 So here is a question on rigid body motion, let's see how we can solve this particular. So a uniform circuit disk is there whose mass is 50 kg and the radius is also given. It is rotating with an angular velocity of 10 radians per second about its own axis which is vertical okay so disk is horizontal so that is the axis is vertical. Two uniform circle rings each of mass 6.25 and radius 0.2 meter are gently placed symmetrically on the disk in such a manner that they are touching each other along the axis of the disk okay and are horizontal. Assume that the friction is large enough such that the ring are at rest related to the disk you need to find out the new angular velocity of the system okay now clearly this is the case of conservation of angular momentum okay but then at times students are in a hurry and they don't pay attention to detail and that is why you will arrive at the wrong answer okay so if you pay attention carefully you will see that what this situation is that you know two rings are of radius 0.2 meter they are touching each other on the axis so this is how the two rings are placed this is one ring and here is another ring okay the disk is of radius 0.4 meter that is why you know the rings can be arranged like this and they touch here alright so this is a situation and clearly we can apply conservation of angular momentum about the axis okay so before these rings were placed the angular momentum was what m r square by 2 which is i times omega okay now after the rings are placed let us say that the new moment of inertia is i so i times omega 1 okay so initial angular momentum is equal to final angular momentum now what is i i is a new moment of inertia which is nothing but moment of inertia of the disk plus moment of inertia of the ring about this point let us say that is point p and this is o okay now moment of inertia about o is m into r square okay this is the rings moment of inertia plus you need to move this axis from here to point p okay so plus m r square so this is the moment of inertia of one of the rings but there are two rings of this into two okay the total moment of inertia you will get as capital m r square by 2 plus 2 times small m into small r square okay so you know I can just substitute the values and there is a relation between capital r and small r so basically small r is capital r by 2 isn't it the capital r is 0.4 and small r is 0.2 so just for the simplicity sake I will write in terms of capital r so this will come out to be m r square by 2 fine so now let me substitute the values so m r square by 2 into omega is equal to capital m r square by 2 plus small m r square by 2 into omega 1 okay you can see that r square can get cancelled even the 2 will get cancelled so you will get omega 1 to be equal to capital m divided by capital m plus small m times omega fine now capital m is what 50 kgs okay so 50 divided by 50 plus 6.25 into omega that is 10 okay so this is new angular velocity all right so let me simplify this further so this will be 50 divided by 56.25 into 10 okay this one is new angular velocity there is a small mistake here actually m r square plus m r square into 2 this will give you 4 m r square okay so and small r is capital r by 2 so this is just m r square fine so when you substitute all that this will come out to be this into 2 okay and you will get you will get 50 plus 6.25 into 2 okay which is nothing but 62.5 all right which is 0.8 into 10 and hence you will get the value as 8 radians per second as the answer okay so that's how you have to solve this particular question here you know I myself have made a calculation error so at times the mistake you do is not related to physics but related to calculations and you know in your experience itself you might have seen that most of the time it is non physics mistakes that we do all right so make sure that you don't I mean you should be very careful that you should not do mistakes on things which you know okay so that's how you have to solve this particular question