in this video I'll talk about how to find the angular acceleration of merry-go-round but also we have to find out the and little speed of it I'm the number of revolutions a given quantity in this case is the moment of inertia and a father who applies the force on to thee on to the merry-go-round so let's start with this one the moment of inertia of the merry-go-round is 100 kilogram meter square that is given here and the father is applying a force at the end of medical round to the force is 200 Newton and the force where he is applying is 0.5 meter or 50 centimeter from the axis of rotation so that R or the distance is qualified meter so once you know the force and the the distance from the axis of rotation we can find the torque that is acting on to the the medical round so in rotational dynamics we talked about the torque that makes the objects rotate about an axis the torque it's a vector quantity and the magnitude of the torque is given by our F sine theta so for those who know about torque the torque is R cross F vector okay torque is R cross F vector so it's a vector quantity and this is the magnitude and here we are interested in only finding the the magnitude and if you want to find the direction you can find it simply by R cross F vector which will be in the upward Direction R is 0.5 meter the force is given 200 Newton sine theta here theta is the angle between the R vector and the force in this case this is 90 degree so the side 90 degree if we do the math we will get 100 Newton meter nasty 92 of the torque so if a father is applying the force what would be the angular acceleration so it so you you already have studied in classical in linear motion that when we apply a force onto an object then there is an acceleration and it is given by that force is equal to mass time acceleration the same thing happens in rotational dynamics here instead of force equals to mass M a the force is it replaced by the torque the mass is replaced by the moment of inertia and the linear acceleration is replaced by the angular acceleration and we can calculate the angular expression by simply by tow over I that's what it is here okay this is exactly the Newton's second law of motion in rotational dynamics torque over I what's the torque hundred Newton I is given 100 so if you do the math or 100 over 100 we get one Radian per second squared that's the unit of angular acceleration so it is pretty straightforward to find the angular acceleration now let's find out what is the angular speed when I say the angular speed that is equivalent to finding the linear speed in linear motion and we also know that V equals to u plus 80 for those who have take who have studied the linear motion in this case V is now your Omega V naught is your u again a is the angular acceleration so you see there is a very similarity or equivalency between the linear motion and the rotational motion once you know the the formula the equation for linear motion you can translate that linear motion equation into the rotational dynamics equations okay so the merry-go-round was at rest initially so the Omega not here is 0 what this gyro means here the merry-go-round was it initially at rest and the alpha he had just calculated alpha which is 1 and the time is 20 second so we have to find out what is the speed of the medical route after 20 second that's what he says he had a point the angular speed after 20 second okay so just finding out in the just substituting the time T goes to 20 seconds so after 20 second the angular speed of the merry-go-round will be 20 Radian per second so in 20 seconds now how many revolution this merry-go-round has made so the father was the father has applied the torque or is applying the torque in 20 seconds harmony revolution it has made how do you calculate the revolution in rotational dynamics is exactly equivalent to the displacement in linear motion so the theta is in so we need to find out this theta here and how do we do that so again recall the equation from the linear motion s is equal to UT plus half ay T Square so in linear motion we'll talk about the distance and in rotational dynamics we talk about the theta so you see there is an equivalency between and U which is the linear velocity is now replaced by the angular velocity the time is the same thing and here half is now happy is a constant and a is the linear acceleration here you have and relaxation and the time so again if you know this relation you can translate this relation into the rotational dynamics so now let's plug in all the values Omega not a zero now you have to answer to me why Omega naught is 0 because the merry-go-round was initially at rest half as it is alpha alpha values 1 was just calculated and again time is 20 square so it will be 200 Radian so in 20 seconds the merry-go-round has made 200 Radian so we need to know translate this or change the 200 Radian into the number of revolutions so if anything that is revolving or even rotating about some other axis once it complete one complete rotation or evolution in a one complete rotation the total angle is 2pi or 360 degree so two pi Radian cuz wants to world evolution so one Radian is 1 over 2 pi revolutions so once I know the Radian I simply have to multiply by 1 over 2 pi then it gives me the number of revolutions in this case it is 31.8 evolution so that means the medical round makes about 32 revolutions in 20 seconds so this is it for calculating the angular speed the angular acceleration the number of revolutions for it may be go round once you apply subtle about that torque onto it and here we have made a general assumption that there is no any friction force here and the story would be different if we take into account the frictional forces so this is it from this video if you have any questions write down your questions in the comment section below and do not forget to sailor and subscribe the channel thank you very much