WEBVTT

00:00:00.000 --> 00:00:02.840
This is Giancoli Answers
with Mr. Dychko.

00:00:03.800 --> 00:00:09.000
Angular momentum is conserved here because
there's no external net forces acting

00:00:09.080 --> 00:00:11.600
so the initial angular momentum of
the system is

00:00:11.600 --> 00:00:16.620
the moment of inertia of one disk times
its angular velocity

00:00:16.840 --> 00:00:20.420
and then after the disk is dropped on
the identical disk below

00:00:20.580 --> 00:00:23.340
the moment of inertia of
the system is gonna be

00:00:23.340 --> 00:00:26.960
2 times the moment of inertia of one disk
because since they are identical

00:00:26.960 --> 00:00:29.400
when you combine them together—

00:00:29.460 --> 00:00:32.320
well each disk has the same
moment of inertia and so—

00:00:32.320 --> 00:00:35.200
the moment of inertia of the system of
the two combined will be 2 times

00:00:35.200 --> 00:00:37.200
the moment of inertia of one of them.

00:00:37.320 --> 00:00:42.080
And there will be some different angular
velocity when the two are combined

00:00:42.460 --> 00:00:45.640
but the angular momenta will be the same

00:00:45.640 --> 00:00:47.540
so <i>L f</i> equals <i>L i</i>.

00:00:47.600 --> 00:00:52.280
And so we have 2<i>Iω f</i> equals <i>Iω</i>

00:00:52.520 --> 00:00:56.220
and divide both sides by <i>I</i> and
divide both sides by 2 as well

00:00:56.220 --> 00:00:59.480
and we see that the final angular
velocity will be half

00:00:59.600 --> 00:01:04.200
of the initial angular velocity of the disk
before it was dropped.