion of things and for a way for us to post results to a problem but it wouldn't quite work in the equations not as nice but it would work so we could do something simple clockwise and oops I was using my my Russian watch they always run backwards counterclockwise and clockwise we could do that oh you guys don't have digital watches do you know what counterclockwise and clockwise even means that's a clock don't tell me you haven't looked at it once all all year doing about 12 time a period oh god that you got to stop no no it is still going geez I thought it'd stop so we could do that for discussion just wouldn't work in the equations so mostly what we'll do is with the minus signs but there's another way we could do it and it would work for the general type of circulation where something could be wobbling and rotating because that's a full three-dimensional type motion more than just our two-dimensional motion minus plus and minus wouldn't work there in full three-dimensional motion because I don't know what is a minus and a plus mean when something's going all over the place but there is another way for us to describe this that works for what we're doing here works in the equations and would work in full 3d motion if we bother to get to it and that's where we talk about the possibility this could be a full 3d vector here's how we do it for a example for a counterclockwise motion take your right hand you can borrow mine take my right take your right hand put your fingers in the direction of the motion that automatically puts your thumb in a direction right out of the board so we can call we can say that a rotational vector in the counterclockwise way will represent with a vector that comes out of the board in the k direction so we could say for example we could say for this angle here we could say that's plus let's call it 40 degrees we could say it's 40 degrees counterclockwise or we could say it's 40 degrees or we'd use the radiant equivalent but remember I said we could use degrees if we're just discussing stuff we could say 40 degrees and we'll call that the plus k direction or we we use you know pi over four or whatever 40 degrees is in the k direction that's got magnitude it's got units whether we're radians or degrees you'd still know exactly what I was talking about that's called the right hand rule because it's all different if you use left hand if you put your left hand up there in the curl you get the thumb in the opposite direction now we don't agree with what we're talking about so we take we agree on a right hand rule fingers in the direction of the motion of concern that thumb comes straight out of the board that gives us a direction so a an angular velocity vector that's in one direction into out of the board and longer or shorter gives us all the things we need that perfectly and usefully describes this angular position angular velocity type stuff we're thinking of so that would also work in these equations but so will the plus and minus and we'll see some stuff we'll we'll do a couple problems in a second here and work it out and troubles so far it's not really there's not really been anything new yet except we have to look at position a little bit differently than we did before but but the basics are still very very similar Joey well we can agree on on whichever one just like we could do that with this remember a lot of time we had to talk is plus up or is plus down we can do the same thing here typically though counterclockwise is taken as positive and that also goes with this k vector business because typically that's our coordinate system we use a right handed coordinate system in general which means x rolled into y gives you z and that would be out of the board that would be positive so that all agreed that's that's the definition of a right handed coordinate system x crossed into y gives you z that's a right handed system so we we can call that positive because that would give us a positive k vector but typically that's what you did in trig class anyway wasn't it that was a positive direction and the other way was a negative direction in fact i think alan i had an argument about that a couple of months ago anyway alan yeah that was right and you were you was right let's pretend you weren't okay all right so uh all of it's really changed none of the concepts have changed terribly uh just the symbols have and our definition definition of position but then after that everything just uh it's just we just swapped out the symbols and we got exactly the same stuff so let's see uh there's the possibility then of course just like there was with the particle motion that the velocity could change we might be interested in velocity changes in fact not just velocity changes but the rate in which velocity changes so we've got something spinning so its position is changing we've got something spinning such that it's got some angular velocity and maybe that angular velocity is changing and we're interested in that very type of thing if you're working for a company that's producing uh cd readers for computers a big concern to you is the speed with which that cd is turning what should we call this this was angular velocity we should call this then probably angular acceleration in fact would you you had something else in there average average angular acceleration so we can't use an a because then we wouldn't understand which kind of motion we're talking about so we've got to use a different symbol than a to show us this angular acceleration so keeping with our theme of using greek letters in here we'll use an alpha it's pretty good for for angle for acceleration and it too is a vector the speed can be changing in one direction or the other could be speeding up clockwise could be slowing down clockwise and of course we've got instantaneous acceleration as well time differential so so we've got all these things that we've done before we just have really not much more than a symbol change take out v put in omega nothing's different take out a put in alpha take out s or x or y and put in theta not exactly the same same same thing here we're going to make a big long chart so we've got a chart of each but if you got these and you know what the new symbols are you've got the new equations that's going to be easy we don't have to learn anything new we like learning where we're not learning anything new because it's so easy to do what else can we do with this that we need to know oh there is something a little bit different when we talk about acceleration that's that's really important we've got something here that can rotate let's uh let's look at a point right on the outside now maybe that's that's where maybe this is a gear that's rotating and you've got some kind of linkage that needs to attach there and you need to know the forces in that linkage because you don't want that thing to break loose when this machine is running whatever it might be we've got some point right there that's of concern let's give this this wheel some angular velocity and I I'll just pick it in one direction or the other so I'll pick it in that direction we can say counterclockwise we can say positive we can say omega in the k direction remember those all equal the same thing so that point at that instant has that velocity no different than when we looked at circular motion a couple weeks ago does it seem pretty obvious that the farther this point is whatever it is and I don't care what it is it's just some point of interest for some reason the farther that point is away from the center of rotation the bigger this velocity is going to be because if this object turns once around an object going in this circle a point going in that circle it's got to go a lot farther than an odd point going in this little circle in the same amount of time so it's got to be going faster as farther to go but it's got to do it in the same amount of time if they didn't go once around together in the same amount of time it wouldn't be a rigid body would it so this velocity must have something to do with not just the rotational speed of the object but the distance from the center and those things are related very simply as well velocity equals r omega it's that simple in fact you could have come up with this yourself with a little bit of a little bit of thinking here let's see let's say our original direction our reference direction is there so the object went from the point of interest went from here to here through some angle theta do you remember from trigonometry how to calculate that distance that arc length let me let me change where i'm putting my letters some so we can really talk about the arc length so this is a radius r that's angle theta and this is some distance that that point traveled s do you remember how to calculate arc length from angle am i a trig doing that when you need arc length if you remember arc length was if theta is in ratings did you do that in trig maybe it kind of kind of kind of just sort of came out of the mist all of a sudden the mist of your young memories which is a lot thinner mist than the mist of my memory my advancing age so everybody's relatively comfortable with having seen that before maybe you couldn't have pulled it right out but there it is and you know yeah now i got it i don't remember seeing something like that what if we took the time derivative of this the rate at which the arc length is changing as this thing moves along ds dt well r is a constant is it not the rigid body you bet it's a constant so it comes out of the derivative we've got then d theta dt what's another name for ds dt velocity what's another name for d theta dt angular velocity so you could have come up with this if you'd only remember the arc length and then i told you to determine the rate of speed of something going around that arc length so what about now this is where things get a little bit trickier an object going in a circle like that is only ever moving tangential to the circle is that right the velocity vector is always tangential to the circle at any instant because if it wasn't the only other place it could go and an orthogonal coordinate system is either comes closer to the center or farther away from the center and then it wouldn't be a rigid body again that radius cannot change on a rigid body so this velocity maybe i'll even put a little t on it to remind us that it's always a tangential velocity there's no radial velocity no velocity in the radial direction it's not coming in closer to the center it's not going out farther away from the center just can't do it so let me ask you this is that point let's let's say omega is constant something spinning at a good regular speed uh some of you have seen record players maybe your folks have one still maybe you even have your own using like an auto audio file a little bit record players uh you turn them on take a little bit just a moment or two to come up to speed but then we have to run at the very same speed or the record doesn't play right it's not really true with CDs music CDs might do that but data CDs are always changing speed all over the place as the as the memory goes from the reader thing head goes from point to point to read your files but a record player's got to come up to a good constant speed and run at that speed so let's say that w equals constant for here for for typing so we've got this thing what then is the velocity constant or not yeah at least constant magnitude has got to be so what's the acceleration of this point the acceleration of an object going in a circle isn't that point going in a circle what's the acceleration of that point direction is changing direction is always changing what's the acceleration the centripetal acceleration so uh we've got this centripetal acceleration which is v square over r where remember this is the tangential velocity because that's the only one that's got so that's the magnitude of v but v is r omega because we want to link all this to the rotational speed so this is r squared omega squared over r or r cancel r omega squared so now we can link the centripetal acceleration of this point to the angular speed um accelerations of vector so what's the direction of this vector yeah that's what the centripetal means it's always towards the center so i'll add that little directional component to it always toward center so there we've got we can figure out the magnitude we can figure out the acceleration of that point the centripetal acceleration what about this what about the fact that omega could be changing the centripetal acceleration only depends upon omega but omega could be changing no it means this would be changing but where's alpha in this the fact that we could have an angular acceleration either this point could be going around faster and faster and faster or it could be going around slower and slower and slower we don't have that in there yet the fact that well if alpha changes what happens to this it changes too we didn't look at that last the early part of the ceremony we're looking at circular motion but it's certainly possible there's also the possibility of a tangential acceleration that point could be going around the circular path faster and faster and faster and faster as if you're in a car going around the circular track radius never changes but the needle's going up that's an acceleration that would be in the direction of this velocity it'd be a tangential acceleration that's remember that's all your speedometer ever records is your tangential velocity and your tangential acceleration how do we get that in there we take the time derivative of this equation because that's a tangential velocity this is the tangential acceleration so it's going to be dv dt r is constant comes out we have d omega dt what's another name for d omega dt so this is r alpha so we have the possibility of handling angular acceleration which causes this point to have acceleration in two different directions it's always accelerating towards the center that's the deal with circular paths but it could be speeding up or slowing down around that circular path as well yeah how's your head feel now okay there's that possibility what did we do with acceleration when we looked at particle motion what did we then do with acceleration problems we said well let's stick with constant acceleration problems didn't we i did did you yeah you got that tattoo right you went and got the constant acceleration equation tattoo didn't you bill that's right i'm good that's where yeah on the inside of your eyelids there it is right after right after her phone number well tell my wife i still have that phone number i'll deny oh i can't deny it what's samantha she'll she probably watches this and then texts my wife what i said that day is to get me in trouble all right so let's see we had those constant acceleration equations constant acceleration problems here as well so let's see uh anybody have that sheet handy just so we can do them in the same number what are you looking for check your tattoo you you're busted weren't they you just looked at your tattoo said yeah i got what what do you need you know man all these guys are pulling out some sheet of paper or something bill you only need to blank what are you doing put a bunch of liars and phonies all right let's see first one remember the order didn't matter but the order in which they appeared in the book the first one was the average velocity which is delta s over delta t well the the average of two numbers is you add them together and divide by two so there was the first constant acceleration equation right look familiar the first one on your tattoo yep there it is thank you for following my simple directions all right let's see uh wherever there's an s put a theta wherever there's a v put an omega wherever there's a t leave it alone so omega average equals delta theta over delta t equals omega two plus omega one over two there's your first constant accelerate constant angular acceleration equation and you already know how to use it i'm not even going to give you a new sheet here or make you go get a new tattoo for rotational motion you just swap out the symbols it's that easy even a college freshman could do it it's that easy second one uh a equals delta v over delta t equals v two no not plus equals v two minus v one that's delta v over delta t in fact that was just a definition of acceleration that's all that one was and we swapped the symbols alpha equals delta omega over delta t equals omega two minus omega one over delta t there's a second constant acceleration equation could be easier to swap the symbols out all the ideas are exactly the same no not exactly the same the linear motion is a little different than the rotational and things that rotate rigid bodies that rotate have points that move in linear uh not necessarily linear paths but but but those type of paths that we described there let's see delta s equals one half a delta t squared what's vi delta t that was the third one so you write it in rotational form and you'll be able to determine uh you'll have your third constant angular acceleration equation just that easy let's see take out s put in theta take out a put in alpha leave t alone take out v put in omega leave t alone you got that see i don't even need to teach you anything new this is this is just a day of of let's do the same old stuff and then the fourth constant acceleration equation v two square equals v one squared plus two a delta s and put it in rotational motion form constant acceleration uh so it's either constant a or constant alpha actually both take out the v put in omega pick up a put in alpha take out s put in theta there you go that easy that's why everybody took the optional day they read ahead said hey this is easy i don't need to go in i'm going to stay in bed chat three o'clock and i'm still in bed amazing just amazing all right so let's uh let's try some of this let's do a constant acceleration a constant rotational acceleration problem now be careful with it don't just jump right into it uh a cd turns on turns up to speed goes from rest to 500 rpm what's that stand for rotation revolutions permitted is generally what it stands for revolution so we've got to be careful because that's not the usual those are not the proper units for rotational motion in these equations what did i say were the units of angles radians or rad not revolutions or portions there of they're of course related because someone that's own a revolution is going through some radiant angle thing but we've got to make sure we've got the right right deal to it does this in 5.5 seconds want to find the angular acceleration we don't necessarily have to worry about direction because we didn't say which direction was turning whichever direction it's going to turn from rest of that it's doing it in the same direction remember how to do constant acceleration problems what do you do what do you need to do a constant acceleration problem remember let's see every constant acceleration problem will involve four of the five possible variables three of them you'll have the fourth one you're to find so what are the three variables we have just like our regular constant acceleration problems just things are turning instead of moving what are the what are the three things we have time delta t equals 5.5 seconds initial velocity is but this is initial angular velocity is zero starts from rest what else do you have sort of we have this we have the font that's actually called the frequency that's uh uh the you know the engineering number we've used but it's not going to work in these equations so we've got to fix it it's revolutions per minute we need it to be per seconds because that's where our our basic time unit is one minute on top so it'll cancel the one minute on the bottom how many seconds in a minute all of them 16 and then here's the next part we've got revolutions on the top we don't want revolutions so we put revolutions on the bottom how many radians per revolution 2 pi that is 2 pi radians per revolution now we have the final angular velocity what is that 2.4 radians per second rad per s so there's the three things we are given in this constant acceleration problem the one thing we're supposed to find is alpha which equation has those four things in it that the uh the average acceleration one has no it doesn't number two does we're looking for alpha we've got omega one and two we've got the time oh sorry i thought you said that's the only one that had average yeah that well remember in constant acceleration problems the average acceleration and the instantaneous acceleration are always the same because it never changes when you have a number that doesn't change its average doesn't change either so we use equation number two omega two minus omega one over delta t that's 52.4 minus zero radians per second over 5.5 seconds that's how hard this stuff is that hard what's that equal and a little less than 10 seconds i mean we got a little less than 10 uh 9.5 what are the units radians per second radians per second square the speed is changing 9.5 radians per second per second plus means uh the acceleration is in the same direction and it was turning because we took that to be a plus uh we didn't talk about it you know it's sitting there turning whatever direction is turning it the the thing to whatever plane it's in that's the same plane it always turns in in our class we're not going to let these things wobble as they turn so yeah well i don't know the cdmi office is that way yours might be that way so it just whatever plane it turns in it stays in that plane the brain in spain is main don't enjoy it you didn't want that movie my fair lady that's that's what it took how many uh how long did it take me to get into constant acceleration problems at the start of the term took uh two weeks or something didn't it we're there in one class rotational most because you already have everything nothing changes drastically from what we had before uh up time to go we could very easily count now the number of revolutions because we could find out what the change of position was and we don't have many revolutions and went through okay do that over the weekend see if that helps keep you out of jail yep title getting that call to come baili out joey county sheriff and even though they didn't credit cards