in this video I'll talk about the moment of inertia of a system of particles is the individual particles so we have five masses the mass of each individual object is given and the distance from the axis of rotation is also given and we need to find out the moment of inertia of the system and we also need to find out the rotational kinetic energy of the system so first let me tell you what's the moment of inertia is so in linear motion we'll talk about the mass the more the heavier the mass is more force is required to move it or most force is required to stop it if it is already moving down the heavier the mass is the more and Nursia it is it does have so if we have a heavier mass then in order to move this mass you need more force or already for all for a heavier mass if it is moving more force is required to slow it down or to a stop it but in rotational dynamics the mass is now deflected by called the moment of inertia and the moment of inertia depends on the mass but it also depends upon the distribution of the masses how the masses are distributed their stuff for example here we have four five masses if these five masses are distributed much more further than its moment of inertia would increase that means let's say it is rotating and you have more masses here then you require more torque or more energy to stop it okay so what's my other videos about the mass and the moment of inertia and you'll get a clearer understanding of it is so here just before I solve the problem a little bit understanding or the concept which talks about the differences between mass and the moment of inertia so whenever we saw the rotational motion what we'll talk about the the moment of inertia and in linear motion we talk about the NASA's so how do you calculate the moment of inertia as I mentioned the moment of inertia depends upon the distribution of NASA the mood it is away from the mass from the axis of rotation the more moment of inertia it will have the moment of inertia also means is the more torque is required to make this object a spin or rotate about axes so how do you calculate they this is a formula for calculating the moment of inertia I stands for the moment of inertia which is now the summation of m-i r-i Square and as we have five individual particles I can simply write down a munna order R 1 square plus M 2 R 2 is square M 3 R 3 square and so till we get to the fifth one the mass list with this mass is one kilogram so we have one kilogram and the distance you can put down the negative sign but the negative sign doesn't matter here because it is a simply distance or it is a square so the negative sign want to make any difference and this distance is 20 centimeter so we need to change the 20 centimeter to meter it will be point 2 meter so that's what it is Harlan a squirt now for this mass m2 is 5 kilogram and r2 is 10 centimeter which is 0.1 this mass M 3 is 10 and what is the R 3 the position that position is 0 so the J square M 4 is again 2 and 10 centimeter which is 0.1 five is 15 and point two is squared and if we solve it what I get is point seven one and crazy meter square alright so the unit is crazy meter square kilogram meter square this is the mass and this is the meter square or a square metre kilogram meter square and now let's calculate the kinetic energy rotational kinetic energy so in linear motion the kinetic energy is given by half MV square but in rotational dynamics the mass is replaced by the moment of inertia v and v is replaced by the angular speed Omega and we have half turn here so this is the rotational kinetic energy half I Omega square exactly the same is this one you have to replace mass by I and V by Omega only not all the terms now I is point 7 1 and Omega is 2 point 5 6 if you solve it that's what you get 15 6 point 1 joule and as you can see if if this mass is further and further then it will have more energy if it is in motion or if it is not motion then more energy is required to move at a certain angular speed all right that's what the moment of inertia is or it is an equivalent mass in linear motion that earlier if you're talking about the rotational motion the mass and the moment of inertia are exactly the same thing mass for linear motion and moment of inertia or rotational motion so this is it from this video I hope you liked this video and if you have any questions write down your questions in the comment section below and do not forget to Like share and subscribe the child