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# Basic Physics Lecture 26

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My professor Bill break and substituting for professor Danone today I'm really happy to be able to do this A great topic is dead and sell out when I talk to you about his rotational motion it will do today will be mostly qualitative but it's It's really wonderful because rotational motion is is analogous all the different things you better learning throughout the quarter and look at tested on next week so this will be a great review at the same time there's a lot of fun demonstrations that to go with it so just to get started out when we consider dented linear motion by heart More general term is translational motion because of course you can move in 3 different directions 2nd goal Back for like go sideways go up and down the you can move and the So let us category reviews symbols that go with these differ turned to writing mergers involving translation facial learned about position velocity acceleration mass force momentum kinetic energy worker Newton's 2nd law already 0 for position what would be a typical symbol for position X and it we would have different directions so we work for velocity symbol usually as he can You'll remember that general Position as a vector velocities of vector because it can have Different directions and you just use 1 complimented the velocity it's related to the strategic position in a certain amount of time XLT accelerations symbol for acceleration they also A vector quantity because it can be in different directions These complement of acceleration in a particular direction has the change In 1 Change in velocity in that direction with respect time that we have mass that balance a symbol for mass ears You gotta play with me So I mining as a participatory sport tough ears M. J. forests Symbol giant natural ramped up his it's a scalar but forces of actors so I put that number that momentum symbol P E and its people to Masters velocity vector quantum masses the scalable velocities of factor that makes it a vector kinetic energy formula 1 half and these squared work formula WTO calls Remember this did do work The What is war's over different so I push on something and I luminous He dissidents in the same direction as the force that the work so it's a force behind and saying this index direction we could have call it that a new 2nd lock courses athlete Also where you're not playing its new sector equals and now we have all these things have an exact analog in our rotational motion and so that's what we're gonna go through in today's lecture 1st lot kinematics which means how you describe motion is
Our guys Analogs to there's so for position and stand I love this We will force rotation this isn't angle which is and it's actually a three-dimensional as well because you could relocate 3 different directions but orders call my might Paid a Corsican other angles to prove to you that there are 3 different Directions for rotation of course
I can go this way now the way we describe the direction Rotation is to use the right hand rule so you can take years Figures and have been curl In the direction that the object is spinning your mobile point along the axis of I'm going like the direction for the axis Years OK so that's 1 dimension but of course I can I can do Ingalls and other directions right so I can go side by side so of the direction for that will be It's either this way Where that way And similarly Icahn somersault right so that I do right angle for that idea But it's this way that so there's a 3 dimensions for angle but gave no velocity
For velocity we have angular velocity velocity It's also Actor wanted because they can go in 3 directions for today's lecture will focus on just 1 it has its own symbol its symbol ears the small lowercase Greek letter on May And yet It is equal to not analogous So we look up here Position is like angle is like there's so I have dealt light Over dealt this is gonna be they change in angle and a certain amount of time is Igor your velocity Soviet about Clark years ago by the second-hand has a relatively high doable last minute as a slowing last because changes angle slowly and time for acceleration we have angular acceleration it has its own symbol will use the Greek letter Health once again it truly is a vector quantity because you could have The accelerated in angle in 3 dimensions but for simplicity we won't that so we consider that Accelerated acceleration is going to change hands Angular velocity in a certain amount of time so it's Delta in a given amount of time like that and then our last 1 in which had run out of room Table here for years so that that's Those thanks for Our rotational whips indices bottom this really there's the alpha equals the change in Omega in a certain amount of time now not so that's there We strike kinematics wanna think about describing motion the term for that is dynamic up and sold for dynamics that we have A quantity called They asked for your motion for a rotation we have something that is called so mass could also be thought of inertia that's how did some things like has little It doesn't resist changes motion brave much better error has been massive it has hired her So the term for rotation is called rotational inertia And it has assembled capital like that is rotational inertia and what is rotational inertia wheel rotational inertia does depend on vast just like ordinary translational Anderson does But it also depends on how far away from the axis the yogic
So if we consider This for example here is an object that will have some rotational inertia And It's moving this way so the axis that were interested in is the 1 coming out like that when it set up like that as it has relatively large rotational inertia of that will hear it doesn't rotate Avery readily because it has A relatively large rotational inertia With the same man If I bring the masses in close then it will have a lot less rotational inertia the rotational inertia actually depends on different square from the axis you get really big changes at the same time that and takes much more readily and has much less resistance to change in motion so it will pick up there Motion very readily in fact we can actually do More quantitative Comparison with guest I understand learned about right learn about Works toward the light 4 times Remember this level are right It's like that Off worst times level so but toward I can actually apply toward this time I've got a little we'll here in the middle and then apply force which is gonna be the weight on it so this is going to be
Energy is gonna Taiwan on this thing and then there's a little wheel in his artwork on this system The answer is yes because the the way doesn't go right through the middle here it's off to the side so there's a little level forums like that it's gonna pull and so when I let it go right now will 1st sunny 7 up So that the rotational inertia is bank Then when I applied network to system it will it will be it will rotate death Fast because it has been rotational inertia so let's let me try it we go prodigious before a carrot as to exploit that supply network actually it's accelerated skiing angular acceleration because it's getting more and more toward switched over a Now let's try the same thing again but make the rotational inertia kind so I do that by putting the mass close to the axis of the My backed out do that When it backed up OK and security apply torque St. toward the level and the the same stuff For starters but arms as saying Reddy said Don't forget Oh spends much faster now because it has far less rotational inertia That make sense
OK so that's about rotational inertia to concede Bar Belles heroes like in the picture OK We know that forced the thing that's analogous for force is toward more just like horses a what makes things move 21 translator toward Are what make things rotate so you plight toward You can rotate text symbols that is how it's a vector quantity in general and you learn about more that it is deep level arms crossed with the force that supplied to it so just as reminders a slide shows toward you want you want applied toward this goal In order to turn it so you can apply a certainty for switches Supplied by your muscles in your arms if you have it you don't have the force cross product optimized you apply less you can get more torque By optimized so that are crossed and is at its maximum magnitude that will turn things better But indeed anymore you can make a little harm or longer by putting a pipe on top of your ranch and then you can turn at a time like that so that's a toward R cross F reminder OK and then we still have momentum and kinetic energy sofa momentum we have up she any they you don't have Any external But when is momentum sir when you don't have any external forces that's an isolated system self Where is a similar kind of playing for something called a dealer moments of painkiller momentum Travels civil and actually could figure out by analogy what Elliott's what's play lot the mass stadium Analogous to mass rotational inertia Sigh eyes and what's analogous to beat A maker Is now that's a velocity velocity so that's what A new momentum it looks like that We do the same thing for kinetic energy leaders kinetic energy but if something is rotating away in Hesse Kinetic energy we take weight off this thing's rotate it has Connecticut energy associated with that motion weaken describe In terms of it That so there's still energy formula for it is 1 half what goes with them You go play with me 1 half All and were goes with these words The main square of the kinetic energy as work their stability work so what CA larger force However for Now Planet is not with me you're just don't quite again In a lot of 4 skiers Toward so it is how it ends At And 1 position in years Angle so it's like that so if I want to do work on a bicycle wheel I will want to apply work to it so I play toward by applying of force this way so that All their crimes Will apply work to it and I could do it over a tiny angle Parents I Divide I would do a lot of work and would have a lot of kinetic energy I can apply that same amendment to the toward Over a bigger angled toward over a bigger angle and spins faster I do more work on the object because I wish Frivol barbaric just like in for Translational book and so gains more energy than it has more kinetic energy As it stands around So that's that when and if we have a news lots which are actually There's an alliance for all of Newton's laws as well I did Tibet mentioned the rotational inertia Depends on the direction of the motion we have 3 different directions in general and so it would choose this particular if I put In on the left hand case I got my mask close to the axis so that has relatively low rotational inertia in the right place I got my mask bar if possible from the axis of that has large rotational inertia or so here's a quicker question of where get technology work By disklike best That what I do L is working OK Just do the first one which position has the largest rotational inertia or carried out OK So now I stop And then I which when Aziz display your answers OK so 67 per cent of your brilliant and I know what to say but OK so the correct answer the largest rotational inertia is thee because that's just like capitulation Before the body as much as possible away from the rotation axis which is turned table in the middle Just when I'm a clicker which once a small Because that's the 1 where person's got much gas Possible and the other wanderer intermediate actually see The largest to smallest B is largest city is next because there is more mass in a lake in there is in itself His next a next because the arms were so far away Indeed it is the smallest like that get so that's it Idea behind rotational inertia Now what we with see answer OK Now Newton's laws are analogous for both translational and rotational motion 1st of all Woods It was 1st somebody raise hand for what 1st But Lemieux to fill in the blank against us 91 i'd I used to use can motivate people to talk and when I did physics but knew his 1st an object emotion tennis too Emotions and the stationery tends to And as long as there is no force that's what happened OK so we have an analog for that the rotational motion of an object is rotating it teacher of so here's my we only got going There is no talk Until now several variants that are really good so there is isn't much work associated with the billowing or energy dissipation source said with So wins 1st as it likes to keep rotating stationary elects stay stationery That just like his 1st 4 translational knew exactly where I talk about this when 2nd is ever peoples and end of the 2nd is like that there no obvious pork is rotational inertia Times angular acceleration and I I can't worry demonstrated
I replied A constant Pork before And I change the rotational inertia So when the rotational inertia with small they need acceleration was You would think when it For the sake thank tore the rotational inertia is small the angular acceleration is Large and vise versa gay now cost can do the same thing where we can have a certain hour rotational inertia And apply different ports I want for it and neighbor acceleration is pretty small white with a bitter toward the cost acceleration is so that's just the same as when India's unions lock where you have The factor acceleration mask and force coming into play for none 3rd It's often quoted this way for every action there is Reaction another way of saying is that Forces comment action reaction here so I I push on the floor before pushes on me but actually want jump higher it seems counterintuitive until you understand Why do you want a jump higher push harder on the floor right because that makes before Push harder back through new 3rd locked case so you get they common action reaction PARIS lesser for rotation to torts coming Action Reaction pairs So if I apply a toward this object it applies toward bill applies for 2 rather applies Work to build tried to make me go the opposite direction so here's a book I forgot about this as was back Newton's 2nd adjusted a practical example of this toward people's rotational inertia times angular acceleration so if you're running when you win you won't use Laid back and forth And periodically normal motion K. so when the Lakers out straight it has relatively large rotational inertia review and that it's close to the axis rotation has less so if you want go faster after while you have trouble doing knowing that it be hard to you legs of major rotational inertia and you could do a bit more angular acceleration fell That's the idea behind a new 1 of their applications News 2nd as applied rotation years back A 3rd comes in action reaction PARIS When a person is up in the air and isolated system and there's no toward side so this athlete is jumping up in the air swinging with their arms Because you're an isolated system Torque applied to make arms by the bodies on gives an equal and opposite toward the lower body to rotate the opposite direction So you get this Actually reaction kind here for talks and this is a very important vertically and athletics with involving gymnastics and things like that OK so this is our summary where you have of water but this is just a nice PowerPoint you have are different things that we have and how we have these analogs between all these different quantity of filets to another quick quicker questioned 2 I was going demonstrate 1st so you could wait a minute you want but pretend that I'm playing baseball and is a really good fastball pitcher against me so they throw it fall's or you yet By the time I swear would do well I actually will choke off and the next it comes now I'm able get around by the tent pitched because I only have a fixed amount of time to judge balls but also be abolished right The The 1st of past If Schiff theft Pot Show Ace poster be rotating that rotating Jussi case you're wondering Peres stuff The correctly answered 77 per cent is correct a majority rules as So this is an example of this is actually just like the running example New set alarm So too I'm rotating a subject of the rotation axis city and hear some somewhere talking and that's So the rotation axes exorcist here it puts the mass farther away from rotation axis and so you get more rotational inertia put actually you would choke up there as you put He The mast as close as he possibly could to the rotation axis minimize 40 all of this and this is easy to rotate tried yourself me feel it very readily As much as you rotate ownership supplies the 2nd in order to catch up with the fastball which is that a common a finite amount of time I need to get my I need to have a significant angular acceleration because I'm starting from no rotation and then I'm trying to get up High rotation when I get so I knew lot of Hagler acceleration sense and my body is only so strong which I could apply more toward but I have limited amount toward that I So I always so strong for toward the best way to get more angular acceleration is 2 things I thereby increasing out So he was Karakul boat shared at a gay Now this is too easy sorry Never mind that beat that's highlighted by red For some reason I actually don't like a lot of Cut Microsoft products but for somehow I could get that beta not be ready OK Once again the majority is right it is I'll make efforts solitary remember about momentum Just translational momentum p Equals can be so now media had 7 analogous and what's analogous and the rotational inertia is an analogous to just inertia and the analogous to be busy angular velocity We need make it is that correct into their and up that rotational inertia tides any over last year's crack OK Now I'm gonna do it emits radiation And that is the way it can work so this thing has been so it doesn't apply
As for it Around its axis It doesn't mean it's got a little bit of talk to open not very much so when I stand on this kind of pretty much be an isolated system Remember for conservation of momentum the condition for concentration on mentor was no external forces the condition for conservation of angular momentum years No external Pork because torture analogous the forces so no external forces entered talks so so once I stand on this thing I can be isolated system with no External talks that will mean that I think we're momentum will be conserved now when the did is I'm going to take and I am going in Kansas my rotational inertia by holding these weights out and then of course I can't believe they can adjust my rotational inertia dramatically because I couldn't pull the away In toward z-axis which makes rotational inertia Small put far away from the axis which makes the rotational inertia So Bobby spinning on there and then all pulled awaits him and what was gonna happen
Let's trial or prediction OK now you projected B faster they also because a moment his consort witches The basic assumptions were sodality stridency we make hypotheses in fact now you popular don't but
But 1st men's continue mules escape Each she day E we can travel faster ahead of the e um if if if if a again so the idea here is that you can see why I was happy to substitute for this year's they also adjust Zeus's inside the apartment now has little
So you on the city makes all state And I like that I I like the thrill of knowing to kill yourself OK so so I spend vast is a momentum is conserved but This really shows more but the idea is that I kind of figure It as the saying so in this Case The 1 left eye is a but Omega smaller 1 on the right side is small but made his day in both cases L so that's what we just saw him straight And this should remind you did did didn't fire off the liquid nitrogen canon for you I am sure we can because the White House Level we got pun intended but guess so and so the idea behind them it Isolated system there's no external forces It has no momentum initially So the momentum this way from The Canon heresy We feel the momentum that way from We cannonball were that our case a plastic bottle and can evolve has small mascot huge There's 1 Asked but little And the 2 mentor Equally so it's saying kind of thing with trade-off master velocity but The 2 are Comparable Our Are equal to each other because This conservation property Now another thing that happens when I pulled in is the kinetic energy increases and that's not obvious you and so I assure you a Show that circuits This we decided for sure and momentum Spencer so Think of 1 is when my arms around so my arms around I want is big When my arms and I too is small and correspondingly 1 is small when my arms around in when my arms around that we can just solve this Figure out what's gonna happen to make it to and that made it It's whatever my initial speed was Times the ratio Both D rotational inertia with my arms around the rotational inertia my arms are a case so so just in terms of the experiment Why did I and masses I hold those weights in my arms which factor here I Was I changed I was changing I want as tried I 1 big star with because my arms are actually a very big part of my total weight right but by getting Matt out there to try to make big change rotational inertia and then of course I guess which but What are our best are not to give me a very big push to start with so when I want minimized That was a megawatt has pushed the union It was a megawatt now has a change in energy work well You remember that kinetic energy for 1 half empty square sort analogous thing is what have I square here we just write down a formula for what Initial kinetic energy must compare how much kinetic energy we have After I pulled my arms that governed by the same formula so now what I wanted to do is use this Formula up here Substitute and permitting it to do so I do that make it too is I wanna right to Amigo 1 square that what I get from that Years after do the Algebra I end up with I 1 square overall 2 times Omega 1 square that I remember that 1 half I want a bigger 1 squared is The initial kinetic energy so I find the kinetic energy with yours full then is actually altered by the same factor has Velocity as I want all right Now if you want something kinetic energy when you have to do To give a kinetic energy I do Yes But you do have to apply for sets true why actually know you don't have to apply forces do I do work on the podium right now and I might applied force to the podium So you have to have You work it has forced times OK So I said that my kinetic energy increased liking and there must have been some work done on on the rotating body for that to be true and indeed their ears what With theory now so As I'm spinning around as I'm spinning around The case I knew his 1st love What is They Actually did you circular motion OK So this gets 1st circular motion do you remember What direction the acceleration is something answer Promotion called centripetal acceleration in here acceptable acceleration and points in Towards a sad day so we often called their called we but so in order for this I go around the circle there has to be Centripetal force the pulling and Ford's center in the object of left to its own devices would like why off way So what I have to to do is you know this spirit your spent around the waist was like that so I have to do is get to warmer Call the weights again so that always that I did over distance and wears an energy come up it goes into the system of the rotating body and I have more Connecticut energy than I had before so That's the basic idea years centripetal force supplied by the skaters radially inward The motion the weighted or arms is also in words of the work force and distances positive that work done by the athlete which comes from where the work Done by Athlete Comes from where There was also talk tell China encourage you to think about total system and the whole system is isolated here so I do work with the reservoir of work that I called upon in order to be able to pull those weights Breakfast right Watch a minute's chemical address converting chemical energy into mechanical energy in order to do that work but At It's about somebody picked up the Bulls Get ready What about that But Yeah yeah No no but did you would be isolated words a more complicated system took to analyze in that case Now that's true you wouldn't you would necessarily spent a moon should try But
The city so just spending OK now and operates OK I am back to me Both spun out Some because of my own Rotational inertia of wouldn't work So I because of forgot that I have rotational inertia my my heart but basically you can taken away for the back there was no word that during that time and I'll still be going the initial right If I should get my arms out there and play in the park Would work so that that's er E answer to that with boat OK so here's another Wyman do another experiment when they do here is to appear again and again have these bags out And I'll be spinning and then at some point I just distillate peg go into question when I let go of the bags were they gonna do they sell let's get your hypotheses
That's OK We have mixed opinions here The majority think But there is a special number that they could be in some think it's OK a OK So our what is a key issue in thinking about this this is
Back to actually knew the 1st lot kind of thing because once I like those that bag There is 1 for still on wet weather forces on the back a of gravity so that They will fall down because of gravity But Let's not let's not worry about that direction right now that's that's this way now it we think about the other part when I let go Now there's no force answer which they did they should be going it we just cut that view from above They should just keep going in a straight line the way that they were going right What we're going to born in circular motion so what where are they going to remember about Circular motion which way the velocity goes The velocity goes sucking down above the velocity his can't enter circle right so I should like And they should just wide out Diaz videos 1 your intuition grabs on but is not right They're not spies there's no For spiral around so this is a back to 1 of that trick questions renewed 1st often comes upon test You don't it doesn't care what like go the just flies in it In the direction wants to go get so let's see what were actually works as planned So it is a wanted a decent was this time so we concerns This could never see you want you should be working from above but we'll see what happens their work But at odds Mystery why away from fall down in the direction they were gone OK so we have time for another way sowed the way this 1 works is is another really cool conservation of momentum demonstration so But a new momentum demonstration a case of this we'll has gained momentum as it has a certain amount rotational inertia And it has a newer speak so that's That's why I tend to make Means it it has a certain amount of a a case take it like this And I get on here and I want to say station to start among was stationary Knight somehow I got tickets OK here we go So now what I wanted to is right now what's might get a new momentum There is no net gain momentum this system right so it's gonna happen if I put this thing over Check That Isn't physics Kuo that reduce both to say yes professor hydrogen fuel If a with understand how this works so we set up so so
Also the being stands For the illegal momentum of the wheels that I have any momentum the start with no because We we arranged so I was standing still so the 1 on the left Initial conditions like now when I put the wheel over A momentum as a vector and and hasn't direction to a Dow the wheels spinning opposite way right and will now LB is pointing down but we No by conservation and momentum that the son of these 2 things as they add up to what we had initially Because the system is isolated 1 and so since this down this thing has turn which is gaining momentum of the man has turned out to be Twice the man of initial angle momentum of the bicycle wheel that make sense to understand is that you could make it is almost as something very similar to this sport Linear momentum and inhabit beyond like when you're exams That's that's critical OK what else we have now is another another thing now we talk about conservation momentum and years aggression and often comes at you start object and improve this to you but there's no Towards on falling bodies in the absence of Appreciable wind resistance so you have a body and its isolated and doesn't have any gain momentum to begin with Canada terms Has no legal amended the start with which means a is equal to 0 So can By So you might think no any answers that the correct answer if you have a rigid body but if you have a body they can they had been uses Newton's 3rd law of torque saying in order to turn 1 part of your body while the other party is turning And then went to stop moving Figure back no moment knowing that a new momentum but you'd like that 1 part to rotate 1 way the other part to rotate the other way And it works out of course the most famous example this is not the 1 that might still be pathetic never good at it But most of Famous example of A new job parameter cat upside down will they land on their feet Yeah Any answer is yes they deftly another thing they can do it they start with knowing momentum but they have very flexible bodies and they have these things where they can rotate 1 way or the other proteins in other ways which to the fee based on the ground and land on the ground now I can show you I can show you sort of a calming version of this
Because I'm not Nearly as agile as a cat but Dr. Fauci that serve no comment a case study did you Did you like rotate your upper body It will move your lower body so you can do it like that and you can you can do get like that for a that is that
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