00:01
Hello, in this question we're given this setup where we have an object attached to a string that goes through a hole and it is spinning with some speed v and some rotational speed omega naught, so i'll just call this omega naught, of 1 .75 radians per second.
00:17
And we're told that we then pull on the string from below and our radius decreases to half of what it was.
00:24
We're asked many things, the first of which is, is the angular momentum of the block conserved? why or why not? yes, it is conserved.
00:31
L is conserved whenever there is no external torque.
00:39
And in this case, we're not applying any external torque, we're just making the radius shorter.
00:43
We are doing work on it by pulling down on the string to make the radius shorter, but there is no net torque, so l is conserved.
00:50
Sweet.
00:51
Part b then says, what is the new angular speed? so we want to find what is omega final.
00:55
Well, we're going to use conservation of angular momentum, if that was not given off by the first question.
01:02
So initially, we have our mass, or sorry, initially we have our mass, which has some moment of inertia, initial moment of inertia, i, and it's moving at some initial speed.
01:12
And at the end, we have our final moment of inertia and our final speed.
01:16
So what are our moments of inertia? well, the moments of inertia of a point mass is the mass times how far away it is squared.
01:23
So initially, we have the mass times our initial radius squared times omega naught.
01:29
And at the end, we're going to have m times our final radius squared times omega final.
01:34
Our masses will cancel out, which is nice and convenient.
01:37
You can go ahead and solve for omega final, which will look something like this.
01:39
And we have all of those values, so we can go ahead and plug them in.
01:43
And if we do that, i get a final omega of 7 .00 radians per second...