in this video I'll talk about the rotational the dynamics of wind turbine so we have a wind turbine here which is rotating and for maintenance it is turned off and then it takes two minutes to come to a full stop the inverse speed valid at a time which is given by this equation or this equation it's exactly the same thing so the annual speed is some time dependence which is given by this equation and it's not linear it's not decreasing linearly now we need to find out the angular velocity and angular acceleration average convert acceleration and instantaneous convert acceleration first thing we have to find out the direction of the angular velocity and the angular acceleration how do you find out the direction in order to find out the direction we have to use our the right hand rule what is the right hand rule tell you the right hand rule tells you you need to curl your finger in the direction of the rotation and your thumb your thumb gives you the direction of the angular speed so if you imagine yourself turning your fingers in the direction of rotation that you can clearly see your thumb points in this direction this direction or perpendicular to this wave as hot or sometimes they just have to penetrate and go into this direction okay so that gives you the direction of the angular speed and now what is the direction of angular acceleration the angular acceleration is opposite to the angular speed you might think how come why's that the angular dispersion is opposite to the angular speed and it is opposite because the angular speed is decreasing it is slowing down it is coming to stop and that's why the angular acceleration is opposite to the angle speed let me give you a little bit more intuition for this one let's say you have a ball if you throw a ball up in the air that is the velocity direction but the force is acting downward and this force also has an acceleration which is X less than due to gravity is slowing the speed so whenever you throw a particle upward the velocities in upward direction and the acceleration is in the downward direction and this acceleration which is the force making the speed of this object slow down okay or in other words when the velocity and the X equation are in opposite direction that means it is coming to a stop or it is slowing down okay so now we talked about the direction now let's calculate the average Android exploration before we do this but before we do this let me ask you a question what is the term average means whenever you have to calculate average acceleration have this velocity whatever there you what is asking you do you know the final position or final acceleration and they are the final speed and they DC this initial speed so all is asking about the final information and the initial information and the in order to calculate average angular acceleration you need to know the F the final angular speed and the initial angular speed we know the final angular speed because the turbine has come to a full stop so there's a final angular speed is zero now we can also plug in the time and see it is zero so this is lead hundred a speed expression and it has come to a stop in time cost to 120 second that what is given here it takes two minutes for turbine to come to full stop so if I place the two minute which corresponds to 120 second into this equation two times 120 that's the zero Radian per second so which makes sense because the Taliban has finally come to stop and the intial and alert a speed how do you calculate the initial angular speed you just have to plot time cos to 0 into this equation and what we get is one point four four so now we know the initial angular speed the final angular speed the formula for calculating the average angular speed is this and this board here the little tiny line means that's the average and alpha stands for the average angular acceleration and the Delta here is the change in the annual speed divided by the change in time or the time interval the change means the final angle speed minus initial angular speed that's the final time minus initial time the final angle speed is zero and we just calculated the initial angular speed which is one point four for the total time it takes to come to a stop is 120 seconds and now at the initial time is zero if you solve it what we got the negative 0.01 - I can work out what the negative sign mu the negative sign means the angular speed is decreasing that means the turbine is coming to a stop or as angular speed is decreasing over a time now let me let let's calculate the instantaneous and Lord exploration and you do not get confused with the average and instantaneous let me give you a little bit idea about what what is the average and this continuous angular acceleration means okay it just took a quick thing to recall you let's set two portions driving cars this is this is you and this is your friend and you started from Odessa and both you have decided to go to the Dallas okay both its own or decide to tell us both took exactly the same time five hours this the fiber what's the time is exactly the same so the average is speed let's say I'm just giving a little bit average and then it's ten ten years the average speed for both of you it's exactly the same because both of you have travel exactly the same displacement and the same time so the average is exactly the same but now you what do you have decided sometimes did you move faster let's say 80 mile per hour and at the time you you take a bread lunch break but your person is just moving with the exactly uniform speed but both takes exactly the same time what does that means the instantaneous speed is way different sometimes for you it is just bumping up it is going up and down but your friend that is a constant so that what the average and instantaneous means the instantaneous means at that particular time for example in your car the speedometer tells you the instantaneous speed at that particular time okay so there is a subtle difference here so in order to calculate the average speed you need to know the final information and the initial information and you know in order to calculate the instantaneous you need to know at that particular time so how do you calculate the instantaneous angular acceleration so we given is the angular speed which is a function of time and the instantaneous angular acceleration means the rate of change of the angular speed or in other words you need to take the time derivative of this endless velocity with respect to the time ok so let's do this one so so this is the first derivative D over DT and Omega T is given by 2 T 1 is 240 over 200 s squared but now you need to take a time derivative and I have given an example here so you have D 4x minus 5 square what times DX the first thing you have to take is 2 times 4 minus X and then take the derivative of 4x which will be simply 4 4 times 2 to be 8 times 4 minus X so the same thing here so 2 and then now you have 2t minus 240 and then you need to take this time derivative of this function 2t which will be simply to here so practice this one if you have not familiar with the derivative and you'll get to get it so 2 divided by and this is a constant so I'm just taking this one out ok should just take you out and there's a squared function 1 over 200 s square now we have a two-year to 2 or 200 square and then 2t minus 240 so we've now got the instantaneous and what acceleration is a function of time and you see this one is a linear function linear function while the angular speed is a quadratic function now what I'm going to do is just plugging the different time it is asking at 30 seconds so what are you going to do plug time equals to 30 second into this equation to over 200 squared 2 times 30 minus 240 you get negative and at time equals to 120 second integer division makes sense because it has come to a full stop at under 20 seconds all in two minutes so this is how you calculate the instantaneous angular acceleration average angular acceleration friction from just from the angular velocity information if you have given the angular velocity variation with the time you should we calculate all the information and again practice if you have any questions write down your questions in the comment section below and to not forget to Like share and subscribe the channel thank you very much