in this video I will talk about a rotating fan we are given a fan which is rotating with a constant angular acceleration when it says constant angular expression that means it is speeding up and the rate is given it is just like a linear acceleration if you are in linear motion so now we need to find out what is the angular or giving the given thing is if the angular speed of the fan is false Radian per second at time T equals to 0 that we need to find out the angular speed at a later time which is time T goes to 10 seconds and we also need to find out the angular displacement when it says AMOLED display displacement then it is asking you to calculate theta and the number of revolution made in time T equals to 10 seconds so let's do it for the given quantity or the given values are all of alpha which is the angular acceleration remember this is just like a linear acceleration in linear dynamics an Omega naught the Omega naught is the initial angular speed which is for brodien per second and now we have to find out the angular speed at a later time or at time T equals to 10 seconds then we know that this relation here Omega which is the angular speed at some other time and Omega naught which is the angular speed at time T equals to 0 or the starting time or the initial angular speed alpha is again the angular acceleration T is the time and this relation is exactly identical to the relation V equals to u plus 80 which is you might have studied in the linear dynamics or one-dimensional motion because if you remember this relation you can write down exactly the identical relation in rotational dynamics the only thing you have to do is the V you have a change in the angular speed and this initial is pretty hard to change it to the initial angular speed here is the acceleration you have to change it to linear acceleration at the time at a time so now let's just plug in all the values so we would need to find out Omega Omega naught which is given as the initial angular speed which is for always keep the unit of Omega naught 2 Radian per second the Alpha is given which is 5 and we have to find out at the top tickles to tell second that means the angular speed is 54 Radian per second now we need to find out the angular displacement the annular displacement is just like the linear distance traveled in linear dynamics or linear motion so if you have a study this relation s equals to UT plus half ay T Square that you should be able to write the corresponding or relation in rotational dynamics in this case in protests on dynamics the S is the the angle because it is now revolving about its axis the only thing that is moving or changing is the the the angle here and theta naught is the initial angular position and U is the Omega nought again T is the time have a is again replaced by the Alpha so this is now our relation in rotational dynamics for calculating the angular displacement need to find out theta and theta naught as I mention earlier is the initial angular position so this is your own that means at time T equals to 0 we assume this is the starting point that is the starting point and Omega naught we already know it is 4 and we need to find out the time which is 10 seconds have alpha is the angular acceleration that means it is speeding up just like the moment when you turn the fan on what happens it keeps speeding up and the rate at which the angular speed changes is the TEL affair or the angular acceleration and that is given as 5 and again T is the time which is 10 second episode which you got the 290 already n so this is in Radian now you need to change it to the the degree so this is in degree what is asking here the number of revolutions that means how many complete terms or how many terms it has made in this time T equals to 10 second or this fan how many terms did this blade has turned how do you find out so we know that the one devolution is equal to 360 degree or 2 pi you can also write down as 2 pi if you feel comfortable that way and if you need to calculate in degree the 1 degree is 1 over 360 degree so this is in degree and this oh this is 1 over 3 revolution this sort of in revolution let me write down here or simply called re V that a stands for revolution so now we need we have this much degree so if I need to change the degree' into the revolution I simply have to divide by 1 over 360 just divided by 360 and I get is 4 for the 6.2 revolution that means it has turn are slightly more than for the six complete terms in time t equals to ten seconds so this is a about the rotating fan where we have calculated the angular speed angular displacement and then our number of revolutions again if you have any questions write down your questions in the comment section below and do not forget to like share & subscribe the channel thank you very much