00:01
In the question number 1 it has been given that there was a merry -go -round having mass 120 kg and radius 1 .8 meter.
00:19
Now initially it was revolving with angular velocity 0 .350 evolution per second.
00:31
Now after some time a child which was initially at rest grab the outer edge.
00:45
Let's suppose somewhere at the periphery.
00:49
So we can write the initial angular momentum of this may go round.
00:59
So that will be i.
01:01
Into omega now i will be equals to m r square by 2 that is the moment of inertia of this merry -go -round into omega -1 now this must be equals to i -1 omega -1 must be equals to i -2 omega -2 that is i -2 is the moment of inertia of this merry -round plus the child when the child was at the periphery.
01:42
So in that case it will be mr squared by 2 that is the moment of inertia of this merry ground plus the mr square here the mass of this kid is capital m and radius is r so this is equal multiplied by omega 2.
02:15
Now, putting the values, we can write 120 into r square, that is 1 .8 square by 2 into omega 1 ,000, that is 0 .35 revolution per second equals to mr square by 2, that is 120 into 1 .8 square by 2 plus mr square.
02:42
Now capital m here we can take that is the mass of the child that is 19 kg so here it will be 19 into 1 .8 square that is here r is equal to basically the radius of the merry ground into omega 2 omega 2 is the final angular velocity of the marygo round plus the kid or the child's system so solving this, solving for the omega 2, we will get omega 2 equals to, we will get omega 2 equals to 0 .265 revolution per second.
03:38
So this will be the final angular velocity of child plus merry -go -round system.
03:49
Now coming to the question number 2, that is, three children are riding on the edge of a merry -go -round that is 1 -22 kg and has a radius.
04:03
That means, let's suppose this is the merry -go -round of mass m equals to 122 kg and radius r equals to 1 .6 meter.
04:15
And initial angular velocity 21 .3 rpm that is revolution per minute.
04:31
Now in this question it has been given that initially there was three kids.
04:37
Let's suppose here here here one two three and they are at the periphery when the merrigo round was revolving with omega 1 now after some time this let's say first kid having mass equals to 27 .5 kg comes to center of this merry ground.
05:06
So when it comes at the new position we have to calculate the final angular velocity of this whole system...