1 00:00:00,480 --> 00:00:02,440 Let's say we observe some object-- 2 00:00:02,440 --> 00:00:04,970 let's say for the sake of argument, it's happening in space 3 00:00:05,070 --> 00:00:07,870 It's traveling in a circular path with 4 00:00:08,070 --> 00:00:11,100 the magnitude of its velocity being constant 5 00:00:11,130 --> 00:00:15,050 Let me draw its velocity vector 6 00:00:15,050 --> 00:00:18,510 The length of this arrow is the magnitude of the velocity 7 00:00:18,610 --> 00:00:21,700 I want to be clear. In order for it to be traveling in the circular path 8 00:00:21,700 --> 00:00:24,220 the direction of its velocity needs to be changing 9 00:00:24,420 --> 00:00:27,590 So this time the velocity vector might look like that 10 00:00:27,810 --> 00:00:36,880 After a few seconds the velocity vector might look like this 11 00:00:37,210 --> 00:00:41,210 After another few seconds the velocity vector might look like this 12 00:00:41,210 --> 00:00:46,450 I'm just sampling. I actually could've sampled after a less time and it would be right over there 13 00:00:46,450 --> 00:00:50,780 but I am just sampling sometimes as it travels around the circle 14 00:00:51,000 --> 00:00:57,330 After a few more seconds the velocity vector might look something like that 15 00:00:57,740 --> 00:01:01,120 I want to think about what needs to happen 16 00:01:01,150 --> 00:01:03,310 what kind of force would have to act 17 00:01:03,310 --> 00:01:06,850 in particular the direction of the force would have to act on this object 18 00:01:07,000 --> 00:01:09,500 in order for the velocity vector to change like that? 19 00:01:09,930 --> 00:01:14,510 This remind ourselves if there was no force acting on this body 20 00:01:14,510 --> 00:01:17,680 this comes straight from Newton's 1st Law of motion 21 00:01:17,720 --> 00:01:19,900 then the velocity would not change 22 00:01:19,930 --> 00:01:23,450 neither the magnitude nor the direction of the velocity will change 23 00:01:23,450 --> 00:01:25,640 If there were no force acting on the subject 24 00:01:25,810 --> 00:01:28,940 it would just continue going on in the direction it was going 25 00:01:28,940 --> 00:01:34,230 it wouldn't curve; it wouldn't turn; the direction of its velocity wasn't changing 26 00:01:34,330 --> 00:01:38,620 Let's think about what the direction of that force would have to be 27 00:01:38,770 --> 00:01:43,200 and to do that, I'm gonna copy and paste these velocity vectors and keep 28 00:01:43,200 --> 00:01:48,860 track of what the direction of the change in velocity has to be 29 00:01:49,330 --> 00:01:51,990 Copy and paste that 30 00:01:52,350 --> 00:02:00,210 So that is our first velocity vector 31 00:02:00,660 --> 00:02:05,920 Copy all of these. This is our second one right over here 32 00:02:06,950 --> 00:02:09,810 Copy and paste it 33 00:02:10,900 --> 00:02:14,210 I'm just looking at it from the object's point of view 34 00:02:14,360 --> 00:02:18,760 how does the velocity vector change from each of these points in time to the next? 35 00:02:19,380 --> 00:02:21,860 Let me get all of these in there 36 00:02:22,280 --> 00:02:24,430 This green one 37 00:02:25,790 --> 00:02:29,910 That. Copy and paste it 38 00:02:31,010 --> 00:02:36,890 That. I could keep going, keep drawing velocity vectors around the circle 39 00:02:36,890 --> 00:02:39,530 but let me do this orange one right over here 40 00:02:39,650 --> 00:02:43,050 Copy and paste 41 00:02:45,480 --> 00:02:57,030 So between this magenta time and this purple time 42 00:02:57,060 --> 00:02:59,160 what was the change in velocity? 43 00:02:59,160 --> 00:03:01,950 Well, we could look at that purely from these vectors right here 44 00:03:01,950 --> 00:03:06,110 The change in velocity between those two times was that right over there 45 00:03:06,490 --> 00:03:09,110 That is our change in velocity 46 00:03:09,490 --> 00:03:15,900 So I take this vector and say in what direction was the velocity changing 47 00:03:15,900 --> 00:03:18,440 when this vector was going on this part of the arc 48 00:03:18,700 --> 00:03:22,640 It's roughly--if I just translate that vector right over here 49 00:03:22,770 --> 00:03:24,850 it's roughly going in that direction 50 00:03:24,930 --> 00:03:28,010 So that is the direction of our change in velocity 51 00:03:28,010 --> 00:03:31,160 This triangle is delta; delta is for change 52 00:03:31,570 --> 00:03:33,970 Now think about the next time period 53 00:03:34,630 --> 00:03:38,020 between this blue or purple period and this green period 54 00:03:38,020 --> 00:03:41,750 Our change in velocity would look like that 55 00:03:41,970 --> 00:03:44,260 So while it's traveling along this part of the arc 56 00:03:44,260 --> 00:03:49,180 roughly it's the change in velocity if we draw the vector starting at the object 57 00:03:49,190 --> 00:03:54,710 It would look something like this 58 00:03:55,020 --> 00:03:58,050 I'm just translating this vector right over here 59 00:03:58,290 --> 00:04:00,310 I'll do it one more time 60 00:04:00,340 --> 00:04:05,500 From this green point in time to this orange point in time 61 00:04:05,500 --> 00:04:08,520 and obviously we're just sampling points continuously moving 62 00:04:08,530 --> 00:04:10,980 and the change in velocity actually continues changing 63 00:04:10,980 --> 00:04:12,770 but hopefully you're going to see the pattern here 64 00:04:13,130 --> 00:04:21,339 So between those two points in time, this is our change in velocity 65 00:04:21,339 --> 00:04:23,730 And let me translate that vector right over there 66 00:04:23,780 --> 00:04:25,860 It would look something like that 67 00:04:25,880 --> 00:04:27,590 change in velocity 68 00:04:27,600 --> 00:04:32,330 So what do you see, if I were to keep drawing more of these change in velocity vectors 69 00:04:32,330 --> 00:04:35,330 you would see at this point, the change in velocity would have to be going 70 00:04:35,330 --> 00:04:36,590 generally in that direction 71 00:04:36,710 --> 00:04:40,920 At this point, the change in velocity would have to be going generally in that direction 72 00:04:41,140 --> 00:04:46,490 So what do you see? What's the pattern for any point along this circular curve? 73 00:04:46,780 --> 00:04:48,970 Well, the change in velocity 74 00:04:48,970 --> 00:04:53,340 first of all, is perpendicular to the direction of the velocity itself 75 00:04:53,840 --> 00:04:57,040 And we haven't proved it, but it at least looks like it 76 00:04:57,060 --> 00:04:59,080 Looks like this is perpendicular 77 00:04:59,110 --> 00:05:02,870 And even more interesting, it looks like it's seeking the center 78 00:05:02,870 --> 00:05:10,410 The change in velocity is constantly going in the direction of the center of our circle 79 00:05:11,110 --> 00:05:13,560 And we know from Newton's first law 80 00:05:13,760 --> 00:05:17,620 that if--the magnitude could stay the same but the 81 00:05:17,620 --> 00:05:21,710 velocity change in any way, either the magnitude or the direction or both 82 00:05:21,840 --> 00:05:25,430 there must be a net force acting on the object 83 00:05:25,440 --> 00:05:28,790 And the net force is acting in the direction of the acceleration 84 00:05:28,790 --> 00:05:30,770 which is causing the change in velocity 85 00:05:30,800 --> 00:05:34,450 So the force must be acting in the same direction as this change in velocity 86 00:05:34,470 --> 00:05:37,950 So in order make this object go in this circular 87 00:05:38,160 --> 00:05:44,710 there must be some force kind of pulling the object towards the center 88 00:05:44,730 --> 00:05:48,530 and a force that is perpendicular to its directional motion 89 00:05:48,840 --> 00:05:52,300 And this force is called the centripetal force 90 00:05:52,560 --> 00:05:55,850 Centripetal 91 00:05:55,850 --> 00:05:59,490 Not to be confused with centrifugal force, very different 92 00:05:59,600 --> 00:06:04,400 Centripetal force, centri- you might recognize as center 93 00:06:04,430 --> 00:06:13,910 and then -petal is seeking the center. It is center seeking 94 00:06:14,220 --> 00:06:18,650 So this centripetal force, something is pulling on this object towards the center that 95 00:06:18,680 --> 00:06:21,340 causes it to go into this circular motion 96 00:06:21,490 --> 00:06:25,350 Inward pulling causes inward acceleration 97 00:06:25,350 --> 00:06:28,730 So that's centripetal force 98 00:06:29,040 --> 00:06:34,190 causing centripetal acceleration 99 00:06:34,230 --> 00:06:37,130 which causes the object to go towards the center 100 00:06:37,130 --> 00:06:40,580 The whole point why I did this is that at least it wasn't intuitive to me 101 00:06:40,580 --> 00:06:42,760 that if you have this object going in a circle 102 00:06:42,800 --> 00:06:47,220 that the change in velocity, the acceleration, the force acting on this object 103 00:06:47,240 --> 00:06:51,550 would actually have to be towards the center 104 00:06:51,570 --> 00:06:53,780 The whole reason why I drew these vectors 105 00:06:53,790 --> 00:06:57,220 and then translate them over here and drew these change in velocity vectors 106 00:06:57,340 --> 00:07:04,830 is to show you that the change in velocity is actually towards the center of this circle 107 00:07:05,280 --> 00:07:09,600 Now with that out of the way, you might say, well, where is this happening in in everyday life 108 00:07:09,600 --> 00:07:13,240 or in reality in some way it perform 109 00:07:13,300 --> 00:07:16,880 And the most typical example of this and this is something that I think most of us have done 110 00:07:16,880 --> 00:07:20,900 when we were kid if you had a yoyo 111 00:07:21,170 --> 00:07:23,550 My best attempt to draw a yoyo 112 00:07:24,020 --> 00:07:29,680 If you have a yoyo and if you whip it around on a string 113 00:07:29,940 --> 00:07:36,330 you know that the yoyo goes in a circle 114 00:07:36,350 --> 00:07:42,080 Even though its speed might be constant, or the magnitude of its velocity might be constant 115 00:07:42,200 --> 00:07:45,090 we know that the direction of its velocity is constantly changing 116 00:07:45,090 --> 00:07:49,830 It's going in a circle and what's causing it to go in a circle is your hand right over here 117 00:07:50,010 --> 00:07:54,200 pulling on this string and providing tension into the string 118 00:07:54,490 --> 00:07:59,330 So there's a force, the centripetal force in this yoyo example is the tension in the string 119 00:07:59,480 --> 00:08:03,180 that's constantly pulling on the yoyo towards the center 120 00:08:03,180 --> 00:08:05,720 and that's why that yoyo goes in a circle 121 00:08:05,730 --> 00:08:10,090 Another example that you are probably somewhat familiar with or at least have heard about 122 00:08:10,090 --> 00:08:13,380 is if you have something in orbit around the planet 123 00:08:13,380 --> 00:08:16,630 So let's say this is Earth right here 124 00:08:16,670 --> 00:08:27,620 and you have some type of a satellite that is in orbit around Earth 125 00:08:27,790 --> 00:08:33,140 That satellite has some velocity at any given moment in time 126 00:08:33,260 --> 00:08:37,740 What's keeping it from not flying out into space and keeping it going in a circle 127 00:08:37,770 --> 00:08:39,590 is the force of gravity 128 00:08:39,590 --> 00:08:43,750 So in the example of a satellite or anything in the orbit 129 00:08:43,750 --> 00:08:46,190 even the moon in orbit around the Earth 130 00:08:46,500 --> 00:08:49,830 the thing that's keeping an orbit as opposed to flying out into space 131 00:08:49,890 --> 00:08:53,430 is a centripetal force of Earth's gravity 132 00:08:53,650 --> 00:08:58,010 Now another example, this is probably the most everyday example because we do it all the time 133 00:08:58,480 --> 00:09:01,860 If you imagine a car traveling around the racetrack 134 00:09:01,860 --> 00:09:05,860 Let's draw a racetrack. If I have a racetrack 135 00:09:06,330 --> 00:09:10,250 Before I tell you the answer, I'll have you think about it 136 00:09:10,900 --> 00:09:15,190 It's circular. Let's view the racetrack from above 137 00:09:15,260 --> 00:09:19,470 If I have a car on a racetrack. I want you to pause it before I tell it to you 138 00:09:19,470 --> 00:09:21,700 because I think it's an interesting thing think about 139 00:09:21,730 --> 00:09:24,910 It seems like a very obvious thing that's happening 140 00:09:24,910 --> 00:09:28,040 We've all experienced; we've all taken turns in cars 141 00:09:28,040 --> 00:09:32,810 So we're looking at the top of a car. Tires 142 00:09:32,830 --> 00:09:35,650 When you see a car going at a constant speed 143 00:09:35,800 --> 00:09:40,560 so on the speedometer, it might say, 60 mph, 40 mph, whatever the constant speed 144 00:09:40,560 --> 00:09:44,530 but it's traveling in a circle 145 00:09:44,810 --> 00:09:48,840 so what is keeping--what is the centripetal force in that example? 146 00:09:48,840 --> 00:09:52,340 There's no obvious string being pulled on the car towards the center 147 00:09:52,470 --> 00:09:56,660 There is no some magical gravity pulling it towards the center of the circle 148 00:09:56,660 --> 00:09:59,170 There's obviously gravity pulling you down towards the ground 149 00:09:59,180 --> 00:10:01,280 but nothing pulling it to the side like this 150 00:10:01,430 --> 00:10:07,180 So what's causing this car to go in the circle as opposed to going straight? 151 00:10:07,190 --> 00:10:10,390 And I encourage you to pause it right now before I tell you the answer 152 00:10:10,420 --> 00:10:13,520 Assuming you now unpaused it and I will now tell you the answer 153 00:10:13,670 --> 00:10:17,370 The thing that's keeping it going in the circle is actually the force of friction 154 00:10:17,660 --> 00:10:26,750 It's actually the force between the resist movement to the side between the tires and the road 155 00:10:26,900 --> 00:10:30,270 And a good example of that is if you would remove the friction 156 00:10:30,270 --> 00:10:33,770 if you would make the car driving on oil or on ice 157 00:10:33,800 --> 00:10:39,070 or if you would shave the treads of the tire or something 158 00:10:39,070 --> 00:10:40,990 then the car would not be able to do this 159 00:10:41,000 --> 00:10:43,240 So it's actually the force of friction in this example 160 00:10:43,250 --> 00:00:00,000 I encourage you to think about that