1
00:00:00,480 --> 00:00:01,290
‫Welcome back.

2
00:00:01,890 --> 00:00:11,130
‫So imagine that we have a drone and that drone has four propellers, four motors, and they rotate very,

3
00:00:11,130 --> 00:00:12,020
‫very fast.

4
00:00:12,480 --> 00:00:25,070
‫So you have your M1 and M3 that rotate counterclockwise and then you have M2 and M4 that rotate clockwise.

5
00:00:25,950 --> 00:00:29,940
‫And here's the propeller itself with two blades.

6
00:00:30,990 --> 00:00:38,280
‫Let's just assume that this propeller is motor one and we will also attach a separate body frame to

7
00:00:38,280 --> 00:00:38,490
‫it.

8
00:00:39,540 --> 00:00:42,540
‫You will have X and one.

9
00:00:43,620 --> 00:00:57,960
‫Why stop and one and finally, the Z sub M one as well, and this propeller rotates about its body frame,

10
00:00:58,140 --> 00:01:00,930
‫the axis Z sub and one.

11
00:01:02,020 --> 00:01:10,400
‫And it rotates at omega one radians per second, so counterclockwise.

12
00:01:11,440 --> 00:01:18,700
‫Now, this propeller also has mass moments of inertia about its three axis.

13
00:01:19,940 --> 00:01:28,370
‫However, since we only rotate about its body from Z axis, then we only need to care about the mass

14
00:01:28,370 --> 00:01:32,780
‫movement of inertia, about this Z sub and one.

15
00:01:33,800 --> 00:01:47,740
‫And we call it J, sub T, P, sub M one, and the units are again KG's times meters squared.

16
00:01:48,920 --> 00:01:56,420
‫So this is the mass moment of inertia about the propeller's body frame, Z axis.

17
00:01:57,140 --> 00:02:05,630
‫And then, of course, you have a mass movement of inertia for your motor to model three and more four.

18
00:02:06,410 --> 00:02:11,620
‫However, we're going to assume that they are all equal for all propellers.

19
00:02:12,230 --> 00:02:20,330
‫So we're going to omit these subindices here and we're just going to say that the propellers mass movement

20
00:02:20,330 --> 00:02:28,820
‫of inertia about its body from Z axis, about the propellers body frames, the axis is just Jessopp

21
00:02:28,820 --> 00:02:29,530
‫TPE.

22
00:02:30,620 --> 00:02:40,790
‫So if you look at the drone now, then you see that the rotation of the propeller, M1 and M3, they

23
00:02:41,240 --> 00:02:43,910
‫produce angular momentum like this.

24
00:02:45,170 --> 00:02:54,740
‫This is four and one, and this is four and three, so the angular momentum for M one equals.

25
00:02:56,100 --> 00:03:09,060
‫Jessup, t.P, Times, Elnaggar, one, and the angular momentum for more three equals Jessopp t.P times

26
00:03:09,390 --> 00:03:11,760
‫Omega three like this.

27
00:03:12,870 --> 00:03:15,320
‫And it makes sense that this is the direction, right?

28
00:03:15,720 --> 00:03:19,290
‫It's all happening according to your right hand rule.

29
00:03:19,500 --> 00:03:31,950
‫So if you take your right hand and then you curl your fingers in the direction of the rotation like

30
00:03:31,950 --> 00:03:34,590
‫this, then your thumb will point up.

31
00:03:35,560 --> 00:03:41,600
‫However, in case of M2 and for you are rotating clockwise.

32
00:03:42,130 --> 00:03:43,160
‫So what do you think?

33
00:03:43,630 --> 00:03:48,650
‫In which direction would you have your angular momentum up or down?

34
00:03:49,790 --> 00:03:59,480
‫Try to do it as an exercise, so just write down the equations for the angular momentum for M2 and M4

35
00:03:59,480 --> 00:04:02,830
‫and the direction, and then you'll see it in the next video.

36
00:04:03,230 --> 00:04:04,300
‫Thank you very much.

37
00:04:04,310 --> 00:04:05,300
‫And see you there.