1 00:00:01,880 --> 00:00:07,880 So we know now that we can describe the movement of the political along a line. 2 00:00:09,340 --> 00:00:12,160 By using X, Y and Z components. 3 00:00:13,120 --> 00:00:14,650 But we can do it differently as well. 4 00:00:14,680 --> 00:00:17,530 We can use to coordinate. 5 00:00:18,550 --> 00:00:23,590 A teacup wouldn't stand in court and it was tangential coordinate and a normal court and it. 6 00:00:24,560 --> 00:00:30,560 Now, this is maybe not that intuitive, but it makes a lot of sense once you understand it. 7 00:00:30,950 --> 00:00:32,210 So let me try and explain. 8 00:00:36,650 --> 00:00:40,700 If a particle moves along a path, let's say the path looks something like this. 9 00:00:41,590 --> 00:00:42,790 Here is political. 10 00:00:44,160 --> 00:00:48,930 And it's moving in this direction than if you zoom in. 11 00:00:50,810 --> 00:00:52,580 And this area around the political. 12 00:00:54,820 --> 00:00:55,720 It forms. 13 00:00:57,350 --> 00:01:03,860 The outer edge, it forms the curvature of a circle that has an origin somewhere of their. 14 00:01:05,380 --> 00:01:15,430 So let's call them prime if the particle is over, yeah, then and you zoom in, then there will be 15 00:01:15,940 --> 00:01:16,960 a curvature. 16 00:01:19,130 --> 00:01:25,350 Radius of curvature, O'Brien over there and this distance of a year. 17 00:01:27,410 --> 00:01:36,440 We call this the is now the S is so small that this almost becomes like a straight line. 18 00:01:38,640 --> 00:01:39,330 Calculous. 19 00:01:41,560 --> 00:01:54,850 So the velocity with which the particle moves from here to there, it's just this DETI and that we know 20 00:01:54,850 --> 00:01:55,480 is V. 21 00:01:56,580 --> 00:01:59,250 OK, and that is. 22 00:02:00,440 --> 00:02:06,520 A scalar, but we can give it a direction, we can say this direction is tangential to that point. 23 00:02:06,530 --> 00:02:10,390 So it is a tangent to that circle over there. 24 00:02:12,820 --> 00:02:22,810 So for this case, when the point is there, that would be the direction of the area, the direction 25 00:02:22,810 --> 00:02:25,400 of the Islamic search. 26 00:02:25,480 --> 00:02:26,830 So that is tangential. 27 00:02:27,220 --> 00:02:31,600 So you can immediately see that as this political moves along this path. 28 00:02:33,030 --> 00:02:35,730 The direction of the tangent velocity changes. 29 00:02:38,750 --> 00:02:45,200 Now, because the direction changes of this philosophy as the political moves along this path, that 30 00:02:45,200 --> 00:02:49,220 gives rise to two components for our acceleration. 31 00:02:50,510 --> 00:02:59,000 So there's an acceleration because of the increase in speed of this article as it moves along the path. 32 00:02:59,000 --> 00:03:05,900 And there is also an acceleration due to the fact that these particles velocity changes direction. 33 00:03:07,850 --> 00:03:16,720 So before we get to that, we can say the velocity is V in the tangential direction. 34 00:03:16,730 --> 00:03:23,070 So it is going to write a unit vector with subscript T for the tangential direction. 35 00:03:23,420 --> 00:03:26,570 So as it moves along this line, that direction changes. 36 00:03:26,570 --> 00:03:32,750 It stays tangent to that curvature, the acceleration. 37 00:03:33,830 --> 00:03:36,380 On the other hand, is going to have to component's. 38 00:03:38,060 --> 00:03:49,580 The acceleration is going to have a tangential component in the tangential direction, and it's going 39 00:03:49,580 --> 00:03:54,970 to have a normal component in the normal direction. 40 00:03:55,610 --> 00:04:00,410 So it's going to have acceleration is going to have a component in this direction and it's going to 41 00:04:00,410 --> 00:04:02,210 have a component in that direction. 42 00:04:03,960 --> 00:04:07,100 So now imagine the particle has moved on along this line. 43 00:04:07,100 --> 00:04:08,150 It sits here now. 44 00:04:08,930 --> 00:04:11,150 It's going to have a velocity tangent. 45 00:04:12,860 --> 00:04:19,430 Also, acceleration in that direction, which, of course, can be zero and it's going to have an acceleration 46 00:04:20,120 --> 00:04:21,860 in the normal direction as well. 47 00:04:23,240 --> 00:04:29,300 OK, so this is acceleration in the normal direction, figure of acceleration in the tangent direction, 48 00:04:29,300 --> 00:04:31,610 also velocity in the tangent direction. 49 00:04:34,790 --> 00:04:36,470 Now, a 80. 50 00:04:39,370 --> 00:04:50,000 Is just the DETI, so that is our normal way of writing acceleration like we remember. 51 00:04:50,050 --> 00:04:56,410 So that's the tangential acceleration, this acceleration of a year which is caused by the change in 52 00:04:56,410 --> 00:05:05,140 direction of the velocity as the particle moves along this path, this acceleration of a year is given 53 00:05:05,410 --> 00:05:10,800 by the squared over row. 54 00:05:10,900 --> 00:05:16,930 Now, what is Ro-Ro is that radius of curvature, as you can imagine, as the particle moves along this 55 00:05:17,080 --> 00:05:19,930 line, the radius of curvature changes all the time. 56 00:05:21,640 --> 00:05:31,660 But if we have a particle that moves in a perfect circle, then of course the radius of curvature stays 57 00:05:31,660 --> 00:05:34,150 exactly the same as it moves along. 58 00:05:35,590 --> 00:05:44,290 So as you can imagine, swinging a tennis ball on a on a piece of string, you'll have the normal acceleration 59 00:05:44,650 --> 00:05:51,520 and you'll have the tangential acceleration which goes with your tangential velocity as this ball goes 60 00:05:51,520 --> 00:05:56,050 around the direction of this tangential velocity changes. 61 00:05:58,280 --> 00:06:06,260 This ball can go round with a constant tangential acceleration, but because the direction changes all 62 00:06:06,260 --> 00:06:11,510 the time, you have a normal acceleration, which is also constant.