1 00:00:00,415 --> 00:00:02,103 - [Voiceover] When a major league baseball player throws 2 00:00:02,103 --> 00:00:05,637 a fast ball, that ball's definitely got kinetic energy. 3 00:00:05,637 --> 00:00:07,581 We know that cause if you get in the way, 4 00:00:07,581 --> 00:00:09,429 it could do work on you, that's gonna hurt. 5 00:00:09,429 --> 00:00:10,583 You gotta watch out. 6 00:00:10,583 --> 00:00:14,212 But here's my question: does the fact that most pitches, 7 00:00:14,212 --> 00:00:15,855 unless you're throwing a knuckle ball, 8 00:00:15,855 --> 00:00:19,157 does the fact that most pitches head toward home plate 9 00:00:19,157 --> 00:00:21,805 with the baseball spinning mean that that ball 10 00:00:21,805 --> 00:00:24,197 has extra kinetic energy? 11 00:00:24,197 --> 00:00:26,571 Well it does, and how do we figure that out, 12 00:00:26,571 --> 00:00:28,986 that's the goal for this video. 13 00:00:28,986 --> 00:00:31,267 How do we determine what the rotational 14 00:00:31,267 --> 00:00:33,647 kinetic energy is of an object? 15 00:00:33,647 --> 00:00:35,770 Well if I was coming at this for the first time, 16 00:00:35,770 --> 00:00:37,803 my first guest I'd say okay, 17 00:00:37,803 --> 00:00:40,561 I'd say I know what regular kinetic energy looks like. 18 00:00:40,561 --> 00:00:42,875 The formula for regular kinetic energy is 19 00:00:42,875 --> 00:00:45,954 just one half m v squared. 20 00:00:45,954 --> 00:00:48,567 So let's say alright, I want rotational kinetic energy. 21 00:00:48,567 --> 00:00:50,963 Let me just call that k rotational 22 00:00:50,963 --> 00:00:52,497 and what is that gonna be? 23 00:00:52,497 --> 00:00:54,964 Well I know for objects that are rotating, 24 00:00:54,964 --> 00:00:58,764 the rotational equivalent of mass is moment of inertia. 25 00:00:58,764 --> 00:01:01,461 So I might guess alright instead of mass, 26 00:01:01,461 --> 00:01:04,354 I'd have moment of inertia cause in Newton's second law 27 00:01:04,354 --> 00:01:06,813 for rotation I know that instead of mass there's 28 00:01:06,813 --> 00:01:09,091 moment of inertia so maybe I replace that. 29 00:01:09,091 --> 00:01:12,188 And instead of speed squared, maybe since I have 30 00:01:12,188 --> 00:01:15,284 something rotating I'd have angular speed squared. 31 00:01:15,284 --> 00:01:16,898 It turns out this works. 32 00:01:16,898 --> 00:01:20,014 You can often derive, it's not really a derivation, 33 00:01:20,014 --> 00:01:22,516 you're just kind of guessing educatedly but you could 34 00:01:22,516 --> 00:01:25,797 often get a formula for the rotational analog of some 35 00:01:25,797 --> 00:01:29,780 linear formula by just substituting the rotational analog 36 00:01:29,780 --> 00:01:32,415 for each of the variables, so if I replaced mass with 37 00:01:32,415 --> 00:01:35,247 rotational mass, I get the moment of inertia. 38 00:01:35,247 --> 00:01:37,721 If I replace speed with rotational speed, 39 00:01:37,721 --> 00:01:40,743 I get the angular speed and this is the correct formula. 40 00:01:40,743 --> 00:01:43,303 So in this video we needed to ride this cause that 41 00:01:43,303 --> 00:01:44,913 is not really a derivation, we didn't really 42 00:01:44,913 --> 00:01:47,720 prove this, we just showed that it's plausible. 43 00:01:47,720 --> 00:01:50,111 How do we prove that this is the rotational 44 00:01:50,111 --> 00:01:52,991 kinetic energy of an object that's rotating 45 00:01:52,991 --> 00:01:54,349 like a baseball. 46 00:01:54,349 --> 00:01:56,997 The first thing to recognize is that this rotational 47 00:01:56,997 --> 00:01:59,684 kinetic energy isn't really a new kind of 48 00:01:59,684 --> 00:02:02,301 kinetic energy, it's still just the same old 49 00:02:02,301 --> 00:02:05,721 regular kinetic energy for something that's rotating. 50 00:02:05,721 --> 00:02:07,051 What I mean by that is this. 51 00:02:07,051 --> 00:02:09,820 Imagine this baseball is rotating in a circle. 52 00:02:09,820 --> 00:02:13,320 Every point on the baseball is moving with some speed, 53 00:02:13,320 --> 00:02:15,462 so what I mean by that is this, so this point at the top 54 00:02:15,462 --> 00:02:18,613 here imagine the little piece of leather right here, 55 00:02:18,613 --> 00:02:20,367 it's gonna have some speed forward. 56 00:02:20,367 --> 00:02:23,485 I'm gonna call this mass M one, that little piece 57 00:02:23,485 --> 00:02:27,188 of mass right now and I'll call the speed of it V one. 58 00:02:27,188 --> 00:02:29,744 Similarly, this point on the leather right there, 59 00:02:29,744 --> 00:02:32,288 I'm gonna call that M two, it's gonna be moving down 60 00:02:32,288 --> 00:02:35,713 cause it's a rotating circle, so I'll call that V two 61 00:02:35,713 --> 00:02:38,370 and points closer to the axis are gonna be moving 62 00:02:38,370 --> 00:02:41,027 with smaller speed so this point right here, 63 00:02:41,027 --> 00:02:43,779 we'll call it M three, moving down with a speed V three, 64 00:02:43,779 --> 00:02:46,771 that is not as big as V two or V one. 65 00:02:46,771 --> 00:02:48,082 You can't see that very well, 66 00:02:48,082 --> 00:02:51,587 I'll use a darker green so this M three right here 67 00:02:51,587 --> 00:02:54,921 closer to the axis, axis being right at this point 68 00:02:54,921 --> 00:02:58,781 in the center, closer to the axis so it's speed is smaller 69 00:02:58,781 --> 00:03:01,411 than points that are farther away from this axis, 70 00:03:01,411 --> 00:03:03,373 so you can see this is kinda complicated. 71 00:03:03,373 --> 00:03:05,539 All points on this baseball are gonna be moving with 72 00:03:05,539 --> 00:03:08,126 different speeds so points over here that are really 73 00:03:08,126 --> 00:03:10,796 close to the axis, barely moving at all. 74 00:03:10,796 --> 00:03:12,946 I'll call this M four and it would be 75 00:03:12,946 --> 00:03:15,093 moving at speed V four. 76 00:03:15,093 --> 00:03:17,676 What we mean by the rotational kinetic energy is 77 00:03:17,676 --> 00:03:19,892 really just all the regular kinetic energy these 78 00:03:19,892 --> 00:03:23,846 masses have about the center of mass of the baseball. 79 00:03:23,846 --> 00:03:26,681 So in other words, what we mean by K rotational, 80 00:03:26,681 --> 00:03:29,455 is you just add up all of these energies. 81 00:03:29,455 --> 00:03:32,021 You have one half, this little piece of leather 82 00:03:32,021 --> 00:03:33,737 up here would have some kinetic energy 83 00:03:33,737 --> 00:03:37,487 so you do one half M one, V one squared plus. 84 00:03:38,415 --> 00:03:41,050 And this M two has some kinetic energy, 85 00:03:41,050 --> 00:03:43,152 don't worry that it points downward, 86 00:03:43,152 --> 00:03:45,954 downward doesn't matter for things that aren't vectors, 87 00:03:45,954 --> 00:03:49,258 this V gets squared so kinetic energy's not a vector 88 00:03:49,258 --> 00:03:51,779 so it doesn't matter that one velocity points down 89 00:03:51,779 --> 00:03:54,443 cause this is just the speed and similarly, 90 00:03:54,443 --> 00:03:58,950 you'd add up one half M three, V three squared, 91 00:03:58,950 --> 00:04:00,517 but you might be like this is impossible, 92 00:04:00,517 --> 00:04:02,926 there's infinitely many points in this baseball, 93 00:04:02,926 --> 00:04:05,388 how am I ever going to do this. 94 00:04:05,388 --> 00:04:07,379 Well something magical is about to happen, 95 00:04:07,379 --> 00:04:09,526 this is one of my favorite little derivations, 96 00:04:09,526 --> 00:04:12,133 short and sweet, watch what happens. 97 00:04:12,133 --> 00:04:15,067 K E rotational is really just the sum, 98 00:04:15,067 --> 00:04:17,661 if I add all these up I can write is as a sum 99 00:04:17,661 --> 00:04:21,494 of all the one half M V squares of every point 100 00:04:22,457 --> 00:04:25,416 on this baseball so imagine breaking this baseball 101 00:04:25,416 --> 00:04:27,756 up into very, very small pieces. 102 00:04:27,756 --> 00:04:30,072 Don't do it physically but just think about it mentally, 103 00:04:30,072 --> 00:04:33,039 just visualize considering very small pieces, 104 00:04:33,039 --> 00:04:35,919 particles of this baseball and how fast they're going. 105 00:04:35,919 --> 00:04:38,938 What I'm saying is that if you add all of that up, 106 00:04:38,938 --> 00:04:41,359 you get the total rotational kinetic energy, 107 00:04:41,359 --> 00:04:42,967 this looks impossible to do. 108 00:04:42,967 --> 00:04:44,552 But something magical is about to happen, 109 00:04:44,552 --> 00:04:45,766 here's what we can do. 110 00:04:45,766 --> 00:04:48,352 We can rewrite, see the problem here is V. 111 00:04:48,352 --> 00:04:50,755 All these points have a different speed V, 112 00:04:50,755 --> 00:04:52,711 but we can use a trick, a trick that we love 113 00:04:52,711 --> 00:04:55,125 to use in physics, instead of writing this as V, 114 00:04:55,125 --> 00:04:57,773 we're gonna write V as, so remember that for things 115 00:04:57,773 --> 00:05:01,564 that are rotating, V is just R times omega. 116 00:05:01,564 --> 00:05:04,133 The radius, how far from the axis you are, 117 00:05:04,133 --> 00:05:06,885 times the angular velocity, or the angular speed 118 00:05:06,885 --> 00:05:09,358 gives you the regular speed. 119 00:05:09,358 --> 00:05:12,145 This formula is really handy, so we're gonna replace 120 00:05:12,145 --> 00:05:16,185 V with R omega, and this is gonna give us R omega 121 00:05:16,185 --> 00:05:18,352 and you still have to square it and at this point 122 00:05:18,352 --> 00:05:19,993 you're probably thinking like this is even worse, 123 00:05:19,993 --> 00:05:21,079 what do we do this for. 124 00:05:21,079 --> 00:05:24,023 Well watch, if we add this is up I'll have one half M. 125 00:05:24,023 --> 00:05:26,848 I'm gonna get an R squared and an omega squared, 126 00:05:26,848 --> 00:05:28,958 and the reason this is better is that even though 127 00:05:28,958 --> 00:05:32,626 every point on this baseball has a different speed V, 128 00:05:32,626 --> 00:05:35,491 they all have the same angular speed omega, 129 00:05:35,491 --> 00:05:38,315 that was what was good about these angular quantities 130 00:05:38,315 --> 00:05:41,618 is that they're the same for every point on the baseball 131 00:05:41,618 --> 00:05:43,870 no matter how far away you are from the axis, 132 00:05:43,870 --> 00:05:46,042 and since they're the same for every point I can 133 00:05:46,042 --> 00:05:48,634 bring that out of the summation so I can rewrite 134 00:05:48,634 --> 00:05:51,609 this summation and bring everything that's constant 135 00:05:51,609 --> 00:05:54,818 for all of the masses out of the summation so I can 136 00:05:54,818 --> 00:05:58,220 write this as one half times the summation 137 00:05:58,220 --> 00:06:01,803 of M times R squared and end that quantity, 138 00:06:02,782 --> 00:06:06,597 end that summation and just pull the omega squared out 139 00:06:06,597 --> 00:06:08,565 because it's the same for each term. 140 00:06:08,565 --> 00:06:11,444 I'm basically factoring this out of all of these 141 00:06:11,444 --> 00:06:13,857 terms in the summation, it's like up here, 142 00:06:13,857 --> 00:06:15,548 all of these have a one half. 143 00:06:15,548 --> 00:06:17,487 You could imagine factoring out a one half 144 00:06:17,487 --> 00:06:18,985 and just writing this whole quantity as 145 00:06:18,985 --> 00:06:22,135 one half times M one V one squared plus 146 00:06:22,135 --> 00:06:24,167 M two V two squared and so on. 147 00:06:24,167 --> 00:06:26,055 That's what I'm doing down here for the one half 148 00:06:26,055 --> 00:06:28,615 and for the omega squared, so that's what was good 149 00:06:28,615 --> 00:06:31,077 about replacing V with R omega. 150 00:06:31,077 --> 00:06:32,540 The omega's the same for all of them, 151 00:06:32,540 --> 00:06:33,816 you can bring that out. 152 00:06:33,816 --> 00:06:35,514 You might still be concerned, you might be like, 153 00:06:35,514 --> 00:06:37,993 we're still stuck with the M in here cause you've 154 00:06:37,993 --> 00:06:39,990 got different Ms at different points. 155 00:06:39,990 --> 00:06:42,160 We're stuck with all these R squareds in here, 156 00:06:42,160 --> 00:06:44,628 all these points at the baseball are different Rs, 157 00:06:44,628 --> 00:06:46,328 they're all different points from the axis, 158 00:06:46,328 --> 00:06:48,558 different distances from the axis, we can't bring 159 00:06:48,558 --> 00:06:51,449 those out so now what do we do, well if you're clever 160 00:06:51,449 --> 00:06:53,792 you recognize this term. 161 00:06:53,792 --> 00:06:56,615 This summation term is nothing but the total moment 162 00:06:56,615 --> 00:06:59,296 of inertia of the object. 163 00:06:59,296 --> 00:07:01,628 Remember that the moment of inertia of an object, 164 00:07:01,628 --> 00:07:04,394 we learned previously, is just M R squared, 165 00:07:04,394 --> 00:07:06,410 so the moment of inertia of a point mass 166 00:07:06,410 --> 00:07:09,122 is M R squared and the moment of inertia 167 00:07:09,122 --> 00:07:12,483 of a bunch of point masses is the sum of all 168 00:07:12,483 --> 00:07:15,402 the M R squareds and that's what we've got right here, 169 00:07:15,402 --> 00:07:19,514 this is just the moment of inertia of this baseball 170 00:07:19,514 --> 00:07:22,115 or whatever the object is, it doesn't even have to be 171 00:07:22,115 --> 00:07:24,287 of a particular shape, we're gonna add all 172 00:07:24,287 --> 00:07:26,998 the M R squareds, that's always going to be 173 00:07:26,998 --> 00:07:28,637 the total moment of inertia. 174 00:07:28,637 --> 00:07:30,925 So what we've found is that the K rotational 175 00:07:30,925 --> 00:07:34,066 is equal to one half times this quantity, 176 00:07:34,066 --> 00:07:35,947 which is I, the moment of inertia, 177 00:07:35,947 --> 00:07:38,284 times omega squared and that's the formula 178 00:07:38,284 --> 00:07:40,004 we got up here just by guessing. 179 00:07:40,004 --> 00:07:41,850 But it actually works and this is why it works, 180 00:07:41,850 --> 00:07:43,859 because you always get this quantity down here, 181 00:07:43,859 --> 00:07:46,204 which is one half I omega squared, no matter what 182 00:07:46,204 --> 00:07:47,676 the shape of the object is. 183 00:07:47,676 --> 00:07:49,420 So what this is telling you, what this quantity 184 00:07:49,420 --> 00:07:52,346 gives us is the total rotational kinetic energy 185 00:07:52,346 --> 00:07:55,666 of all the points on that mass about the center 186 00:07:55,666 --> 00:07:58,591 of the mass but here's what it doesn't give you. 187 00:07:58,591 --> 00:08:01,036 This term right here does not include 188 00:08:01,036 --> 00:08:03,451 the translational kinetic energy so the fact that 189 00:08:03,451 --> 00:08:06,292 this baseball was flying through the air does not 190 00:08:06,292 --> 00:08:08,142 get incorporated by this formula. 191 00:08:08,142 --> 00:08:10,264 We didn't take into account the fact that 192 00:08:10,264 --> 00:08:12,391 the baseball was moving through the air, 193 00:08:12,391 --> 00:08:13,976 in other words, we didn't take into account 194 00:08:13,976 --> 00:08:16,791 that the actual center of mass in this baseball 195 00:08:16,791 --> 00:08:19,200 was translating through the air. 196 00:08:19,200 --> 00:08:21,365 But we can do that easily with this formula here. 197 00:08:21,365 --> 00:08:24,279 This is the translational kinetic energy. 198 00:08:24,279 --> 00:08:26,930 Sometimes instead of writing regular kinetic energy, 199 00:08:26,930 --> 00:08:29,841 now that we've got two we should specify this is really 200 00:08:29,841 --> 00:08:31,791 translational kinetic energy. 201 00:08:31,791 --> 00:08:34,361 We've got a formula for translational kinetic energy, 202 00:08:34,361 --> 00:08:37,701 the energy something has due to the fact that the center 203 00:08:37,701 --> 00:08:40,522 of mass of that object is moving and we have a formula 204 00:08:40,522 --> 00:08:42,972 that takes into account the fact that something can have 205 00:08:42,972 --> 00:08:45,494 kinetic energy due to its rotation. 206 00:08:45,494 --> 00:08:48,316 That's this K rotational, so if an object's rotating, 207 00:08:48,316 --> 00:08:50,483 it has rotational kinetic energy. 208 00:08:50,483 --> 00:08:52,718 If an object is translating it has 209 00:08:52,718 --> 00:08:54,500 translational kinetic energy, 210 00:08:54,500 --> 00:08:56,515 i.e. if the center of mass is moving, 211 00:08:56,515 --> 00:08:59,986 and if the object is translating and it's rotating 212 00:08:59,986 --> 00:09:02,435 then it would have those both of these kinetic energies, 213 00:09:02,435 --> 00:09:04,948 both at the same time and this is the beautiful thing. 214 00:09:04,948 --> 00:09:08,430 If an object is translating and rotating and you want 215 00:09:08,430 --> 00:09:11,390 to find the total kinetic energy of the entire thing, 216 00:09:11,390 --> 00:09:14,004 you can just add these two terms up. 217 00:09:14,004 --> 00:09:17,147 If I just take the translational one half M V squared, 218 00:09:17,147 --> 00:09:20,573 and this would then be the velocity of the center of mass. 219 00:09:20,573 --> 00:09:22,157 So you have to be careful. 220 00:09:22,157 --> 00:09:23,749 Let me make some room here, so let me get rid 221 00:09:23,749 --> 00:09:25,130 of all this stuff here. 222 00:09:25,130 --> 00:09:28,741 If you take one half M, times the speed of the center 223 00:09:28,741 --> 00:09:31,655 of mass squared, you'll get the total translational 224 00:09:31,655 --> 00:09:33,239 kinetic energy of the baseball. 225 00:09:33,239 --> 00:09:36,386 And if we add to that the one half I omega squared, 226 00:09:36,386 --> 00:09:39,184 so the omega about the center of mass you'll get 227 00:09:39,184 --> 00:09:43,688 the total kinetic energy, both translational and rotational, 228 00:09:43,688 --> 00:09:46,624 so this is great, we can determine the total kinetic energy 229 00:09:46,624 --> 00:09:49,889 altogether, rotational motion, translational motion, 230 00:09:49,889 --> 00:09:52,580 from just taking these two terms added up. 231 00:09:52,580 --> 00:09:54,049 So what would an example of this be, 232 00:09:54,049 --> 00:09:55,796 let's just get rid of all this. 233 00:09:55,796 --> 00:09:59,180 Let's say this baseball, someone pitched this thing, 234 00:09:59,180 --> 00:10:02,582 and the radar gun shows that this baseball was hurled 235 00:10:02,582 --> 00:10:04,799 through the air at 40 meters per second. 236 00:10:04,799 --> 00:10:07,452 So it's heading toward home plate at 40 meters per second. 237 00:10:07,452 --> 00:10:09,858 The center of mass of this baseball is going 238 00:10:09,858 --> 00:10:12,551 40 meters per second toward home plate. 239 00:10:12,551 --> 00:10:15,094 Let's say it's also, someone really threw the fastball. 240 00:10:15,094 --> 00:10:18,107 This thing's rotating with an angular velocity 241 00:10:18,107 --> 00:10:20,190 of 50 radians per second. 242 00:10:22,264 --> 00:10:24,376 We know the mass of a baseball, I've looked it up. 243 00:10:24,376 --> 00:10:28,781 The mass of a baseball is about 0.145 kilograms 244 00:10:28,781 --> 00:10:31,795 and the radius of the baseball, so a radius of a baseball 245 00:10:31,795 --> 00:10:35,388 is around seven centimeters, so in terms of meters that 246 00:10:35,388 --> 00:10:38,865 would be 0.07 meters, so we can figure out what's 247 00:10:38,865 --> 00:10:41,240 the total kinetic energy, well there's gonna be 248 00:10:41,240 --> 00:10:43,202 a rotational kinetic energy and there's gonna be 249 00:10:43,202 --> 00:10:45,048 a translational kinetic energy. 250 00:10:45,048 --> 00:10:47,875 The translational kinetic energy, gonna be one half 251 00:10:47,875 --> 00:10:50,835 the mass of the baseball times the center of mass speed 252 00:10:50,835 --> 00:10:53,993 of the baseball squared which is gonna give us one half. 253 00:10:53,993 --> 00:10:57,626 The mass of the baseball was 0.145 and the center of mass 254 00:10:57,626 --> 00:11:00,650 speed of the baseball is 40, that's how fast the center 255 00:11:00,650 --> 00:11:02,712 of mass of this baseball is traveling. 256 00:11:02,712 --> 00:11:06,712 If we add all that up we get 116 Jules of regular 257 00:11:06,712 --> 00:11:08,894 translational kinetic energy. 258 00:11:08,894 --> 00:11:11,246 How much rotational kinetic energy is there, 259 00:11:11,246 --> 00:11:13,281 so we're gonna have rotational kinetic energy 260 00:11:13,281 --> 00:11:16,088 due to the fact that the baseball is also rotating. 261 00:11:16,088 --> 00:11:19,587 How much, well we're gonna use one half I omega squared. 262 00:11:19,587 --> 00:11:22,484 I'm gonna have one half, what's the I, well the baseball is 263 00:11:22,484 --> 00:11:26,328 a sphere, if you look up the moment of inertia of a sphere 264 00:11:26,328 --> 00:11:29,665 cause I don't wanna have to do summation of all 265 00:11:29,665 --> 00:11:32,999 the M R squareds, if you do that using calculus, 266 00:11:32,999 --> 00:11:34,873 you get this formula. 267 00:11:34,873 --> 00:11:36,995 That means in an algebra based physics class 268 00:11:36,995 --> 00:11:38,900 you just have to look this up, it's either in your book 269 00:11:38,900 --> 00:11:41,635 in a chart or a table or you could always look it up online. 270 00:11:41,635 --> 00:11:45,763 For a sphere the moment of inertia is two fifths M R squared 271 00:11:45,763 --> 00:11:48,619 in other words two fifths the mass of a baseball 272 00:11:48,619 --> 00:11:50,459 times the raise of the baseball squared. 273 00:11:50,459 --> 00:11:53,627 That's just I, that's the moment of inertia of a sphere. 274 00:11:53,627 --> 00:11:56,235 So we're assuming this baseball is a perfect sphere. 275 00:11:56,235 --> 00:11:59,358 It's got uniform density, that's not completely true. 276 00:11:59,358 --> 00:12:00,954 But it's a pretty good approximation. 277 00:12:00,954 --> 00:12:03,019 Then we multiply by this omega squared, 278 00:12:03,019 --> 00:12:04,754 the angular speed squared. 279 00:12:04,754 --> 00:12:07,137 So what do we get, we're gonna get one half times 280 00:12:07,137 --> 00:12:11,222 two fifths, the mass of a baseball was 0.145. 281 00:12:11,222 --> 00:12:13,284 The radius of the baseball was about, what did we say, 282 00:12:13,284 --> 00:12:18,027 .07 meters so that's .07 meters squared and then finally 283 00:12:18,027 --> 00:12:20,494 we multiply by omega squared and this would make it 284 00:12:20,494 --> 00:12:23,238 50 radians per second and we square 285 00:12:23,238 --> 00:12:25,821 it which adds up to 0.355 Jules 286 00:12:28,705 --> 00:12:31,416 so hardly any of the energy of this baseball 287 00:12:31,416 --> 00:12:33,034 is in its rotation. 288 00:12:33,034 --> 00:12:36,449 Almost all of the energy is in the form of translational 289 00:12:36,449 --> 00:12:38,521 energy, that kinda makes sense. 290 00:12:38,521 --> 00:12:40,895 It's the fact that this baseball is hurling toward 291 00:12:40,895 --> 00:12:43,901 home plate that's gonna make it hurt if it hits you 292 00:12:43,901 --> 00:12:46,049 as opposed to the fact that it was spinning when 293 00:12:46,049 --> 00:12:48,545 it hits you, that doesn't actually cause as much damage 294 00:12:48,545 --> 00:12:50,705 as the fact that this baseball's kinetic energy 295 00:12:50,705 --> 00:12:54,466 is mostly in the form of translational kinetic energy. 296 00:12:54,466 --> 00:12:57,154 But if you wanted the total kinetic energy of the baseball, 297 00:12:57,154 --> 00:12:59,135 you would add both of these terms up. 298 00:12:59,135 --> 00:13:02,641 K total would be the translational kinetic energy 299 00:13:02,641 --> 00:13:04,937 plus the rotational kinetic energy. 300 00:13:04,937 --> 00:13:09,104 That means the total kinetic energy which is the 116 Jules 301 00:13:10,046 --> 00:13:12,546 plus 0.355 Jules which give us 302 00:13:14,425 --> 00:13:15,592 116.355 Jules. 303 00:13:18,343 --> 00:13:20,590 So recapping if an object is both rotating 304 00:13:20,590 --> 00:13:23,156 and translating you can find the translational 305 00:13:23,156 --> 00:13:26,787 kinetic energy using one half M the speed of the 306 00:13:26,787 --> 00:13:29,564 center of mass of that object squared and you can 307 00:13:29,564 --> 00:13:32,071 find the rotational kinetic energy by using 308 00:13:32,071 --> 00:13:34,552 one half I, the moment of inertia. 309 00:13:34,552 --> 00:13:36,161 We'll infer whatever shape it is, 310 00:13:36,161 --> 00:13:38,640 if it's a point mass going in a huge circle 311 00:13:38,640 --> 00:13:41,035 you could use M R squared, if it's a sphere 312 00:13:41,035 --> 00:13:43,635 rotating about its center you could use two fifths 313 00:13:43,635 --> 00:13:46,209 M R squared, cylinders are one half M R squared, 314 00:13:46,209 --> 00:13:49,007 you can look these up in tables to figure out 315 00:13:49,007 --> 00:13:52,032 whatever the I is that you need times the angular 316 00:13:52,032 --> 00:13:56,319 speed squared of the object about that center of mass. 317 00:13:56,319 --> 00:13:58,423 And if you add these two terms up you get the 318 00:13:58,423 --> 00:00:00,000 total kinetic energy of that object.