English subtitles for clip: File:First law.ogv

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Last time

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we discussed

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that

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an acceleration is

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caused by push

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or by pull.

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Today we will express this more qualitatively

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in

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three laws, which I called

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Newton's laws.

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The first law

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really goes back to the

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fir… first part of the 17th century,

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which was Galileo who

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expressed what he called

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the law of inertia,

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and I'mma read you this law:

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A body at rest

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remains at rest

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and a body in motion

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continues to move

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at constant velocity

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along a straight line,

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unless acted upon

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by an external force.

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And now I will read to you

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Newton's own words

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in his famous book “principia”:

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Every body

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perseveres in its state of rest

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or of uniform motion

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in a right line,

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unless it is compelled

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to change that state

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by forces impressed upon it.

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And Newton's first law

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is clearly against our daily experiences.

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Things that move

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don't move along a straight line,

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and don't continue to move

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and the reason is

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there's gravity.

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And there's another reason

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even if you remove gravity

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then there's friction

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there's air drag

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and so things will always come to a hold.

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But we believe though

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that in the absence of any forces

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indeed an object

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if it had a certain velocity

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would continue along a straight line

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forever, 'n' ever, 'n' ever.

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Now, this law

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this very fundamental law

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does not hold in all reference frames.

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For instance, it doesn't hold

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in a reference frame

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which itself is being accelerated.

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Imagine,

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that I accelerate myself right here,

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I either jump my horse,

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or I take my bicycle,

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or my motorcycle, or my car,

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and you see me being accelerated

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in this direction.

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And you sit there.

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Any you say: “Uh-huh!”

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“His velocity is changing.”

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“Therefore, according to the first law

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there must be a force on, on him.”

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And you say:

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“Hey there!

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Do you feel that force‽”

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And I say: “Yeah, I do!”

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“I really feel, that …

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I feel someone's pushing me.“

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Consistent with the first law.

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Perfect.

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First law works for you.

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Now I'm here,

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I'm being accelerated in this direction.

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And you all come towards me

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being accelerated in this direction

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I say: “Uh-huh!”

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“The first law should work.”

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“So, these people

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should feel a push.”

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I say: “Hey there!”

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“Do you feel the push‽”

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And you say: “I feel nothing.”

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“There is no push, there is no pull.”

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Therefore, the first law

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doesn't work for <i>my</i> frame of reference,

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if I'm being accelerated towards you.

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So, now comes the question

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“When <i>does</i> the first law work?”

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Well, the first law works

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when the frame of reference

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is, what we call,

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an inertial frame of reference.

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An inertial frame of reference

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would then be a frame, in which

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there are no accelerations of any kind.

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Is that possible?

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Is this 26.100, is this lecture hall,

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an inertial reference frame?

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For one,

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the earth rotates about its own axis

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and 26.100 goes with it,

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that gives a centripetal acceleration.

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Number two:

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The earth goes around the sun.

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That gives it a centripetal acceleration,

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including the earth,

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including you, including 26.100.

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The sun goes around the milky way.

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And you can go on 'n' on.

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So clearly,

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26.100 is <i>not</i> an inertial reference frame.

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We can try to make an estimate

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on how large these accelerations are,

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that we experience,

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here, in 26.100.

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And let's start with the one

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that is due to the earth rotation:

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So here's the earth …

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… rotating with angular velocity ω.

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And …

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… here's the equator.

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And the earth has a certain radius.

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Radius of the earth –

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this is the symbol for earth.

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I know, that

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26.100 is here

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but let's just take the worst case

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that you're on the equator.

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You're dying.

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You go around like this

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and in order to do that

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you need a centripetal acceleration

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a<sub>c</sub>

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which, as we have seen last time,

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= ω² ⁢ R<sub>🜨</sub>

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How large is that one?

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Well, the period of rotation

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for the earth is

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24 hours times 3,600 seconds.

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So,

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ω = 2 ⁢ π divided by 24 times 3,600

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and that would then be in radians per second.

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And so you can calculate now

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what ω² ⁢ R<sub>🜨</sub> is.

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if you know, that the radius of the earth

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is about 6,400 kilometers.

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Make sure, that you convert this to meters, of course.

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And you will find then

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that the centripetal acceleration

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at the equator, which is the worst case,

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since it's less here,

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is 0.034 meters per second squared.

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And this is way, way less,

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this is 300 times smaller

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than the gravitation acceleration

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that you experience here on earth.

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And if we take the motion of the earth

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around the sun

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then it's an additional factor of

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five times lower.

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In other words, these accelerations

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even though they're real

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and they can be measured easily with

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today's high-tech instrumentation

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they are much much lower than

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what we're used to

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which is the gravitational acceleration.

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And therefore in spite of these accelerations

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we will ac… accept this whole

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as a reasonably good

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inertial frame of reference

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in which the first law

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then should hold.

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Can Newton's law be proven?

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The answer is: No,

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because it's impossible

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to be sure

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that your reference frame

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is without any accelerations.

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Do we believe in this?

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Yes, we do.

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We believe in it,

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since it is consistent

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within the uncertainty

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of the measurements with all experiments

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that have been done.