00:01
In this problem, at t equals to 0 seconds, a particle of mass 7 .22 kg, right? so here, mass that is m, 7 .22 kgis are given to us, right? and it is told that a kg starts from rest at the origin and moves with a velocity vector v, right? your vector v equals to 6 .00 t square right i cap minus 4 .00 t j cap plus 4 .00 k cap right meter per second enter your answers using unit vector notation right so angular momentum is asked, angular momentum at t equals to 0.
01:36
And angular momentum, right? this is at t is equals to 0.
01:41
This is first one, a part.
01:44
And secondly, it is asked at t equals to 0 .860 seconds.
01:51
Right? now.
02:00
Okay.
02:03
So now basically what is angular momentum? let us just understand.
02:10
So first of all, this is just a basic discussion.
02:15
So angular momentum of an object having mass m has a linear velocity v with respect to the fixed point can be given by l equals to mvr sine theta, isn't it? but in the vector form you can also write it as angular momentum l equals to r cross p vector p right in terms of vector product okay so now p is nothing but this is momentum that is m into v okay so now from here we need to calculate of we are given with this right therefore vector p will be equals to m into v right mv right so this could also be right therefore this means p is equals to m that is 7 .22 kgis right please write unit so that it would be much clearer that are you going correct or not right so unit also helps a lot to understand the problem and find the solution of this problem right so now here this is like this okay so this is 4 .00 t j gap plus 4 .00 k gap is it right so now this is meter per second right so now this becomes equals to this will be 7 .22 6 is equal to 43 .32 i cap.
04:18
This must be t square.
04:21
I must write here.
04:22
This is t square.
04:29
This is t square and this is i cap minus we have 7 .22 multiplied by 4 right so this gives us the value 28 .88 t right j cap right so these are the unit vectors similarly we have plus this must be again 28 .8 28 .8 8 k cap right so what will be the units then the units will be again this will be kg meter per second all right now this is the value of momentum vector angular momentum i'm sorry momentum right but we want to find out the angular momentum okay now what will be r now right so now the r could be calculated from this equation right since to calculate r we know vector v equals to d s by by d t right this is the this is nothing but this is the differentiation of it right now this is equal to again this is same you can write here like this so it will be 6 .00 t square i cap minus 4 .00 t j cap plus 4 .00 k gap right meter per second right now you can see that uh what you could do is this is t s right and we have 6 .00 t square i cap minus 4 .00 t j cap plus 4 .00 k cap right this is in meter per second right so what you could do is you could just multiply it by, you could just multiply it by d .b.
08:00
So now dt.
08:03
And you just need to integrate it...