0:00
Hi there.
00:01
So for this problem, we are told that a particle has a mass m equals to 1 kilogram and move with a position that is given.
00:12
And that vector of position is equal to 3 in the j unit vector plus 2 times the time to 2 squared in the seed components.
00:31
And this is in meters and width, three and seconds.
00:35
Now, we need to determine at a time t equals to two seconds, the angular momentum.
00:45
So we need to determine the angular momentum vector.
00:50
Let's put things here, it's defined by else.
00:54
Okay, so we know that the angular momentum is defined as the cross product between the position vector and a, the momentum vector.
01:04
Now we know that a momentum vector is defined as the mass times the vector of velocity.
01:14
So what we are going to do in here is to introduce that definition here.
01:18
So we can take out the mass because it is a constant.
01:21
And we are going to have in here that this is the broader between the position vector cross product with the velocity vector.
01:30
So now what we need to find is, is the velocity vector, but we know that the velocity vector can be obtained by the temporal derivative of the position.
01:47
So we just need to simply derive this quantity with respect to time.
01:52
Now, the first one is zero because it doesn't depend on the time, but the second one will give us something because it depends on the time.
02:01
So as you can see, this is going to be the derivative of t to the square that we know is 2 times t.
02:08
So we're going to have 2 times 2 times t in the k unit bedward.
02:15
So we're going to have in here 4 times t in the k unit bedward.
02:20
And this is positive, as you can see.
02:23
Now, we just introduced this into the previous expression for the angular momentum.
02:29
So we just now substitute all of the values that we have.
02:32
We have a mass of one kilogram.
02:35
And the cross product between the position vector, and the position vector is this whole thing in here, which is three in the j unit bed door, plus two times t to the square in the k unit bed door.
02:53
And this cross product with four times the time in the k unit bed door...