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  • Good morning.

    早晨好

  • It's February already.

    已經是二月份了。

  • I'm back from my hiatus.

    我從我的間隙中回來了。

  • I was so burned out doing all those SAT problems. But now

    我當時做那些SAT題都快累死了。但現在

  • I'm ready and I will start doing some physics.

    我'準備好了,我將開始做一些物理學。

  • So we had done a bunch of projectile motion, what

    所以我們做了一堆彈丸運動,什麼?

  • happens you throw something in the air or

    發生你扔東西在空氣中或

  • drop it from a cliff.

    從懸崖上掉下來。

  • But now I want to introduce you to is how do you actually

    但現在我想給大家介紹的是,你到底是怎麼做的?

  • affect the acceleration of an object?

    影響物體的加速度?

  • And to do that I'm going to introduce you to Newton's

    為了做到這一點,我將向你介紹牛頓的。

  • three laws.

    三法。

  • To some degree what we were doing before was derivative of

    在某種程度上,我們之前所做的事情是衍生出的。

  • what I'm going to do now.

    我現在要做什麼。

  • But this is kind of the backbone of classical physics.

    但這也算是經典物理學的主幹。

  • So Newton's three laws.

    所以牛頓'三定律。

  • And you've probably heard of these before.

    而你'可能已經聽說過這些。

  • Newtow's three laws.

    紐託'的三大法則。

  • Sometimes they're called Newton's Laws of Motion.

    有時他們'叫牛頓運動定律。

  • I've actually looked this up on the web just to make sure

    我在網上看了一下,只是為了確保

  • and see if there's any correct way of writing it, but every

    並看看是否有什麼正確的寫法,但每一個。

  • website seems to have a different

    網站似乎有不同

  • paraphrase of the laws.

    對法律的解讀。

  • But hopefully, I can give you an intuitive sense

    但希望能給你一個直觀的感受。

  • of what they are.

    的是什麼。

  • So the first law is an object at rest. An object at rest

    所以第一條規律是靜止的物體。靜止的物體

  • tends to stay at rest. And an object in motion

    往往會保持靜止狀態。而運動中的物體

  • tends to stay in motion.

    往往會保持運動狀態。

  • This is what I learned when I was a kid and now when I look

    這是我小時候學過的,現在看來

  • at Wikipedia and things, there are some paraphrases.

    在維基百科和東西,有一些解說。

  • And we'll go over those paraphrases because I think

    我們會去看那些解說詞,因為我覺得

  • they're instructive.

    他們'是指導性的。

  • Stay in motion.

    保持運動。

  • And you might say, Sal, this is obvious.

    你可能會說,薩爾,這很明顯。

  • Why does Newton get so much credit

    為什麼牛頓的功勞這麼大

  • for stating the obvious?

    因為我說的很明顯?

  • Obviously, if I look at my sofa for example, it is an

    很明顯,如果我看我的沙發,比如說,它是一個。

  • object at rest and if I keep staring at it, it tends to

    物體在靜止狀態下,如果我一直盯著它看,它就會傾向於

  • stay at rest. Likewise, when I look at a car crossing an

    保持休息。同樣,當我看著一輛輛汽車橫穿一條條道路時,我也會覺得很奇怪。

  • intersection-- that's not a red light, that's crossing an

    十字路口 -- 那不是一個紅燈,那是穿越一個。

  • intersection, it's an object in motion.

    交點,它是一個運動中的物體。

  • And then, I don't know-- 10 seconds later, it's still

    然後,我不知道... ... 10秒鐘後,它仍然是

  • staying in motion and of course, it will stay in motion

    當然,它也會一直運行下去。

  • unless you press the brakes or whatever.

    除非你按下剎車什麼的。

  • So you might say, well Sal, this is the most

    所以你可能會說,好吧,薩爾,這是最。

  • obvious thing ever.

    很明顯的事情,有史以來。

  • This doesn't even need to be written down.

    這根本不需要寫下來。

  • But let's say you were Newton and you came to me-- it was in

    但讓我們說你是牛頓,你來找我--這是在。

  • the 17th century.

    17世紀。

  • And you said, Sal, I have these new laws.

    你說,薩爾,我有這些新法律。

  • And the first is an object at rest tends to stay at rest,

    而第一個是靜止的物體往往會保持靜止狀態。

  • and an object in motion tends to stay in motion.

    而運動中的物體往往會保持運動狀態。

  • And I would say Newton, I can already disprove your law.

    而我想說牛頓,我已經可以推翻你的定律了。

  • Let's say I have an apple and I'm holding it up at let's say

    讓我們'說我有一個蘋果和我'舉著它在讓我們'說。

  • my-- I'm holding it up with my arm, so it's roughly my

    我的... 我用手扶著它,所以它大概是我的。

  • shoulder level.

    肩部水準。

  • So I'm holding an apple.

    所以我'拿著一個蘋果。

  • This is an apple.

    這是一個蘋果。

  • Looks like a heart, but it's an apple.

    看起來像一顆心,但它'是一個蘋果。

  • So I'm holding it with my hand, I'm drawing my hand.

    所以我'用手拿著它,我'用手畫著。

  • I don't know if that makes sense to you, but I'm holding

    我不知道這對你是否有意義,但我拿著。

  • it with my hand.

    它與我的手。

  • And what happens when I let go of that apple?

    當我放開那個蘋果的時候會發生什麼?

  • So while I'm holding it with my hand it's an object at

    所以當我用手拿著它的時候,它是一個物體在

  • rest, right?

    休息,對吧?

  • But then when I let go, what happens?

    但當我放手的時候,會發生什麼?

  • It falls.

    它落下了。

  • Falls to the ground.

    倒在地上。

  • So I'll say, Newton, I just disproved your first law.

    所以我'會說,牛頓,我剛剛推翻了你的第一定律。

  • Because this was an object at rest. And I did nothing to it.

    因為這是一個靜止的物體。而我什麼都沒做

  • I just let go.

    我只是放手。

  • I didn't apply, I didn't push it, I didn't pull it.

    我沒有'應用,我沒有'推它,我沒有'拉它。

  • I didn't throw it.

    我沒有扔。

  • I didn't do anything.

    我什麼也沒做。

  • And when I let go it just fell to the ground.

    我一鬆手,它就掉在了地上。

  • It started moving without me doing anything, even though it

    我什麼都沒做,它就開始動了,儘管它... ...

  • was an object at rest.

    是一個靜止的物體。

  • And then Newton will say, oh, well that's because there's a

    然後牛頓會說,哦,那是因為有一個。

  • thing called gravity.

    叫做重力的東西。

  • And it's the force of gravity.

    而這'就是重力的力量。

  • And I would say, Newton, you need to start to learn to not

    我想說的是,牛頓,你需要開始學會不... ...

  • make up things.

    編造事情。

  • Just because you're law doesn't make sense, you don't

    就因為你的法律沒有意義,你就不'。

  • need to make up artificial forces in the universe.

    需要在宇宙中編造人工力量。

  • But anyway, he would end up being right.

    但無論如何,他最終會是對的。

  • And the way to think about this, if I did this exact same

    如果我做了同樣的事情,我就會想到這個問題

  • experiment while I was in space and let's just say-- I

    實驗,而我在太空中,讓我們'只是說 - 我

  • was going to say orbit because it would look like that, but

    本來想說軌道,因為它看起來像,但

  • even orbit is kind of a-- you're still kind of falling

    即使是軌道是一種 - 你'仍然是一種下降。

  • towards the earth, it's just you're moving-- well, I won't

  • go into that.

    進而。

  • I'll go into orbit at another time.

    我'將在另一個時間進入軌道。

  • But let's say we were just in deep space and me and the

    但是,讓我們說我們只是在深空,而我和...

  • apple were just floating around in space.

    蘋果只是漂浮在太空中。

  • Maybe we're stationary.

    也許我們'是靜止的。

  • It's hard to say.

    這'很難說。

  • We're floating with respect to what?

    我們在漂浮著與什麼有關?

  • And then, if we're in space and I let go of this apple,

    然後,如果我們在太空中,我放開這個蘋果。

  • what happens to the apple?

    蘋果會怎麼樣?

  • Nothing.

    什麼都沒有。

  • It's not going to fall anywhere.

    它'不會掉到哪裡去。

  • It's not going to move.

    它'不會動。

  • And so whenever you think about Newton's laws-- and

    所以每當你想到牛頓定律時...

  • that's why this is so amazing.

    這就是為什麼這個是如此驚人。

  • He didn't know about space.

    他不知道空間。

  • He's living in this planet that everything tends to fall

    他生活在這個星球上,所有的東西都會掉下來。

  • and things start moving for no reason because of whatever,

    和事情開始無緣無故的移動,因為什麼。

  • gravity, and the wind and whatever else.

    地心引力,還有風和其他什麼東西。

  • And he actually theorized that there could be a place where

    而且他實際上理論上認為,可能有一個地方,在那裡

  • there's no forces acting on objects where if I were to let

    沒有任何力量作用在物體上,如果我讓

  • go of this apple, it would just stay where it is.

    去這個蘋果,它就會留在原地。

  • And similarly, the object in motion

    同樣,運動中的物體

  • tends to stay in motion.

    往往會保持運動狀態。

  • And there again I would've told Newton, well, that

    在那裡,我又會告訴牛頓,好吧,那個

  • doesn't make sense.

    不'說不通。

  • If I were to-- I don't know.

    如果我... 我不知道。

  • If I were to push a-- well, I don't know if they had bowling

    如果我推一個 - 好吧,我不知道如果他們有保齡球

  • balls back then.

    當時的球。

  • But if I were to roll a bowling ball down a-- well

    但如果我用保齡球滾下去... ...

  • let's say up a hill-- At some point that bowling ball's

    讓我們說,在山上 - 在某些時候,保齡球的

  • going to slow down.

    要慢下來了。

  • If I rolled it up a hill, at some point it's just

    如果我把它滾上山,在某些時候,它只是'。

  • going to slow down.

    要慢下來了。

  • And maybe if I got it right it would just stop at the top if

    如果我做對了,也許它就會停在頂部,如果。

  • I did it perfectly.

    我做得很完美。

  • And I could say, look, this was an object in motion.

    我可以說,看,這是一個運動中的物體。

  • At some point it stops or it actually turns back around.

    在某些時候,它停了下來,或者它實際上又轉了回來。

  • Or even if I were to roll it this way, at some point it's

    或者說,即使我這樣滾,在某些時候,它'的。

  • just going to stop.

    只是要停止。

  • Right The bowling ball's going to stop.

    右邊的保齡球要停了。

  • If I were to push something as hard as I could, maybe it

    如果我盡我所能地去推動一些東西,也許它... ...

  • travels for a couple of feet, but then it's going to stop.

    旅行了幾英尺,但隨後它'要停止。

  • And he'll say, oh, well you know, there's these forces

    他說,哦,好吧,你知道,有這些力量。

  • that you're not realizing there's a force.

    你沒有意識到有一種力量。

  • There's the wind resistance in the bowling ball example.

    有'保齡球例子中的風阻。

  • There's the force of friction in the example where I just

    在我剛才的例子中,有摩擦力。

  • pushed something.

    推的東西。

  • And I would've said, well Newton, you're just making up

    我會說,好吧,牛頓,你只是在瞎編。

  • these forces again.

    這些力量又。

  • And this is why this is so not intuitive.

    這也是為什麼這一切都不直觀的原因。

  • Because he had to essentially realize that there were all of

    因為他必須從本質上意識到,有所有的

  • these forces acting on something when to someone at

    這些作用力在對某人時

  • that time, you wouldn't have realized that and you wouldn't

    那時候,你不會意識到這一點,你不會

  • have been able to even conceive that there's a place

    竟然能夠想象到有一個地方

  • called space, for example, where these

    稱為空間,例如,其中這些

  • things wouldn't happen.

    事情就不會發生。

  • If I push something in space, it will keep going.

    如果我在空間裡推一個東西,它就會繼續前進。

  • It would be an object in motion and it will keep that

    它將是一個運動中的物體,它將保持這種。

  • velocity until some other force acts on it.

    速度,直到有其他力作用於它。

  • So it wasn't that intuitive.

    所以並不是那麼直觀。

  • And so a more modern way to write this is to say that

    所以,更現代的寫法是這樣說的

  • there is a frame of reference, there exists a frame of

    有參照系,就有參照系。

  • reference-- and I'll explain what a frame of reference is.

    參考 -- 我會解釋什麼是參考框架。

  • But there exists a frame of reference where this is true.

    但存在一個參照系,在這個參照系中,這是真實的。

  • That could be the new way of saying Newton's

    這可能是牛頓'的新說法。

  • first law of motion.

    第一運動定律。

  • So what's a frame of reference?

    那麼什麼是參照系呢?

  • So everything in physics-- if I'm moving,

    所以物理學中的一切--如果我在動。

  • moving relative to what?

    相對於什麼而動?

  • Moving relative to the observer?

    相對於觀察者移動?

  • Moving relative to the earth?

    相對於地球移動?

  • You don't know.

    你不知道

  • So a frame of reference is what is the observer doing?

    所以,一個參考框架就是觀察者在做什麼?

  • So example: when I'm in space and I let go of the apple, me

    所以,舉例來說:當我'在空間裡,我放開蘋果的時候,我

  • and the apple are kind of in this-- I am observing the

    和蘋果是一種在這 - 我觀察到的

  • apple from what I call an inertial frame of reference.

    蘋果從我所謂的慣性參照系。

  • So this is a frame of reference actually where

    所以這是一個參考框架,其實在這裡

  • Newton's laws hold.

    牛頓定律成立。

  • If I take the apple on earth and I let go and it drops, the

    如果我拿著地上的蘋果,我一鬆手,它就掉下來了,那。

  • reason why this first law didn't hold is because I'm not

    為什麼第一條定律不成立,是因為我不是

  • really in an inertial frame of reference.

    真正在慣性參照系中。

  • Because me and the apple are both constantly being pulled

    因為我和蘋果都在不斷地被拉扯。

  • on by this force called gravity.

    在這個被稱為重力的力的作用下。

  • So although it looks like nothing's going on, me and the

    所以,雖然看起來什麼都沒有發生,但我和那個...

  • apple are in the same-- nothing's really acting on us.

    蘋果都在同一個------沒有什麼'的真正作用於我們。

  • There is.

    有。

  • There's this force of acceleration.

    有'這種加速的力量。

  • Similarly, if I'm in a car and that car is

    同樣的,如果我在車內,而那輛車是。

  • accelerating, right?

    加速,對嗎?

  • So let's say the car-- looks more like a pickup truck, so

    所以,讓我們說車 -- 看起來更像一個皮卡,所以... ...

  • I'll go with the pickup truck.

    我'會選擇皮卡。

  • Let's say you have a pair of dice hanging from your rear

    比方說,你的後背上掛著一對骰子

  • view mirror.

    視鏡。

  • This is the dice right here.

    這是骰子就在這裡。

  • What happens when the car accelerates?

    汽車加速時會發生什麼?

  • Well the dice move back, right?

    骰子往後移,對嗎?

  • And so when you're sitting in the truck itself, it looks

    所以,當你坐在卡車本身,它看起來

  • like the dice are just moving back.

    像骰子只是移動回來。

  • No one's really doing anything to it.

    沒有人'真的對它做什麼。

  • Let's say the car had no windows and you would just all

    讓我們'的說,汽車沒有窗戶,你會只是都

  • of a sudden mysteriously feel-- well, you'd feel a

    突然神祕的感覺 - 好吧,你'會覺得一個。

  • little squeezing on your chest too, but you would also just

    小擠壓你的胸部了,但你也會只是。

  • see these dice move back.

    看到這些骰子移動回來。

  • And you'd say, hey.

    而你'會說,嘿。

  • Newton's first law doesn't hold.

    牛頓'第一定律不成立。

  • And what I would say is well that's because you're in a

    我想說的是,好吧,那是因為你'在一個

  • non-inertial frame of reference.

    非慣性參照系。

  • To someone outside of the truck, they would see, oh

    對卡車外的人來說,他們會看到,哦。

  • well, the truck is moving, the truck is actually accelerating

    好了,卡車是移動的, 卡車實際上是加速。

  • and that's why the dice move back.

    這就是為什麼骰子會往後移動。

  • So in I guess you could say the horizontal dimension, and

    所以,在我猜測你可以說水準維度,和。

  • I'm probably just confusing you, but I want to give you a

    我可能只是把你搞糊塗了,但我想給你一個。

  • really intuitive feel about why this isn't so intuitive.

    真的很直觀的感覺,為什麼這不是那麼直觀。

  • In the horizontal direction, because there are no forces of

    在水準方向,因為沒有力的

  • gravity or whatever acting in this direction, and if I'm

    在這個方向上的重力或其他什麼作用,如果我'm

  • outside of the truck, I could then-- I would be in an

    卡車外,我可以... ... 我將在一個。

  • inertial frame of reference in at least

    慣性參照系

  • the horizontal dimension.

    的水準尺寸。

  • I mean we always have gravity pulling down on us.

    我的意思是,我們總是有重力拉著我們。

  • But from the outside of the truck, I could observe that

    但是從卡車外面,我可以觀察到

  • oh, you know, Newton's law holds because the whole frame

    哦,你知道,牛頓定律成立,因為整個框架。

  • of reference, this truck is actually being accelerated.

    的參考,這輛卡車實際上正在加速。

  • So me being outside of that, I would be in an inertial frame

    所以,我在這之外,我將在一個慣性框架中。

  • of reference.

    的參考文獻。

  • Hopefully I haven't confused you too much.

    希望我沒有給你帶來太多困惑。

  • The way to think about it is that an inertial frame of

    思考的方式是,一個慣性框架的。

  • reference is just a frame of reference where there's no

    參照物只是一個參照物,在那裡沒有's

  • outside forces acting on the whole frame of reference.

    外力作用在整個參照系上。

  • And a frame of reference is just what is

    而參照系正是

  • the observer doing?

    觀察者在做什麼?

  • What am I doing?

    我在做什麼?

  • Am I moving with the object?

    我是隨著物體移動的嗎?

  • Am I being accelerated with the object?

    我是不是被物體加速了?

  • Or, are neither me nor the object being acted upon?

    或者,我和對象都沒有被作用?

  • And that's the way to think about it.

    而這'就是思考的方式。

  • Oh, I already ran out of time.

    哦,我已經沒有時間了。

  • I only got one law done.

    我只完成了一項法律。

  • So I'll see you in the next video.

    所以,我'會在下一個視頻中看到你。

Good morning.

早晨好

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