1 00:00:03,900 --> 00:00:06,540 Let's examine again an object that's 2 00:00:06,540 --> 00:00:08,610 undergoing circular motion. 3 00:00:08,610 --> 00:00:14,160 And we'll choose our polar coordinates r hat, theta hat. 4 00:00:14,160 --> 00:00:16,710 We'll make it cylindrical with a k hat. 5 00:00:16,710 --> 00:00:19,920 Now that we've completed our kinematic description 6 00:00:19,920 --> 00:00:24,430 of the motion, now let's see how we apply Newton's second law 7 00:00:24,430 --> 00:00:28,430 to circular motion. 8 00:00:28,430 --> 00:00:32,320 Well, when we write Newton's second law as F 9 00:00:32,320 --> 00:00:37,680 equals ma, that-- remember, we can divide these two sides. 10 00:00:37,680 --> 00:00:42,490 This side, the how, is a geometric description 11 00:00:42,490 --> 00:00:43,770 of the motion. 12 00:00:43,770 --> 00:00:46,420 And this side is the why, and this 13 00:00:46,420 --> 00:00:49,580 is the dynamics of the motion. 14 00:00:49,580 --> 00:00:52,630 And the dynamics come from analyzing the forces that 15 00:00:52,630 --> 00:00:54,780 are acting on this object. 16 00:00:54,780 --> 00:00:59,050 So when we're applying this mathematically 17 00:00:59,050 --> 00:01:04,720 to circular motion, F equals ma-- this is a vector equation. 18 00:01:04,720 --> 00:01:08,260 And so what we need to do is think about each component 19 00:01:08,260 --> 00:01:09,370 separately. 20 00:01:09,370 --> 00:01:12,820 Sometimes I can just distinguish the components 21 00:01:12,820 --> 00:01:15,710 that I'm talking about over here. 22 00:01:15,710 --> 00:01:19,440 And so we have that the radial component of the forces-- 23 00:01:19,440 --> 00:01:22,420 and that comes from an analysis of the dynamics, 24 00:01:22,420 --> 00:01:27,750 the physics of the problem-- and this side is mass times 25 00:01:27,750 --> 00:01:32,150 the radial component of the acceleration, ar. 26 00:01:32,150 --> 00:01:34,320 Now these are very different things. 27 00:01:34,320 --> 00:01:37,490 And it's by the second law that we're 28 00:01:37,490 --> 00:01:42,500 equating in quantity these two components. 29 00:01:42,500 --> 00:01:46,039 Now if we wrote that equation-- this side out in a little bit 30 00:01:46,039 --> 00:01:48,270 more detail-- we'll save ourselves 31 00:01:48,270 --> 00:01:51,430 a little space when we handle the tangential direction-- 32 00:01:51,430 --> 00:01:55,539 the forces come from analysis of free body force diagrams. 33 00:01:55,539 --> 00:01:59,430 And over here, we know the acceleration is always inward. 34 00:01:59,430 --> 00:02:04,060 And I'll choose to write this as r omega squared. 35 00:02:04,060 --> 00:02:06,250 And so this will be our starting point 36 00:02:06,250 --> 00:02:11,140 for analyzing the radial motion for an object that's 37 00:02:11,140 --> 00:02:12,870 undergoing circular motion. 38 00:02:12,870 --> 00:02:16,430 Now remember, there could be a tangential motion, too. 39 00:02:16,430 --> 00:02:20,610 And in the tangential direction, the tangential forces 40 00:02:20,610 --> 00:02:23,790 are equal to ma tangential. 41 00:02:23,790 --> 00:02:26,960 And as we saw, this is again the second law, 42 00:02:26,960 --> 00:02:28,720 equating two different things. 43 00:02:28,720 --> 00:02:33,520 We have that we can write the tangential force as r 44 00:02:33,520 --> 00:02:37,170 d squared theta dt squared. 45 00:02:37,170 --> 00:02:43,300 And sometimes we've been writing that as r alpha z. 46 00:02:43,300 --> 00:02:46,620 But this equation here is what we're 47 00:02:46,620 --> 00:02:50,320 going to apply for the tangential forces. 48 00:02:50,320 --> 00:02:53,680 If the tangential forces are 0, then there's 49 00:02:53,680 --> 00:02:57,220 no angular-- there's no tangential acceleration. 50 00:02:57,220 --> 00:02:59,570 We know that for circular motion, 51 00:02:59,570 --> 00:03:01,360 the radial force can never be zero, 52 00:03:01,360 --> 00:03:04,160 because this term is always non-zero 53 00:03:04,160 --> 00:03:06,410 and points radially inward. 54 00:03:06,410 --> 00:03:08,730 And now we'll look at a variety of examples 55 00:03:08,730 --> 00:03:12,580 applying Newton's second law to circular motion.