in this video I'll talk about the rotational and translational kinetic energy of a helicopter so we have the helicopter with the four blades the length of each blade is 5 meter and the mass of its blade is 60 kilogram the total mass of the helicopter is 200 kilo gram now we need to find out what is the rotational kinetic energy of the blade if they rotate about 350 revolution per minute and then if the helicopter is flying are moving at 80 mile per hour what is this translational kinetic energy and what should be the total kinetic energy which one is greater the transpersonal and kinetic energy will be calculating everything in this problem so let's start with this one so the mass of each blade is given with a 60 kilo gram the length of each blade is 5 meter and the blade is revolving or rotating about 350 revolutions per minute an infinity change evolution per minute to Radian per second you have to multiply by 5 over 30 and it's calculated here one revolution per minute is one devolution per minute equals to 2 pi because one devolution corresponds to 2 pi the entry moosh one complete circle and the total angle will be 2 pi that's what it means and one minute is equal to 60 seconds so 2 over 60 now it will be PI over 30 so in order to change from revolution per minute to Radian per second you have to multiply by PI over 30 and if you solve it you get 36 point six five Radian per second the mass of the helicopter just including the blades as well is 200 kilogram and the translational speed is given 80 km/h 80 km/h we need to change 80 kilometer per hour 2 meter per second so the one kilometer corresponds to 1000 meter and 1 hour corresponds to 3600 second so simply do the math it'll get 22 point 2 2 meter per second that means in one second it moves about 22 point to 2 meter so first thing we'll do is calculate the moment of inertia of its blade the blade can be assumed as a single rod as a rod here and we have four blades here so the total moment of inertia will be four times the moment of inertia of each blade and remember it is rotating about this axis here this axis or in other words it is rotating about this axis all the blades are rotating about this axis so it is not through the center of mass it is somewhere at the end it is rotating about the end so the moment of inertia of a blade or a rod about one end is given by M and squared over 3 where this is the mass of the blade be it stands for the blade L is the length of the blade and then you'll get another factor 3 here ok and this is already calculated so you have to watch my other videos to see how to calculate the moment of inertia of a rod about the one end so for now let's plug in all the values the mass of each blade is 60 the length of the blade is 5 and 3 if I solve it you get 2,000 kilogram meter square meter this is the moment of inertia of the total place of all the four plates about this axis of rotation so now let's calculate the rotational kinetic energy the formula for calculating the kinetic energy in rotational dynamics is 1/2 pi Omega square and I is the moment of inertia and Omega is the angular speed so we have we have the moment of inertia I we just calculated with 2,000 kilogram Omega is the angular speed we just calculated this one 2 Omega which is thirty six point six five thirty six point six five and we solve it this is the energy you will get this is the rotational kinetic energy let me ask you a question now here we have taken the moment of inertia of the blade the entire blade here we did not take the masses of the other other other masses into account we did not calculate the moment of inertia of this helicopter we just calculated the moment of inertia of each blade why and you can see here the the one the the answer is the one of the blades is rotating this one is just moving the entire this mass is will be moving in a in a one direction or it has only the linear motion the 1d rotational motion has the place the place at the one good thing that is rotating so we just took thee when calculated in a rotational kinetic energy well it took thee the the moment of inertia of the Braves into account because only the blades are rotating or revolving now let's calculate the translational kinetic energy so when the helicopter is moving the entire system is also moving here with a certain velocity even the blades are moving along in the MV in the direction of the motion so in order to calculate the translational kinetic energy the formula is half MV Square where m is the mass total mass of the helicopter V is the linear velocity so it's everything is given the mass is 200 kilogram the velocity we just have calculated is 22 point 2 2 so if you solve it this is the kinetic energy of thee or the translational kinetic energy of the helicopter this is for the entire helicopter and this is for the this is only for the blades so the total kinetic energy of the total kinetic energy of the helicopter should not be the blade village really helicopter including blades is given by this formula that's the kinetic energy a scalar quantity was simply adding these two numbers now KRS stands for the rotational and kts stands for the translational kinetic energy so this is now the total kinetic energy of the helicopter including blades so now let's compare the translational kinetic energy to rotational kinetic energy so I'm just finding out the ratio of translational kinetic energy to the translational rotational / translational so if we just plug in all the numbers what we get is 4.5 3 what is it 4 point 5 3 means this means the rotational kinetic energy is 4 and 1/2 times greater than the trance let's build kinetic energy okay so the blade in fact has more kinetic energy than the the the translational kinetic energy of the entire helicopter okay let me dip it one more time the blade the blade has a more translational kinetic energy than the entire translational kinetic energy of the helicopter so this is it from 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