1
00:00:01,250 --> 00:00:03,170
Here, we will talk
about in the calculation

2
00:00:03,170 --> 00:00:05,300
of angular momentum.

3
00:00:05,300 --> 00:00:07,430
People often forget
that angular momentum

4
00:00:07,430 --> 00:00:09,830
can be calculated
for any object,

5
00:00:09,830 --> 00:00:11,310
even for an object
that's traveling

6
00:00:11,310 --> 00:00:14,390
in a straight line and
not rotating at all.

7
00:00:14,390 --> 00:00:16,340
For example, here
I have an object

8
00:00:16,340 --> 00:00:21,460
with mass m moving at a
speed v along a street line.

9
00:00:21,460 --> 00:00:23,320
Another important
thing to keep in mind

10
00:00:23,320 --> 00:00:26,720
is that angular momentum does
not have a definite value.

11
00:00:26,720 --> 00:00:29,650
It depends on the choice of
origin, which is arbitrary,

12
00:00:29,650 --> 00:00:32,140
although some choices
are easier to calculate

13
00:00:32,140 --> 00:00:34,510
or more useful than others.

14
00:00:34,510 --> 00:00:37,210
Here, I will choose this
completely random point

15
00:00:37,210 --> 00:00:38,890
to be my origin.

16
00:00:38,890 --> 00:00:40,730
Notice that it can be
any point in space.

17
00:00:43,480 --> 00:00:46,480
Angular momentum is
a lot like torque.

18
00:00:46,480 --> 00:00:49,030
They both involve a cross
product of a distance vector

19
00:00:49,030 --> 00:00:50,740
with another vector.

20
00:00:50,740 --> 00:00:54,670
For angular momentum, it's
the distance vector r,

21
00:00:54,670 --> 00:00:58,510
the vector from the
origin to the object,

22
00:00:58,510 --> 00:01:02,200
cross p, the momentum
of the object, or mv.

23
00:01:05,500 --> 00:01:07,510
Once again, we can
write the magnitude

24
00:01:07,510 --> 00:01:11,860
of this cross-product as
r times mv times the size

25
00:01:11,860 --> 00:01:14,260
of the theta between the two.

26
00:01:14,260 --> 00:01:16,300
But it's often more
helpful to think

27
00:01:16,300 --> 00:01:22,000
about this as r times
sine theta times mv.

28
00:01:22,000 --> 00:01:24,539
In other words, the r sine
theta is the component

29
00:01:24,539 --> 00:01:27,039
of the position vector that's
perpendicular to the direction

30
00:01:27,039 --> 00:01:27,706
of the momentum.

31
00:01:30,160 --> 00:01:32,960
Let's practice with
a few other examples.

32
00:01:32,960 --> 00:01:38,450
If I have a ball moving up and
I have my origin at the side,

33
00:01:38,450 --> 00:01:41,060
then this is the
perpendicular distance.

34
00:01:41,060 --> 00:01:46,223
So the angular momentum is
r perpendicular times mv.

35
00:01:46,223 --> 00:01:49,070
A reference point that's
the same horizontal distance

36
00:01:49,070 --> 00:01:52,640
away from the object will see
the same angular momentum.

37
00:01:52,640 --> 00:01:55,610
Notice that in this case,
the angular momentum is not

38
00:01:55,610 --> 00:01:57,922
changing as the ball moves,
because the perpendicular

39
00:01:57,922 --> 00:01:59,380
distance is not
changing with time.

40
00:02:02,580 --> 00:02:05,080
In this case, if the ball
is moving at an angle,

41
00:02:05,080 --> 00:02:06,780
we again, have to
take the perpendicular

42
00:02:06,780 --> 00:02:10,800
component of the position vector
to find the angular momentum.

43
00:02:10,800 --> 00:02:14,830
This second reference point is
now a different distance away.

44
00:02:14,830 --> 00:02:16,490
So the angular
momentum is larger.

45
00:02:19,660 --> 00:02:22,600
Now, let's talk about the
sign of angular momentum.

46
00:02:22,600 --> 00:02:24,970
You can calculate the
sine of a cross product

47
00:02:24,970 --> 00:02:27,070
with the right hand rule.

48
00:02:27,070 --> 00:02:29,650
Make sure your vectors
are tail to tail when

49
00:02:29,650 --> 00:02:31,390
you compare the directions.

50
00:02:31,390 --> 00:02:34,630
So in this case, we have that
r cross v points into the page.

51
00:02:37,640 --> 00:02:40,400
In the case of circular
motion, r and v

52
00:02:40,400 --> 00:02:42,079
are always perpendicular.

53
00:02:42,079 --> 00:02:45,020
So we can just multiply
the magnitudes together.

54
00:02:45,020 --> 00:02:48,950
And the sine tells us which way
we're going around the circle.

55
00:02:48,950 --> 00:02:52,160
If we consider out of
the page to be positive

56
00:02:52,160 --> 00:02:54,840
and the angular
momentum is positive,

57
00:02:54,840 --> 00:02:59,130
then the object is
circulating counter-clockwise.

58
00:02:59,130 --> 00:03:01,140
If the angular
momentum is negative,

59
00:03:01,140 --> 00:03:04,220
the object is
circulating clockwise.