1 00:00:03,770 --> 00:00:08,020 Here are two people. They're both standing, but they're standing in two completely different 2 00:00:08,020 --> 00:00:13,530 ways. Which person would it be easier to push over? If you wanted to push this person [left] 3 00:00:13,530 --> 00:00:18,199 over, where would you apply a force? What about this [right] person? The answers to 4 00:00:18,199 --> 00:00:22,380 all these questions can be explained using the concept of torque. 5 00:00:22,380 --> 00:00:26,510 This video is part of the Representations video series. Information can be represented 6 00:00:26,510 --> 00:00:32,590 in words, through mathematical symbols, graphically, or in 3-D models. Representations are used 7 00:00:32,590 --> 00:00:38,000 to develop a deeper and more flexible understanding of objects, systems, and processes. 8 00:00:38,000 --> 00:00:44,060 Hi. I'm Sanjay Sarma. Professor of mechanical engineering at MIT, In this video, we'll be 9 00:00:44,060 --> 00:00:46,820 talking torque and balance. 10 00:00:46,820 --> 00:00:51,510 In order to understand these core concepts, you'll need a working knowledge of vectors 11 00:00:51,510 --> 00:00:57,390 and their uses. Specifically, you must be familiar with force, displacement, and torque. 12 00:00:57,390 --> 00:01:02,760 We will also assume that you know how to compute a cross product, and how to use the Right-Hand 13 00:01:02,760 --> 00:01:08,060 Rule, and that you have done problems involving the center of mass of an object. 14 00:01:08,060 --> 00:01:13,109 Our objective is to improve your ability to draw torque diagrams, and give you some practice 15 00:01:13,109 --> 00:01:18,959 with setting them up. By the end you should also understand what is needed for human beings 16 00:01:18,959 --> 00:01:21,310 to balance. 17 00:01:21,310 --> 00:01:25,959 We'll start with an activity. Everyone stand up and spread out across the room. You'll 18 00:01:25,959 --> 00:01:28,630 need a partner for this activity. 19 00:01:28,630 --> 00:01:33,908 When I say "go," your goal is to carefully push your partner over. Use the smallest amount 20 00:01:33,908 --> 00:01:38,380 of force you can. You will switch partners halfway through, so be gentle. 21 00:01:38,380 --> 00:01:43,899 When you push, consider where you should push, and in what direction. Try many different 22 00:01:43,899 --> 00:01:45,889 approaches. 23 00:01:45,889 --> 00:01:50,469 Here are some questions that may help you think about this in a scientific manner. When 24 00:01:50,469 --> 00:01:53,848 it comes to your push, where will you push? 25 00:01:53,848 --> 00:01:58,908 What direction will you push? How hard will you push? Consider your partner as well: how 26 00:01:58,908 --> 00:02:05,090 is your partner standing? What is the floor like under your partner's feet? Can your partner 27 00:02:05,090 --> 00:02:07,149 balance well? 28 00:02:07,149 --> 00:02:39,220 Are you ready? Go! 29 00:02:39,220 --> 00:03:11,390 Switch partners! 30 00:03:11,390 --> 00:03:16,170 Your teacher will now lead you in a short discussion about this activity. Pause the 31 00:03:16,170 --> 00:03:24,120 video here. 32 00:03:24,120 --> 00:03:28,630 Let's continue our investigation of torque and balance in the human body. Take a look 33 00:03:28,630 --> 00:03:35,270 at this next video clip, in which MIT researchers Colin Fredericks and Jennifer French demonstrate 34 00:03:35,270 --> 00:03:38,930 the effectiveness of properly applied torque. 35 00:03:38,930 --> 00:03:44,980 [Colin speaking] This is called "Sai son" stance. This is a basic stance in martial 36 00:03:44,980 --> 00:03:48,870 arts. Known for it's stability along a particular direction. 37 00:03:48,870 --> 00:03:52,210 This is my colleague, mathematician Jennifer French. 38 00:03:52,210 --> 00:03:56,400 Jen knows the stance is strong along certain directions–such as the one she is pulling 39 00:03:56,400 --> 00:03:58,120 in now. 40 00:03:58,120 --> 00:03:59,850 [laughing] Oops. 41 00:03:59,850 --> 00:04:03,370 It can also withstand a great deal of force in the opposite direction. 42 00:04:03,370 --> 00:04:09,980 I'm not going to be knocked over if she is pushing or pulling along that particular line. 43 00:04:09,980 --> 00:04:14,940 However, Jen knows the stance's weak point. 44 00:04:14,940 --> 00:04:22,199 If she pushes along a different line, it'll knock me right down to the ground. 45 00:04:22,199 --> 00:04:24,879 This isn't just martial arts. This is science. 46 00:04:24,879 --> 00:04:28,659 Torque controls my ability to balance and we're going to show you how today. 47 00:04:28,659 --> 00:04:34,610 [Sanjay speaking] To analyze the situation, let's look at what physical properties are 48 00:04:34,610 --> 00:04:36,550 important here. 49 00:04:36,550 --> 00:04:42,030 What forces do you think are involved? Pause the video to discuss. 50 00:04:46,340 --> 00:04:53,199 Next, draw a simple diagram that you can use to find the net torque on this man. Pause 51 00:04:53,199 --> 00:04:56,399 the video while you do this. 52 00:05:01,069 --> 00:05:05,919 The simplest way to represent this man is with a rectangle. You should remove any other 53 00:05:05,920 --> 00:05:12,479 details, and draw our forces so that we can tell exactly where they are applied to his body. 54 00:05:12,479 --> 00:05:16,900 Finally, if you were to draw a diagram showing someone resisting a push, how would you do 55 00:05:16,900 --> 00:05:21,129 it? Which of these three is most appropriate? 56 00:05:21,129 --> 00:05:24,329 Pause the video to discuss. 57 00:05:28,090 --> 00:05:34,120 You may be wondering why we can use a two-dimensional diagram to discuss a three-dimensional situation. 58 00:05:34,129 --> 00:05:40,509 The reason is that all of our forces are applied in the same plane, simplifying the problem. 59 00:05:40,509 --> 00:05:45,058 While our torque vectors point in and out of the screen on this diagram, we can represent 60 00:05:45,058 --> 00:05:51,889 that fairly easily. In a more complex situation, we may need to draw something more fully three-dimensional, 61 00:05:51,889 --> 00:05:56,389 as our torques might point in other directions. 62 00:05:56,389 --> 00:06:02,129 This next video clip will walk you through a partial analysis of this situation. You 63 00:06:02,129 --> 00:06:07,089 will need a way to take notes and draw diagrams while you watch. 64 00:06:10,820 --> 00:06:15,379 [Jen speaking] I couldn't push Colin over by applying force in the stable direction. 65 00:06:15,379 --> 00:06:19,739 Yet when I applies the same force in a different direction, I could push him over. 66 00:06:19,740 --> 00:06:21,340 How did I know this? 67 00:06:21,340 --> 00:06:22,360 Torque. 68 00:06:22,360 --> 00:06:26,759 Here you see two 2-dimensional views representing Colin. 69 00:06:26,759 --> 00:06:29,740 The width of the base represents the distance between his feet. 70 00:06:29,740 --> 00:06:32,939 The wide square is the view of Colin from the side and stable states. 71 00:06:32,939 --> 00:06:36,839 The narrow rectangle is the view of Colin from straight on. 72 00:06:36,839 --> 00:06:41,319 Lets draw in the forces acting on Colin as I push him in the stable directions. 73 00:06:41,319 --> 00:06:43,219 Start by drawing the center of mass. 74 00:06:43,219 --> 00:06:44,999 Which we assume is at the center of the square. 75 00:06:44,999 --> 00:06:48,529 The force of gravity pulls straight down with magnitude three halfs. 76 00:06:48,529 --> 00:06:52,990 There is also the force of my push of length one. Which we place in the location where 77 00:06:52,990 --> 00:06:55,360 the force is applied. 78 00:06:55,360 --> 00:07:00,759 This push shifts Colin's weight entirely to his back foot. So the normal force is applied 79 00:07:00,759 --> 00:07:04,210 there with a magnitude equal and opposite that of force p. 80 00:07:04,210 --> 00:07:08,849 The force of friction is also at this foot. Equal and opposite the magnitude and direction 81 00:07:08,849 --> 00:07:10,319 of the push force. 82 00:07:11,240 --> 00:07:14,339 Recall that torque is r cross F. 83 00:07:14,339 --> 00:07:18,210 That is, torque occurs when a force is applied some displacement distance from a reference 84 00:07:18,210 --> 00:07:19,080 point. 85 00:07:19,080 --> 00:07:22,729 We can choose any reference point we like, and the net torque we compute will be the 86 00:07:22,729 --> 00:07:23,439 same. 87 00:07:23,439 --> 00:07:26,599 For this problem I will choose the reference point to be the pivot point. 88 00:07:26,599 --> 00:07:30,469 Why don't you try this problem but choose the center of mass as the reference point. 89 00:07:30,469 --> 00:07:32,550 Lets get back to the problem. 90 00:07:32,550 --> 00:07:36,569 The push force and the gravitation force are applied some distance from the pivot point 91 00:07:36,569 --> 00:07:37,360 at the foot. 92 00:07:37,360 --> 00:07:38,869 So they will create torque. 93 00:07:38,869 --> 00:07:43,150 However, the friction force and normal force are applied at the pivot point. 94 00:07:43,150 --> 00:07:47,210 So R is zero and we can ignore that when we compute the net torque. 95 00:07:47,210 --> 00:07:49,479 Lets compute the torque due to the push force. 96 00:07:49,479 --> 00:07:53,279 The vector r is the displacement from the pivot point to where the force is applied. 97 00:07:53,279 --> 00:07:56,580 We decompose this vector into its x and y components. 98 00:07:56,580 --> 00:08:01,520 We use a coordinate system with origin at the pivot point to determine the r vector 99 00:08:01,520 --> 00:08:05,900 to be 4i + 3j. 100 00:08:05,900 --> 00:08:12,499 The magnitude of the push force is negative one i. 101 00:08:12,499 --> 00:08:17,469 The magnitude of torque can be found as the magnitude of r times the magnitude of F times 102 00:08:17,469 --> 00:08:18,219 sin theta. 103 00:08:18,219 --> 00:08:20,849 Where theta is the angle between the two vectors. 104 00:08:20,849 --> 00:08:27,619 Thus the magnitude is the area of the parallelogram formed by r and F. 105 00:08:27,619 --> 00:08:33,750 Since the area of this parallelogram is also the area of the rectangle formed by F and 106 00:08:33,750 --> 00:08:37,890 r sin theta or the component of r that is perpendicular to F. 107 00:08:37,890 --> 00:08:41,289 We can see this magnitude visually as the area of this rectangle. 108 00:08:41,289 --> 00:08:46,130 We will show the magnitudes in this way because it is very easy to see the relative magnitudes 109 00:08:46,130 --> 00:08:47,790 of the various torques. 110 00:08:47,790 --> 00:08:49,200 So... 111 00:08:49,200 --> 00:08:58,280 For the push force the area is 3, which mean the magnitude of the torque is 3. 112 00:08:58,290 --> 00:09:03,020 The direction of the torque vector is along the axis of rotation caused by this force. 113 00:09:03,020 --> 00:09:05,290 We find the direction using the right hand wall. 114 00:09:05,290 --> 00:09:09,690 Point our fingers along r and curl along F. 115 00:09:09,720 --> 00:09:15,430 In this case we find the direction to be out of the board or positive k. 116 00:09:15,430 --> 00:09:23,050 So this tells us that the torque due to the push force is equal to 3k. 117 00:09:23,050 --> 00:09:28,200 We can also find the torque vector by taking the determinate of the following three by 118 00:09:28,200 --> 00:09:29,990 three matrix. 119 00:09:29,990 --> 00:09:33,530 The first row is i, j, and k. 120 00:09:33,530 --> 00:09:38,390 The second row are the x, y, and z components of the r vector. 121 00:09:38,390 --> 00:09:43,060 And the third row are the x, y , and z components of the force vector. 122 00:09:43,060 --> 00:09:50,060 Because r and F lie in the same plane, the z components are zero. 123 00:09:50,060 --> 00:09:56,180 In our example, the force is pointing in the negative i direction and r we found to be 124 00:09:56,180 --> 00:09:57,980 4 i plus 3 j. 125 00:09:57,980 --> 00:10:06,090 Computing it this way, we also find that the torque is 3k. 126 00:10:06,090 --> 00:10:08,490 Now let's find the torque due to gravity. 127 00:10:08,490 --> 00:10:12,080 The vector r is found by connecting the pivot point to the center of mass. 128 00:10:12,080 --> 00:10:17,220 We leave to you to pause the video and to determine the components of r using this coordinate 129 00:10:17,220 --> 00:10:20,830 system. 130 00:10:20,830 --> 00:10:26,540 We find the magnitude of the torque by taking the component of r that is perpendicular to 131 00:10:26,540 --> 00:10:32,600 F pointing in the x direction, and the magnitude is the area of the rectangle between these 132 00:10:32,600 --> 00:10:33,850 two vectors. 133 00:10:33,850 --> 00:10:36,880 Again, we find the direction using the right hand rule. 134 00:10:36,880 --> 00:10:42,530 We find the torque to be pointing into the board at the pivot point. 135 00:10:42,530 --> 00:10:47,940 Since the x component of the r vector is 2, and the force due to gravity is 3 halves, 136 00:10:47,940 --> 00:10:49,830 pointing in the negative j direction. 137 00:10:49,830 --> 00:10:55,020 The magnitude of the torque due to gravity is 3 and it points in the negative k direction. 138 00:10:55,020 --> 00:10:58,600 So the torque is negative 3 k at the pivot point. 139 00:10:58,600 --> 00:11:04,210 Adding the push torque and the gravity torque together we find that we get zero. 140 00:11:04,210 --> 00:11:08,950 This means that there is no rotation about the pivot point. 141 00:11:08,950 --> 00:11:10,890 Now let's look in the unstable direction. 142 00:11:10,890 --> 00:11:16,450 We have all the same forces as before- force of gravity at the center of mass, the push 143 00:11:16,450 --> 00:11:25,080 force, a normal force at the back foot, as well as a friction force. 144 00:11:25,080 --> 00:11:29,900 The magnitudes of these forces are all the same as in the other diagram. 145 00:11:29,910 --> 00:11:35,370 Let's compute the torque due to the push force. The vector r connects the pivot point to the 146 00:11:35,370 --> 00:11:39,110 place where the force is applied. 147 00:11:39,110 --> 00:11:44,050 Using our coordinate axes with the origin placed at the pivot point, we find this vector 148 00:11:44,050 --> 00:11:51,300 to be i plus 3 j. 149 00:11:51,300 --> 00:11:55,390 We find the magnitude of the torque vector is the area of the rectangle formed by force 150 00:11:55,390 --> 00:11:59,440 vector and the component of r, perpendicular to F. 151 00:11:59,440 --> 00:12:06,070 Thus the area is one times three, or three. 152 00:12:06,070 --> 00:12:08,830 In order to find the direction, we use the right hand rule. Point our fingers along r, 153 00:12:08,830 --> 00:12:14,090 curl in the direction of F, and our thumb points out of the board, so the direction 154 00:12:14,090 --> 00:12:16,090 of our torque is k. 155 00:12:16,090 --> 00:12:21,300 Since the magnitude is 3, that tells us that torque due to the push is 3 k at the pivot 156 00:12:21,300 --> 00:12:22,500 point. 157 00:12:22,500 --> 00:12:25,670 Finally, let's find the torque due to gravity. 158 00:12:25,670 --> 00:12:29,620 Start by drawing the r vector from the pivot point to the center of mass. 159 00:12:29,620 --> 00:12:33,320 Now let's decompose this vector into it's x and y components. 160 00:12:33,320 --> 00:12:42,620 We leave this as an exercise to you, using the coordinate system shown here. 161 00:12:42,620 --> 00:12:46,510 The magnitude of the torque due to gravity at the pivot point is found by the area of 162 00:12:46,510 --> 00:12:52,570 the rectangle form by the force vector and the x component of the r vector. 163 00:12:52,570 --> 00:12:56,500 The direction is found using the right hand rule, pointing our fingers along r and curling 164 00:12:56,500 --> 00:12:57,800 around F. 165 00:12:57,800 --> 00:13:02,260 In other words, into the board or negative k. 166 00:13:02,260 --> 00:13:11,680 So the torque due to gravity is one-half times three-halves or three-fourths pointing in 167 00:13:11,680 --> 00:13:14,310 the negative k direction. 168 00:13:14,310 --> 00:13:17,170 The net torque about the pivot point is the sum of these two. 169 00:13:17,170 --> 00:13:22,200 In other words, the torque push plus the torque due to gravity is the net torque around the 170 00:13:22,200 --> 00:13:26,550 pivot point, which is two and a quarter the positive k direction. 171 00:13:26,550 --> 00:13:36,450 That means there is a total net rotation about the pivot point. Causing Colin to fall over. 172 00:13:36,450 --> 00:13:41,550 We leave it as an exercise for you to use the determinate in order to compute the torque 173 00:13:41,550 --> 00:13:42,650 vectors. 174 00:13:42,650 --> 00:13:47,090 If you computed the net torque using the center of mass as the reference point, you should 175 00:13:47,090 --> 00:13:51,680 notice that the net torques that you found are equal to the net torques that we computed 176 00:13:51,680 --> 00:13:53,020 here. 177 00:13:54,840 --> 00:13:59,940 [Sanjay speaking] Now that you've seen torque and balancing in detail, let's consider a 178 00:13:59,940 --> 00:14:04,600 more complex problem. This one is a bit tricky. I'll show you how it works. 179 00:14:04,600 --> 00:14:07,380 I'm going to take a chair and place it next to the wall. 180 00:14:07,380 --> 00:14:13,760 I'll put my toes up to the wall, and step back, toe-to-heel, twice. 181 00:14:13,760 --> 00:14:17,680 I step sideways until I'm over the chair. 182 00:14:17,680 --> 00:14:23,520 Then I bend forward until my head touches the wall, pick up the chair, and stand up... 183 00:14:23,520 --> 00:14:25,690 er... or not. 184 00:14:25,690 --> 00:14:30,430 This is something that most women can do, but men cannot. 185 00:14:30,430 --> 00:14:37,810 Maybe you think it's a trick? Here's a video of some of your professors trying to lift 186 00:14:37,810 --> 00:14:39,350 [Jen speaking]Okay, walk up to the wall. 187 00:14:39,350 --> 00:14:39,850 Yes. 188 00:14:39,850 --> 00:14:41,810 Then heel toe heel toe. 189 00:14:41,810 --> 00:14:43,620 That's it. One more time. 190 00:14:43,620 --> 00:14:46,860 And now translate over but don't come in or out. 191 00:14:46,860 --> 00:14:47,680 Okay. 192 00:14:47,680 --> 00:14:50,740 Now bend over to the the wall. Bend over. Put your head on the wall. 193 00:14:50,740 --> 00:14:51,240 Mmm-hmm. 194 00:14:51,240 --> 00:14:53,560 Pick the chair up. 195 00:14:53,560 --> 00:14:54,760 Now stand up. 196 00:14:54,770 --> 00:14:55,300 Hah! 197 00:14:55,300 --> 00:15:01,240 [laughing] 198 00:15:01,240 --> 00:15:03,180 That's fair enough. Don't hurt yourself. 199 00:15:03,180 --> 00:15:06,140 No, no. There was actually no way. [laughing] 200 00:15:07,320 --> 00:15:09,200 Toes against the wall. 201 00:15:10,980 --> 00:15:11,600 One. 202 00:15:12,260 --> 00:15:16,400 Two. Okay, translate over. You might be able to do it because his feet are proportionately 203 00:15:16,400 --> 00:15:17,740 small. 204 00:15:17,740 --> 00:15:19,860 Okay, down. 205 00:15:19,860 --> 00:15:21,260 Pick it up. 206 00:15:21,260 --> 00:15:23,080 [giggle] 207 00:15:23,080 --> 00:15:26,200 Pick up the chair first. Please pick up of the chair please. 208 00:15:26,200 --> 00:15:27,720 Now stand up. 209 00:15:27,720 --> 00:15:29,400 [laughing] 210 00:15:31,380 --> 00:15:33,600 Okay. One over. 211 00:15:33,600 --> 00:15:35,540 Bend over. 212 00:15:37,380 --> 00:15:39,880 Ohhh, okay. 213 00:15:39,880 --> 00:15:41,280 Alright. 214 00:15:41,960 --> 00:15:45,960 Okay, then do it one more time with the other foot. 215 00:15:45,960 --> 00:15:52,060 Okay, now can translate over a little bit? Just move over but don't go in or out. 216 00:15:53,500 --> 00:15:58,320 Well, no. You want a line there. Actually... be in a little. 217 00:15:58,320 --> 00:15:59,880 There you go. 218 00:15:59,880 --> 00:16:02,000 No no no- you're fine! Just even up your feet. 219 00:16:02,000 --> 00:16:02,500 Okay. 220 00:16:02,500 --> 00:16:05,960 Bend over. Put your hands on the wall, just so you don't hit your head. 221 00:16:05,960 --> 00:16:07,560 Okay... 222 00:16:07,560 --> 00:16:10,320 now pick up the chair. 223 00:16:10,320 --> 00:16:12,280 Now stand up. 224 00:16:12,280 --> 00:16:17,100 No no. Don't do it again. You have to pick up the chair. Clean pick up. 225 00:16:17,100 --> 00:16:19,080 Now stand up. 226 00:16:21,200 --> 00:16:26,120 Alright! [clapping] 227 00:16:26,880 --> 00:16:28,520 [Sanjay speaking] Now it's your turn to try. 228 00:16:28,520 --> 00:16:32,480 Get together with your partner again and bring a chair over to the wall. 229 00:16:32,480 --> 00:16:42,020 Why don't you pause the video and give it a try? 230 00:16:42,020 --> 00:16:45,900 Now that you've attempted the chair lift, let's return to our seats and discuss what 231 00:16:45,900 --> 00:16:47,550 happened. 232 00:16:47,550 --> 00:16:51,990 If you wanted to figure out why this happens, what information would you need? 233 00:16:51,990 --> 00:16:54,690 What assumptions would you have to make? 234 00:16:54,690 --> 00:16:59,600 Discuss the matter with your partner. Try to draw a diagram of the situation. 235 00:16:59,600 --> 00:17:03,040 Pause the video here while you work this out. 236 00:17:07,060 --> 00:17:11,359 Many of you should be wondering about the center of mass for this situation. 237 00:17:11,369 --> 00:17:17,099 This diagram shows typical locations for the center of mass in men (on the left) and women 238 00:17:17,099 --> 00:17:18,809 (on the right). 239 00:17:18,809 --> 00:17:22,880 Not only are men typically taller, but their center of mass is usually higher in their 240 00:17:22,880 --> 00:17:23,970 bodies. 241 00:17:23,970 --> 00:17:28,309 This is not always true, but it is fairly typical. 242 00:17:28,309 --> 00:17:33,230 Using this information, work with your partner to try to explain what is happening. 243 00:17:33,230 --> 00:17:37,230 Why can women lift the chair when men cannot? 244 00:17:37,230 --> 00:17:40,280 You do not need to obtain a numerical solution. 245 00:17:40,280 --> 00:17:45,530 Instead, use reasoned arguments, diagrams, and well-supported assumptions to prove your 246 00:17:45,530 --> 00:17:46,910 answer. 247 00:17:46,910 --> 00:17:52,690 Only use calculations if you cannot support your answer in any other way. 248 00:17:52,690 --> 00:17:56,210 Pause the video and give it a try. 249 00:17:59,770 --> 00:18:01,980 Are you ready to see the solution? 250 00:18:01,980 --> 00:18:04,780 Let's take a look. 251 00:18:04,780 --> 00:18:09,030 For this section we will measure torques around the center of mass. 252 00:18:09,030 --> 00:18:13,280 This will simplify our work so that we don't have to worry about the person's mass and 253 00:18:13,280 --> 00:18:15,809 the pull of gravity. 254 00:18:15,809 --> 00:18:18,590 This diagram shows the man lifting the chair. 255 00:18:18,590 --> 00:18:23,050 You can see that the center of mass is outside his body, and has been moved farther forward 256 00:18:23,050 --> 00:18:25,580 and down by the chair. 257 00:18:25,580 --> 00:18:27,660 This diagram shows the same for the woman. 258 00:18:27,660 --> 00:18:34,100 Her center of mass is also outside her body, but is much closer to her legs. 259 00:18:34,100 --> 00:18:39,490 If we draw a line for the man to indicate where his toes are, you see that the center 260 00:18:39,490 --> 00:18:41,820 of mass is beyond the edge of his foot! 261 00:18:41,820 --> 00:18:47,420 No matter how hard he tries, he simply cannot apply force in the right place to lift that 262 00:18:47,420 --> 00:18:49,290 chair. 263 00:18:49,290 --> 00:18:54,180 On our diagram, we can see that the torque will always point in the direction out of 264 00:18:54,180 --> 00:18:55,170 the screen. 265 00:18:55,170 --> 00:19:00,660 It will rotate the man counterclockwise, pushing his head harder into the wall. 266 00:19:00,660 --> 00:19:04,490 The harder he pushes, the worse it will be. 267 00:19:04,490 --> 00:19:08,430 The woman, however, has her center of mass above her feet. 268 00:19:08,430 --> 00:19:13,830 She can stand up because her feet are able to apply force in the proper location and 269 00:19:13,830 --> 00:19:14,680 direction. 270 00:19:14,680 --> 00:19:22,380 If we draw a torque diagram, we can see that the direction of torque applied by her feet 271 00:19:22,380 --> 00:19:24,490 will be into the screen. 272 00:19:24,490 --> 00:19:29,790 By applying more force, she can rotate her upper body clockwise and stand up, whereas 273 00:19:29,790 --> 00:19:32,920 the man cannot. 274 00:19:32,920 --> 00:19:37,610 Today we hope that you have improved your ability to draw torque diagrams, and to analyze 275 00:19:37,610 --> 00:19:41,050 torque problems that occur in the real world. 276 00:19:41,050 --> 00:19:45,710 Torque is an important quantity that comes into play in countless situations around us, 277 00:19:45,710 --> 00:19:50,660 from machinery to buildings to the simple act of walking. I hope you enjoyed this look 278 00:19:50,660 --> 00:19:55,320 at one of its fascinating applications.