[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.42,0:00:02.10,Default,,0000,0000,0000,,- [Voiceover] When a major\Nleague baseball player throws
Dialogue: 0,0:00:02.10,0:00:05.64,Default,,0000,0000,0000,,a fast ball, that ball's\Ndefinitely got kinetic energy.
Dialogue: 0,0:00:05.64,0:00:07.58,Default,,0000,0000,0000,,We know that cause if you get in the way,
Dialogue: 0,0:00:07.58,0:00:09.43,Default,,0000,0000,0000,,it could do work on\Nyou, that's gonna hurt.
Dialogue: 0,0:00:09.43,0:00:10.58,Default,,0000,0000,0000,,You gotta watch out.
Dialogue: 0,0:00:10.58,0:00:14.21,Default,,0000,0000,0000,,But here's my question: does\Nthe fact that most pitches,
Dialogue: 0,0:00:14.21,0:00:15.86,Default,,0000,0000,0000,,unless you're throwing a knuckle ball,
Dialogue: 0,0:00:15.86,0:00:19.16,Default,,0000,0000,0000,,does the fact that most\Npitches head toward home plate
Dialogue: 0,0:00:19.16,0:00:21.80,Default,,0000,0000,0000,,with the baseball spinning\Nmean that that ball
Dialogue: 0,0:00:21.80,0:00:24.20,Default,,0000,0000,0000,,has extra kinetic energy?
Dialogue: 0,0:00:24.20,0:00:26.57,Default,,0000,0000,0000,,Well it does, and how\Ndo we figure that out,
Dialogue: 0,0:00:26.57,0:00:28.99,Default,,0000,0000,0000,,that's the goal for this video.
Dialogue: 0,0:00:28.99,0:00:31.27,Default,,0000,0000,0000,,How do we determine what the rotational
Dialogue: 0,0:00:31.27,0:00:33.65,Default,,0000,0000,0000,,kinetic energy is of an object?
Dialogue: 0,0:00:33.65,0:00:35.77,Default,,0000,0000,0000,,Well if I was coming at\Nthis for the first time,
Dialogue: 0,0:00:35.77,0:00:37.80,Default,,0000,0000,0000,,my first guest I'd say okay,
Dialogue: 0,0:00:37.80,0:00:40.56,Default,,0000,0000,0000,,I'd say I know what regular\Nkinetic energy looks like.
Dialogue: 0,0:00:40.56,0:00:42.88,Default,,0000,0000,0000,,The formula for regular kinetic energy is
Dialogue: 0,0:00:42.88,0:00:45.95,Default,,0000,0000,0000,,just one half m v squared.
Dialogue: 0,0:00:45.95,0:00:48.57,Default,,0000,0000,0000,,So let's say alright, I want\Nrotational kinetic energy.
Dialogue: 0,0:00:48.57,0:00:50.96,Default,,0000,0000,0000,,Let me just call that k rotational
Dialogue: 0,0:00:50.96,0:00:52.50,Default,,0000,0000,0000,,and what is that gonna be?
Dialogue: 0,0:00:52.50,0:00:54.96,Default,,0000,0000,0000,,Well I know for objects that are rotating,
Dialogue: 0,0:00:54.96,0:00:58.76,Default,,0000,0000,0000,,the rotational equivalent of\Nmass is moment of inertia.
Dialogue: 0,0:00:58.76,0:01:01.46,Default,,0000,0000,0000,,So I might guess alright instead of mass,
Dialogue: 0,0:01:01.46,0:01:04.35,Default,,0000,0000,0000,,I'd have moment of inertia\Ncause in Newton's second law
Dialogue: 0,0:01:04.35,0:01:06.81,Default,,0000,0000,0000,,for rotation I know that\Ninstead of mass there's
Dialogue: 0,0:01:06.81,0:01:09.09,Default,,0000,0000,0000,,moment of inertia so maybe I replace that.
Dialogue: 0,0:01:09.09,0:01:12.19,Default,,0000,0000,0000,,And instead of speed\Nsquared, maybe since I have
Dialogue: 0,0:01:12.19,0:01:15.28,Default,,0000,0000,0000,,something rotating I'd\Nhave angular speed squared.
Dialogue: 0,0:01:15.28,0:01:16.90,Default,,0000,0000,0000,,It turns out this works.
Dialogue: 0,0:01:16.90,0:01:20.01,Default,,0000,0000,0000,,You can often derive, it's\Nnot really a derivation,
Dialogue: 0,0:01:20.01,0:01:22.52,Default,,0000,0000,0000,,you're just kind of guessing\Neducatedly but you could
Dialogue: 0,0:01:22.52,0:01:25.80,Default,,0000,0000,0000,,often get a formula for the\Nrotational analog of some
Dialogue: 0,0:01:25.80,0:01:29.78,Default,,0000,0000,0000,,linear formula by just\Nsubstituting the rotational analog
Dialogue: 0,0:01:29.78,0:01:32.42,Default,,0000,0000,0000,,for each of the variables,\Nso if I replaced mass with
Dialogue: 0,0:01:32.42,0:01:35.25,Default,,0000,0000,0000,,rotational mass, I get\Nthe moment of inertia.
Dialogue: 0,0:01:35.25,0:01:37.72,Default,,0000,0000,0000,,If I replace speed with rotational speed,
Dialogue: 0,0:01:37.72,0:01:40.74,Default,,0000,0000,0000,,I get the angular speed and\Nthis is the correct formula.
Dialogue: 0,0:01:40.74,0:01:43.30,Default,,0000,0000,0000,,So in this video we needed\Nto ride this cause that
Dialogue: 0,0:01:43.30,0:01:44.91,Default,,0000,0000,0000,,is not really a derivation,\Nwe didn't really
Dialogue: 0,0:01:44.91,0:01:47.72,Default,,0000,0000,0000,,prove this, we just showed\Nthat it's plausible.
Dialogue: 0,0:01:47.72,0:01:50.11,Default,,0000,0000,0000,,How do we prove that\Nthis is the rotational
Dialogue: 0,0:01:50.11,0:01:52.99,Default,,0000,0000,0000,,kinetic energy of an\Nobject that's rotating
Dialogue: 0,0:01:52.99,0:01:54.35,Default,,0000,0000,0000,,like a baseball.
Dialogue: 0,0:01:54.35,0:01:56.100,Default,,0000,0000,0000,,The first thing to recognize\Nis that this rotational
Dialogue: 0,0:01:56.100,0:01:59.68,Default,,0000,0000,0000,,kinetic energy isn't really a new kind of
Dialogue: 0,0:01:59.68,0:02:02.30,Default,,0000,0000,0000,,kinetic energy, it's\Nstill just the same old
Dialogue: 0,0:02:02.30,0:02:05.72,Default,,0000,0000,0000,,regular kinetic energy for\Nsomething that's rotating.
Dialogue: 0,0:02:05.72,0:02:07.05,Default,,0000,0000,0000,,What I mean by that is this.
Dialogue: 0,0:02:07.05,0:02:09.82,Default,,0000,0000,0000,,Imagine this baseball\Nis rotating in a circle.
Dialogue: 0,0:02:09.82,0:02:13.32,Default,,0000,0000,0000,,Every point on the baseball\Nis moving with some speed,
Dialogue: 0,0:02:13.32,0:02:15.46,Default,,0000,0000,0000,,so what I mean by that is\Nthis, so this point at the top
Dialogue: 0,0:02:15.46,0:02:18.61,Default,,0000,0000,0000,,here imagine the little\Npiece of leather right here,
Dialogue: 0,0:02:18.61,0:02:20.37,Default,,0000,0000,0000,,it's gonna have some speed forward.
Dialogue: 0,0:02:20.37,0:02:23.48,Default,,0000,0000,0000,,I'm gonna call this mass\NM one, that little piece
Dialogue: 0,0:02:23.48,0:02:27.19,Default,,0000,0000,0000,,of mass right now and I'll\Ncall the speed of it V one.
Dialogue: 0,0:02:27.19,0:02:29.74,Default,,0000,0000,0000,,Similarly, this point on\Nthe leather right there,
Dialogue: 0,0:02:29.74,0:02:32.29,Default,,0000,0000,0000,,I'm gonna call that M two,\Nit's gonna be moving down
Dialogue: 0,0:02:32.29,0:02:35.71,Default,,0000,0000,0000,,cause it's a rotating circle,\Nso I'll call that V two
Dialogue: 0,0:02:35.71,0:02:38.37,Default,,0000,0000,0000,,and points closer to the\Naxis are gonna be moving
Dialogue: 0,0:02:38.37,0:02:41.03,Default,,0000,0000,0000,,with smaller speed so\Nthis point right here,
Dialogue: 0,0:02:41.03,0:02:43.78,Default,,0000,0000,0000,,we'll call it M three, moving\Ndown with a speed V three,
Dialogue: 0,0:02:43.78,0:02:46.77,Default,,0000,0000,0000,,that is not as big as V two or V one.
Dialogue: 0,0:02:46.77,0:02:48.08,Default,,0000,0000,0000,,You can't see that very well,
Dialogue: 0,0:02:48.08,0:02:51.59,Default,,0000,0000,0000,,I'll use a darker green\Nso this M three right here
Dialogue: 0,0:02:51.59,0:02:54.92,Default,,0000,0000,0000,,closer to the axis, axis\Nbeing right at this point
Dialogue: 0,0:02:54.92,0:02:58.78,Default,,0000,0000,0000,,in the center, closer to the\Naxis so it's speed is smaller
Dialogue: 0,0:02:58.78,0:03:01.41,Default,,0000,0000,0000,,than points that are\Nfarther away from this axis,
Dialogue: 0,0:03:01.41,0:03:03.37,Default,,0000,0000,0000,,so you can see this is kinda complicated.
Dialogue: 0,0:03:03.37,0:03:05.54,Default,,0000,0000,0000,,All points on this baseball\Nare gonna be moving with
Dialogue: 0,0:03:05.54,0:03:08.13,Default,,0000,0000,0000,,different speeds so points\Nover here that are really
Dialogue: 0,0:03:08.13,0:03:10.80,Default,,0000,0000,0000,,close to the axis, barely moving at all.
Dialogue: 0,0:03:10.80,0:03:12.95,Default,,0000,0000,0000,,I'll call this M four and it would be
Dialogue: 0,0:03:12.95,0:03:15.09,Default,,0000,0000,0000,,moving at speed V four.
Dialogue: 0,0:03:15.09,0:03:17.68,Default,,0000,0000,0000,,What we mean by the\Nrotational kinetic energy is
Dialogue: 0,0:03:17.68,0:03:19.89,Default,,0000,0000,0000,,really just all the regular\Nkinetic energy these
Dialogue: 0,0:03:19.89,0:03:23.85,Default,,0000,0000,0000,,masses have about the center\Nof mass of the baseball.
Dialogue: 0,0:03:23.85,0:03:26.68,Default,,0000,0000,0000,,So in other words, what\Nwe mean by K rotational,
Dialogue: 0,0:03:26.68,0:03:29.46,Default,,0000,0000,0000,,is you just add up all of these energies.
Dialogue: 0,0:03:29.46,0:03:32.02,Default,,0000,0000,0000,,You have one half, this\Nlittle piece of leather
Dialogue: 0,0:03:32.02,0:03:33.74,Default,,0000,0000,0000,,up here would have some kinetic energy
Dialogue: 0,0:03:33.74,0:03:37.49,Default,,0000,0000,0000,,so you do one half M\None, V one squared plus.
Dialogue: 0,0:03:38.42,0:03:41.05,Default,,0000,0000,0000,,And this M two has some kinetic energy,
Dialogue: 0,0:03:41.05,0:03:43.15,Default,,0000,0000,0000,,don't worry that it points downward,
Dialogue: 0,0:03:43.15,0:03:45.95,Default,,0000,0000,0000,,downward doesn't matter for\Nthings that aren't vectors,
Dialogue: 0,0:03:45.95,0:03:49.26,Default,,0000,0000,0000,,this V gets squared so\Nkinetic energy's not a vector
Dialogue: 0,0:03:49.26,0:03:51.78,Default,,0000,0000,0000,,so it doesn't matter that\None velocity points down
Dialogue: 0,0:03:51.78,0:03:54.44,Default,,0000,0000,0000,,cause this is just the\Nspeed and similarly,
Dialogue: 0,0:03:54.44,0:03:58.95,Default,,0000,0000,0000,,you'd add up one half M\Nthree, V three squared,
Dialogue: 0,0:03:58.95,0:04:00.52,Default,,0000,0000,0000,,but you might be like this is impossible,
Dialogue: 0,0:04:00.52,0:04:02.93,Default,,0000,0000,0000,,there's infinitely many\Npoints in this baseball,
Dialogue: 0,0:04:02.93,0:04:05.39,Default,,0000,0000,0000,,how am I ever going to do this.
Dialogue: 0,0:04:05.39,0:04:07.38,Default,,0000,0000,0000,,Well something magical is about to happen,
Dialogue: 0,0:04:07.38,0:04:09.53,Default,,0000,0000,0000,,this is one of my favorite\Nlittle derivations,
Dialogue: 0,0:04:09.53,0:04:12.13,Default,,0000,0000,0000,,short and sweet, watch what happens.
Dialogue: 0,0:04:12.13,0:04:15.07,Default,,0000,0000,0000,,K E rotational is really just the sum,
Dialogue: 0,0:04:15.07,0:04:17.66,Default,,0000,0000,0000,,if I add all these up\NI can write is as a sum
Dialogue: 0,0:04:17.66,0:04:21.49,Default,,0000,0000,0000,,of all the one half M V\Nsquares of every point
Dialogue: 0,0:04:22.46,0:04:25.42,Default,,0000,0000,0000,,on this baseball so imagine\Nbreaking this baseball
Dialogue: 0,0:04:25.42,0:04:27.76,Default,,0000,0000,0000,,up into very, very small pieces.
Dialogue: 0,0:04:27.76,0:04:30.07,Default,,0000,0000,0000,,Don't do it physically but\Njust think about it mentally,
Dialogue: 0,0:04:30.07,0:04:33.04,Default,,0000,0000,0000,,just visualize considering\Nvery small pieces,
Dialogue: 0,0:04:33.04,0:04:35.92,Default,,0000,0000,0000,,particles of this baseball\Nand how fast they're going.
Dialogue: 0,0:04:35.92,0:04:38.94,Default,,0000,0000,0000,,What I'm saying is that\Nif you add all of that up,
Dialogue: 0,0:04:38.94,0:04:41.36,Default,,0000,0000,0000,,you get the total\Nrotational kinetic energy,
Dialogue: 0,0:04:41.36,0:04:42.97,Default,,0000,0000,0000,,this looks impossible to do.
Dialogue: 0,0:04:42.97,0:04:44.55,Default,,0000,0000,0000,,But something magical is about to happen,
Dialogue: 0,0:04:44.55,0:04:45.77,Default,,0000,0000,0000,,here's what we can do.
Dialogue: 0,0:04:45.77,0:04:48.35,Default,,0000,0000,0000,,We can rewrite, see the problem here is V.
Dialogue: 0,0:04:48.35,0:04:50.76,Default,,0000,0000,0000,,All these points have a different speed V,
Dialogue: 0,0:04:50.76,0:04:52.71,Default,,0000,0000,0000,,but we can use a trick,\Na trick that we love
Dialogue: 0,0:04:52.71,0:04:55.12,Default,,0000,0000,0000,,to use in physics, instead\Nof writing this as V,
Dialogue: 0,0:04:55.12,0:04:57.77,Default,,0000,0000,0000,,we're gonna write V as, so\Nremember that for things
Dialogue: 0,0:04:57.77,0:05:01.56,Default,,0000,0000,0000,,that are rotating, V\Nis just R times omega.
Dialogue: 0,0:05:01.56,0:05:04.13,Default,,0000,0000,0000,,The radius, how far from the axis you are,
Dialogue: 0,0:05:04.13,0:05:06.88,Default,,0000,0000,0000,,times the angular velocity,\Nor the angular speed
Dialogue: 0,0:05:06.88,0:05:09.36,Default,,0000,0000,0000,,gives you the regular speed.
Dialogue: 0,0:05:09.36,0:05:12.14,Default,,0000,0000,0000,,This formula is really\Nhandy, so we're gonna replace
Dialogue: 0,0:05:12.14,0:05:16.18,Default,,0000,0000,0000,,V with R omega, and this\Nis gonna give us R omega
Dialogue: 0,0:05:16.18,0:05:18.35,Default,,0000,0000,0000,,and you still have to\Nsquare it and at this point
Dialogue: 0,0:05:18.35,0:05:19.99,Default,,0000,0000,0000,,you're probably thinking\Nlike this is even worse,
Dialogue: 0,0:05:19.99,0:05:21.08,Default,,0000,0000,0000,,what do we do this for.
Dialogue: 0,0:05:21.08,0:05:24.02,Default,,0000,0000,0000,,Well watch, if we add this\Nis up I'll have one half M.
Dialogue: 0,0:05:24.02,0:05:26.85,Default,,0000,0000,0000,,I'm gonna get an R squared\Nand an omega squared,
Dialogue: 0,0:05:26.85,0:05:28.96,Default,,0000,0000,0000,,and the reason this is\Nbetter is that even though
Dialogue: 0,0:05:28.96,0:05:32.63,Default,,0000,0000,0000,,every point on this baseball\Nhas a different speed V,
Dialogue: 0,0:05:32.63,0:05:35.49,Default,,0000,0000,0000,,they all have the same\Nangular speed omega,
Dialogue: 0,0:05:35.49,0:05:38.32,Default,,0000,0000,0000,,that was what was good about\Nthese angular quantities
Dialogue: 0,0:05:38.32,0:05:41.62,Default,,0000,0000,0000,,is that they're the same for\Nevery point on the baseball
Dialogue: 0,0:05:41.62,0:05:43.87,Default,,0000,0000,0000,,no matter how far away\Nyou are from the axis,
Dialogue: 0,0:05:43.87,0:05:46.04,Default,,0000,0000,0000,,and since they're the\Nsame for every point I can
Dialogue: 0,0:05:46.04,0:05:48.63,Default,,0000,0000,0000,,bring that out of the\Nsummation so I can rewrite
Dialogue: 0,0:05:48.63,0:05:51.61,Default,,0000,0000,0000,,this summation and bring\Neverything that's constant
Dialogue: 0,0:05:51.61,0:05:54.82,Default,,0000,0000,0000,,for all of the masses out\Nof the summation so I can
Dialogue: 0,0:05:54.82,0:05:58.22,Default,,0000,0000,0000,,write this as one half times the summation
Dialogue: 0,0:05:58.22,0:06:01.80,Default,,0000,0000,0000,,of M times R squared\Nand end that quantity,
Dialogue: 0,0:06:02.78,0:06:06.60,Default,,0000,0000,0000,,end that summation and just\Npull the omega squared out
Dialogue: 0,0:06:06.60,0:06:08.56,Default,,0000,0000,0000,,because it's the same for each term.
Dialogue: 0,0:06:08.56,0:06:11.44,Default,,0000,0000,0000,,I'm basically factoring\Nthis out of all of these
Dialogue: 0,0:06:11.44,0:06:13.86,Default,,0000,0000,0000,,terms in the summation, it's like up here,
Dialogue: 0,0:06:13.86,0:06:15.55,Default,,0000,0000,0000,,all of these have a one half.
Dialogue: 0,0:06:15.55,0:06:17.49,Default,,0000,0000,0000,,You could imagine factoring out a one half
Dialogue: 0,0:06:17.49,0:06:18.98,Default,,0000,0000,0000,,and just writing this whole quantity as
Dialogue: 0,0:06:18.98,0:06:22.14,Default,,0000,0000,0000,,one half times M one V one squared plus
Dialogue: 0,0:06:22.14,0:06:24.17,Default,,0000,0000,0000,,M two V two squared and so on.
Dialogue: 0,0:06:24.17,0:06:26.06,Default,,0000,0000,0000,,That's what I'm doing\Ndown here for the one half
Dialogue: 0,0:06:26.06,0:06:28.62,Default,,0000,0000,0000,,and for the omega squared,\Nso that's what was good
Dialogue: 0,0:06:28.62,0:06:31.08,Default,,0000,0000,0000,,about replacing V with R omega.
Dialogue: 0,0:06:31.08,0:06:32.54,Default,,0000,0000,0000,,The omega's the same for all of them,
Dialogue: 0,0:06:32.54,0:06:33.82,Default,,0000,0000,0000,,you can bring that out.
Dialogue: 0,0:06:33.82,0:06:35.51,Default,,0000,0000,0000,,You might still be\Nconcerned, you might be like,
Dialogue: 0,0:06:35.51,0:06:37.99,Default,,0000,0000,0000,,we're still stuck with\Nthe M in here cause you've
Dialogue: 0,0:06:37.99,0:06:39.99,Default,,0000,0000,0000,,got different Ms at different points.
Dialogue: 0,0:06:39.99,0:06:42.16,Default,,0000,0000,0000,,We're stuck with all\Nthese R squareds in here,
Dialogue: 0,0:06:42.16,0:06:44.63,Default,,0000,0000,0000,,all these points at the\Nbaseball are different Rs,
Dialogue: 0,0:06:44.63,0:06:46.33,Default,,0000,0000,0000,,they're all different\Npoints from the axis,
Dialogue: 0,0:06:46.33,0:06:48.56,Default,,0000,0000,0000,,different distances from\Nthe axis, we can't bring
Dialogue: 0,0:06:48.56,0:06:51.45,Default,,0000,0000,0000,,those out so now what do we\Ndo, well if you're clever
Dialogue: 0,0:06:51.45,0:06:53.79,Default,,0000,0000,0000,,you recognize this term.
Dialogue: 0,0:06:53.79,0:06:56.62,Default,,0000,0000,0000,,This summation term is\Nnothing but the total moment
Dialogue: 0,0:06:56.62,0:06:59.30,Default,,0000,0000,0000,,of inertia of the object.
Dialogue: 0,0:06:59.30,0:07:01.63,Default,,0000,0000,0000,,Remember that the moment\Nof inertia of an object,
Dialogue: 0,0:07:01.63,0:07:04.39,Default,,0000,0000,0000,,we learned previously,\Nis just M R squared,
Dialogue: 0,0:07:04.39,0:07:06.41,Default,,0000,0000,0000,,so the moment of inertia of a point mass
Dialogue: 0,0:07:06.41,0:07:09.12,Default,,0000,0000,0000,,is M R squared and the moment of inertia
Dialogue: 0,0:07:09.12,0:07:12.48,Default,,0000,0000,0000,,of a bunch of point\Nmasses is the sum of all
Dialogue: 0,0:07:12.48,0:07:15.40,Default,,0000,0000,0000,,the M R squareds and that's\Nwhat we've got right here,
Dialogue: 0,0:07:15.40,0:07:19.51,Default,,0000,0000,0000,,this is just the moment of\Ninertia of this baseball
Dialogue: 0,0:07:19.51,0:07:22.12,Default,,0000,0000,0000,,or whatever the object is,\Nit doesn't even have to be
Dialogue: 0,0:07:22.12,0:07:24.29,Default,,0000,0000,0000,,of a particular shape, we're gonna add all
Dialogue: 0,0:07:24.29,0:07:26.100,Default,,0000,0000,0000,,the M R squareds, that's\Nalways going to be
Dialogue: 0,0:07:26.100,0:07:28.64,Default,,0000,0000,0000,,the total moment of inertia.
Dialogue: 0,0:07:28.64,0:07:30.92,Default,,0000,0000,0000,,So what we've found is\Nthat the K rotational
Dialogue: 0,0:07:30.92,0:07:34.07,Default,,0000,0000,0000,,is equal to one half times this quantity,
Dialogue: 0,0:07:34.07,0:07:35.95,Default,,0000,0000,0000,,which is I, the moment of inertia,
Dialogue: 0,0:07:35.95,0:07:38.28,Default,,0000,0000,0000,,times omega squared and that's the formula
Dialogue: 0,0:07:38.28,0:07:40.00,Default,,0000,0000,0000,,we got up here just by guessing.
Dialogue: 0,0:07:40.00,0:07:41.85,Default,,0000,0000,0000,,But it actually works\Nand this is why it works,
Dialogue: 0,0:07:41.85,0:07:43.86,Default,,0000,0000,0000,,because you always get\Nthis quantity down here,
Dialogue: 0,0:07:43.86,0:07:46.20,Default,,0000,0000,0000,,which is one half I omega\Nsquared, no matter what
Dialogue: 0,0:07:46.20,0:07:47.68,Default,,0000,0000,0000,,the shape of the object is.
Dialogue: 0,0:07:47.68,0:07:49.42,Default,,0000,0000,0000,,So what this is telling\Nyou, what this quantity
Dialogue: 0,0:07:49.42,0:07:52.35,Default,,0000,0000,0000,,gives us is the total\Nrotational kinetic energy
Dialogue: 0,0:07:52.35,0:07:55.67,Default,,0000,0000,0000,,of all the points on that\Nmass about the center
Dialogue: 0,0:07:55.67,0:07:58.59,Default,,0000,0000,0000,,of the mass but here's\Nwhat it doesn't give you.
Dialogue: 0,0:07:58.59,0:08:01.04,Default,,0000,0000,0000,,This term right here does not include
Dialogue: 0,0:08:01.04,0:08:03.45,Default,,0000,0000,0000,,the translational kinetic\Nenergy so the fact that
Dialogue: 0,0:08:03.45,0:08:06.29,Default,,0000,0000,0000,,this baseball was flying\Nthrough the air does not
Dialogue: 0,0:08:06.29,0:08:08.14,Default,,0000,0000,0000,,get incorporated by this formula.
Dialogue: 0,0:08:08.14,0:08:10.26,Default,,0000,0000,0000,,We didn't take into account the fact that
Dialogue: 0,0:08:10.26,0:08:12.39,Default,,0000,0000,0000,,the baseball was moving through the air,
Dialogue: 0,0:08:12.39,0:08:13.98,Default,,0000,0000,0000,,in other words, we\Ndidn't take into account
Dialogue: 0,0:08:13.98,0:08:16.79,Default,,0000,0000,0000,,that the actual center\Nof mass in this baseball
Dialogue: 0,0:08:16.79,0:08:19.20,Default,,0000,0000,0000,,was translating through the air.
Dialogue: 0,0:08:19.20,0:08:21.36,Default,,0000,0000,0000,,But we can do that easily\Nwith this formula here.
Dialogue: 0,0:08:21.36,0:08:24.28,Default,,0000,0000,0000,,This is the translational kinetic energy.
Dialogue: 0,0:08:24.28,0:08:26.93,Default,,0000,0000,0000,,Sometimes instead of writing\Nregular kinetic energy,
Dialogue: 0,0:08:26.93,0:08:29.84,Default,,0000,0000,0000,,now that we've got two we\Nshould specify this is really
Dialogue: 0,0:08:29.84,0:08:31.79,Default,,0000,0000,0000,,translational kinetic energy.
Dialogue: 0,0:08:31.79,0:08:34.36,Default,,0000,0000,0000,,We've got a formula for\Ntranslational kinetic energy,
Dialogue: 0,0:08:34.36,0:08:37.70,Default,,0000,0000,0000,,the energy something has due\Nto the fact that the center
Dialogue: 0,0:08:37.70,0:08:40.52,Default,,0000,0000,0000,,of mass of that object is\Nmoving and we have a formula
Dialogue: 0,0:08:40.52,0:08:42.97,Default,,0000,0000,0000,,that takes into account the\Nfact that something can have
Dialogue: 0,0:08:42.97,0:08:45.49,Default,,0000,0000,0000,,kinetic energy due to its rotation.
Dialogue: 0,0:08:45.49,0:08:48.32,Default,,0000,0000,0000,,That's this K rotational,\Nso if an object's rotating,
Dialogue: 0,0:08:48.32,0:08:50.48,Default,,0000,0000,0000,,it has rotational kinetic energy.
Dialogue: 0,0:08:50.48,0:08:52.72,Default,,0000,0000,0000,,If an object is translating it has
Dialogue: 0,0:08:52.72,0:08:54.50,Default,,0000,0000,0000,,translational kinetic energy,
Dialogue: 0,0:08:54.50,0:08:56.52,Default,,0000,0000,0000,,i.e. if the center of mass is moving,
Dialogue: 0,0:08:56.52,0:08:59.99,Default,,0000,0000,0000,,and if the object is\Ntranslating and it's rotating
Dialogue: 0,0:08:59.99,0:09:02.44,Default,,0000,0000,0000,,then it would have those both\Nof these kinetic energies,
Dialogue: 0,0:09:02.44,0:09:04.95,Default,,0000,0000,0000,,both at the same time and\Nthis is the beautiful thing.
Dialogue: 0,0:09:04.95,0:09:08.43,Default,,0000,0000,0000,,If an object is translating\Nand rotating and you want
Dialogue: 0,0:09:08.43,0:09:11.39,Default,,0000,0000,0000,,to find the total kinetic\Nenergy of the entire thing,
Dialogue: 0,0:09:11.39,0:09:14.00,Default,,0000,0000,0000,,you can just add these two terms up.
Dialogue: 0,0:09:14.00,0:09:17.15,Default,,0000,0000,0000,,If I just take the translational\None half M V squared,
Dialogue: 0,0:09:17.15,0:09:20.57,Default,,0000,0000,0000,,and this would then be the\Nvelocity of the center of mass.
Dialogue: 0,0:09:20.57,0:09:22.16,Default,,0000,0000,0000,,So you have to be careful.
Dialogue: 0,0:09:22.16,0:09:23.75,Default,,0000,0000,0000,,Let me make some room\Nhere, so let me get rid
Dialogue: 0,0:09:23.75,0:09:25.13,Default,,0000,0000,0000,,of all this stuff here.
Dialogue: 0,0:09:25.13,0:09:28.74,Default,,0000,0000,0000,,If you take one half M,\Ntimes the speed of the center
Dialogue: 0,0:09:28.74,0:09:31.66,Default,,0000,0000,0000,,of mass squared, you'll\Nget the total translational
Dialogue: 0,0:09:31.66,0:09:33.24,Default,,0000,0000,0000,,kinetic energy of the baseball.
Dialogue: 0,0:09:33.24,0:09:36.39,Default,,0000,0000,0000,,And if we add to that the\None half I omega squared,
Dialogue: 0,0:09:36.39,0:09:39.18,Default,,0000,0000,0000,,so the omega about the\Ncenter of mass you'll get
Dialogue: 0,0:09:39.18,0:09:43.69,Default,,0000,0000,0000,,the total kinetic energy, both\Ntranslational and rotational,
Dialogue: 0,0:09:43.69,0:09:46.62,Default,,0000,0000,0000,,so this is great, we can\Ndetermine the total kinetic energy
Dialogue: 0,0:09:46.62,0:09:49.89,Default,,0000,0000,0000,,altogether, rotational\Nmotion, translational motion,
Dialogue: 0,0:09:49.89,0:09:52.58,Default,,0000,0000,0000,,from just taking these two terms added up.
Dialogue: 0,0:09:52.58,0:09:54.05,Default,,0000,0000,0000,,So what would an example of this be,
Dialogue: 0,0:09:54.05,0:09:55.80,Default,,0000,0000,0000,,let's just get rid of all this.
Dialogue: 0,0:09:55.80,0:09:59.18,Default,,0000,0000,0000,,Let's say this baseball,\Nsomeone pitched this thing,
Dialogue: 0,0:09:59.18,0:10:02.58,Default,,0000,0000,0000,,and the radar gun shows that\Nthis baseball was hurled
Dialogue: 0,0:10:02.58,0:10:04.80,Default,,0000,0000,0000,,through the air at 40 meters per second.
Dialogue: 0,0:10:04.80,0:10:07.45,Default,,0000,0000,0000,,So it's heading toward home\Nplate at 40 meters per second.
Dialogue: 0,0:10:07.45,0:10:09.86,Default,,0000,0000,0000,,The center of mass of\Nthis baseball is going
Dialogue: 0,0:10:09.86,0:10:12.55,Default,,0000,0000,0000,,40 meters per second toward home plate.
Dialogue: 0,0:10:12.55,0:10:15.09,Default,,0000,0000,0000,,Let's say it's also, someone\Nreally threw the fastball.
Dialogue: 0,0:10:15.09,0:10:18.11,Default,,0000,0000,0000,,This thing's rotating\Nwith an angular velocity
Dialogue: 0,0:10:18.11,0:10:20.19,Default,,0000,0000,0000,,of 50 radians per second.
Dialogue: 0,0:10:22.26,0:10:24.38,Default,,0000,0000,0000,,We know the mass of a\Nbaseball, I've looked it up.
Dialogue: 0,0:10:24.38,0:10:28.78,Default,,0000,0000,0000,,The mass of a baseball\Nis about 0.145 kilograms
Dialogue: 0,0:10:28.78,0:10:31.80,Default,,0000,0000,0000,,and the radius of the baseball,\Nso a radius of a baseball
Dialogue: 0,0:10:31.80,0:10:35.39,Default,,0000,0000,0000,,is around seven centimeters,\Nso in terms of meters that
Dialogue: 0,0:10:35.39,0:10:38.86,Default,,0000,0000,0000,,would be 0.07 meters, so\Nwe can figure out what's
Dialogue: 0,0:10:38.86,0:10:41.24,Default,,0000,0000,0000,,the total kinetic energy,\Nwell there's gonna be
Dialogue: 0,0:10:41.24,0:10:43.20,Default,,0000,0000,0000,,a rotational kinetic\Nenergy and there's gonna be
Dialogue: 0,0:10:43.20,0:10:45.05,Default,,0000,0000,0000,,a translational kinetic energy.
Dialogue: 0,0:10:45.05,0:10:47.88,Default,,0000,0000,0000,,The translational kinetic\Nenergy, gonna be one half
Dialogue: 0,0:10:47.88,0:10:50.84,Default,,0000,0000,0000,,the mass of the baseball\Ntimes the center of mass speed
Dialogue: 0,0:10:50.84,0:10:53.99,Default,,0000,0000,0000,,of the baseball squared which\Nis gonna give us one half.
Dialogue: 0,0:10:53.99,0:10:57.63,Default,,0000,0000,0000,,The mass of the baseball was\N0.145 and the center of mass
Dialogue: 0,0:10:57.63,0:11:00.65,Default,,0000,0000,0000,,speed of the baseball is 40,\Nthat's how fast the center
Dialogue: 0,0:11:00.65,0:11:02.71,Default,,0000,0000,0000,,of mass of this baseball is traveling.
Dialogue: 0,0:11:02.71,0:11:06.71,Default,,0000,0000,0000,,If we add all that up we\Nget 116 Jules of regular
Dialogue: 0,0:11:06.71,0:11:08.89,Default,,0000,0000,0000,,translational kinetic energy.
Dialogue: 0,0:11:08.89,0:11:11.25,Default,,0000,0000,0000,,How much rotational\Nkinetic energy is there,
Dialogue: 0,0:11:11.25,0:11:13.28,Default,,0000,0000,0000,,so we're gonna have\Nrotational kinetic energy
Dialogue: 0,0:11:13.28,0:11:16.09,Default,,0000,0000,0000,,due to the fact that the\Nbaseball is also rotating.
Dialogue: 0,0:11:16.09,0:11:19.59,Default,,0000,0000,0000,,How much, well we're gonna\Nuse one half I omega squared.
Dialogue: 0,0:11:19.59,0:11:22.48,Default,,0000,0000,0000,,I'm gonna have one half, what's\Nthe I, well the baseball is
Dialogue: 0,0:11:22.48,0:11:26.33,Default,,0000,0000,0000,,a sphere, if you look up the\Nmoment of inertia of a sphere
Dialogue: 0,0:11:26.33,0:11:29.66,Default,,0000,0000,0000,,cause I don't wanna have\Nto do summation of all
Dialogue: 0,0:11:29.66,0:11:32.100,Default,,0000,0000,0000,,the M R squareds, if you\Ndo that using calculus,
Dialogue: 0,0:11:32.100,0:11:34.87,Default,,0000,0000,0000,,you get this formula.
Dialogue: 0,0:11:34.87,0:11:36.100,Default,,0000,0000,0000,,That means in an algebra\Nbased physics class
Dialogue: 0,0:11:36.100,0:11:38.90,Default,,0000,0000,0000,,you just have to look this\Nup, it's either in your book
Dialogue: 0,0:11:38.90,0:11:41.64,Default,,0000,0000,0000,,in a chart or a table or you\Ncould always look it up online.
Dialogue: 0,0:11:41.64,0:11:45.76,Default,,0000,0000,0000,,For a sphere the moment of\Ninertia is two fifths M R squared
Dialogue: 0,0:11:45.76,0:11:48.62,Default,,0000,0000,0000,,in other words two fifths\Nthe mass of a baseball
Dialogue: 0,0:11:48.62,0:11:50.46,Default,,0000,0000,0000,,times the raise of the baseball squared.
Dialogue: 0,0:11:50.46,0:11:53.63,Default,,0000,0000,0000,,That's just I, that's the\Nmoment of inertia of a sphere.
Dialogue: 0,0:11:53.63,0:11:56.24,Default,,0000,0000,0000,,So we're assuming this\Nbaseball is a perfect sphere.
Dialogue: 0,0:11:56.24,0:11:59.36,Default,,0000,0000,0000,,It's got uniform density,\Nthat's not completely true.
Dialogue: 0,0:11:59.36,0:12:00.95,Default,,0000,0000,0000,,But it's a pretty good approximation.
Dialogue: 0,0:12:00.95,0:12:03.02,Default,,0000,0000,0000,,Then we multiply by this omega squared,
Dialogue: 0,0:12:03.02,0:12:04.75,Default,,0000,0000,0000,,the angular speed squared.
Dialogue: 0,0:12:04.75,0:12:07.14,Default,,0000,0000,0000,,So what do we get, we're\Ngonna get one half times
Dialogue: 0,0:12:07.14,0:12:11.22,Default,,0000,0000,0000,,two fifths, the mass of\Na baseball was 0.145.
Dialogue: 0,0:12:11.22,0:12:13.28,Default,,0000,0000,0000,,The radius of the baseball\Nwas about, what did we say,
Dialogue: 0,0:12:13.28,0:12:18.03,Default,,0000,0000,0000,,.07 meters so that's .07\Nmeters squared and then finally
Dialogue: 0,0:12:18.03,0:12:20.49,Default,,0000,0000,0000,,we multiply by omega squared\Nand this would make it
Dialogue: 0,0:12:20.49,0:12:23.24,Default,,0000,0000,0000,,50 radians per second and we square
Dialogue: 0,0:12:23.24,0:12:25.82,Default,,0000,0000,0000,,it which adds up to 0.355 Jules
Dialogue: 0,0:12:28.70,0:12:31.42,Default,,0000,0000,0000,,so hardly any of the\Nenergy of this baseball
Dialogue: 0,0:12:31.42,0:12:33.03,Default,,0000,0000,0000,,is in its rotation.
Dialogue: 0,0:12:33.03,0:12:36.45,Default,,0000,0000,0000,,Almost all of the energy is\Nin the form of translational
Dialogue: 0,0:12:36.45,0:12:38.52,Default,,0000,0000,0000,,energy, that kinda makes sense.
Dialogue: 0,0:12:38.52,0:12:40.90,Default,,0000,0000,0000,,It's the fact that this\Nbaseball is hurling toward
Dialogue: 0,0:12:40.90,0:12:43.90,Default,,0000,0000,0000,,home plate that's gonna\Nmake it hurt if it hits you
Dialogue: 0,0:12:43.90,0:12:46.05,Default,,0000,0000,0000,,as opposed to the fact\Nthat it was spinning when
Dialogue: 0,0:12:46.05,0:12:48.54,Default,,0000,0000,0000,,it hits you, that doesn't\Nactually cause as much damage
Dialogue: 0,0:12:48.54,0:12:50.70,Default,,0000,0000,0000,,as the fact that this\Nbaseball's kinetic energy
Dialogue: 0,0:12:50.70,0:12:54.47,Default,,0000,0000,0000,,is mostly in the form of\Ntranslational kinetic energy.
Dialogue: 0,0:12:54.47,0:12:57.15,Default,,0000,0000,0000,,But if you wanted the total\Nkinetic energy of the baseball,
Dialogue: 0,0:12:57.15,0:12:59.14,Default,,0000,0000,0000,,you would add both of these terms up.
Dialogue: 0,0:12:59.14,0:13:02.64,Default,,0000,0000,0000,,K total would be the\Ntranslational kinetic energy
Dialogue: 0,0:13:02.64,0:13:04.94,Default,,0000,0000,0000,,plus the rotational kinetic energy.
Dialogue: 0,0:13:04.94,0:13:09.10,Default,,0000,0000,0000,,That means the total kinetic\Nenergy which is the 116 Jules
Dialogue: 0,0:13:10.05,0:13:12.55,Default,,0000,0000,0000,,plus 0.355 Jules which give us
Dialogue: 0,0:13:14.42,0:13:15.59,Default,,0000,0000,0000,,116.355 Jules.
Dialogue: 0,0:13:18.34,0:13:20.59,Default,,0000,0000,0000,,So recapping if an object is both rotating
Dialogue: 0,0:13:20.59,0:13:23.16,Default,,0000,0000,0000,,and translating you can\Nfind the translational
Dialogue: 0,0:13:23.16,0:13:26.79,Default,,0000,0000,0000,,kinetic energy using one\Nhalf M the speed of the
Dialogue: 0,0:13:26.79,0:13:29.56,Default,,0000,0000,0000,,center of mass of that\Nobject squared and you can
Dialogue: 0,0:13:29.56,0:13:32.07,Default,,0000,0000,0000,,find the rotational\Nkinetic energy by using
Dialogue: 0,0:13:32.07,0:13:34.55,Default,,0000,0000,0000,,one half I, the moment of inertia.
Dialogue: 0,0:13:34.55,0:13:36.16,Default,,0000,0000,0000,,We'll infer whatever shape it is,
Dialogue: 0,0:13:36.16,0:13:38.64,Default,,0000,0000,0000,,if it's a point mass\Ngoing in a huge circle
Dialogue: 0,0:13:38.64,0:13:41.04,Default,,0000,0000,0000,,you could use M R\Nsquared, if it's a sphere
Dialogue: 0,0:13:41.04,0:13:43.64,Default,,0000,0000,0000,,rotating about its center\Nyou could use two fifths
Dialogue: 0,0:13:43.64,0:13:46.21,Default,,0000,0000,0000,,M R squared, cylinders\Nare one half M R squared,
Dialogue: 0,0:13:46.21,0:13:49.01,Default,,0000,0000,0000,,you can look these up\Nin tables to figure out
Dialogue: 0,0:13:49.01,0:13:52.03,Default,,0000,0000,0000,,whatever the I is that\Nyou need times the angular
Dialogue: 0,0:13:52.03,0:13:56.32,Default,,0000,0000,0000,,speed squared of the object\Nabout that center of mass.
Dialogue: 0,0:13:56.32,0:13:58.42,Default,,0000,0000,0000,,And if you add these\Ntwo terms up you get the
Dialogue: 0,0:13:58.42,0:14:01.42,Default,,0000,0000,0000,,total kinetic energy of that object.