DNA replication and RNA transcription and translation

WEBVTT
Kind: captions
Language: en

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- [Voiceover] We've already
talked about how DNA's structure

00:00:03.258 --> 00:00:05.778
as this double helix, this twisted ladder,

00:00:05.778 --> 00:00:10.022
makes it suitable for being the
molecular basis of heredity.

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And what we wanna do in this video is get

00:00:11.954 --> 00:00:14.297
a better appreciation
for why it is suitable,

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and the mechanism by which it is

00:00:16.442 --> 00:00:18.588
the molecular basis for heredity.

00:00:18.588 --> 00:00:19.861
And we're gonna focus
on a conceptual level,

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I'm not gonna go into all of the,

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I guess you could say biochemical details.

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Really just give you the
conceptual idea of what happens.

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So right over here this
could be a fragment of DNA,

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I have, what, I have--

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This is eight base pairs depicted.

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And just to be clear,
and we talked about this

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in the introductory video to DNA,

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DNA is much more than, you
know, a handful of base pairs.

00:00:42.332 --> 00:00:47.042
The DNA molecule can be tens
of millions of base pairs long.

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So for example this might be a section

00:00:49.138 --> 00:00:51.050
of a much longer molecule,

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so the much longer strand of DNA,

00:00:54.819 --> 00:00:57.891
and even there I'm probably
not giving justice to it.

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But this might just be this
very, very small section,

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let me do this in a different color,

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this little section right over here,

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zoomed in.

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So once again it might
be part of a molecule

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that has not seven or eight base pairs,

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but might have 70 million base pairs.

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So just like that.

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So let's understand what a
molecular basis of heredity

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would need to do.

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Well first of all it would
need to be replicable.

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Or we would need to be
able to replicate it.

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As a cell divides,

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the two new cells would want to have

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the same genetic material.

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So how does DNA replicate?

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And this process is called replication.

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And we covered this in the
introduction video as well,

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but it's nice to see
the different processes

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next to each other.

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And replication, you can imagine taking

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either splitting these
two sides of the ladder,

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and actually let's do that.

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So let me copy and paste,

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so if I take that side right over there,

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so let me copy and then paste it.

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And then there we go,

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a little bit of it is
dropping below the video

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but I think that serves the purpose.

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And then let's copy and
paste the other side.

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So let me select that.

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And then I copy and then I paste,

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and it's just like that.

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And so you can imagine if
you were to split these,

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these things you could call
them two sides of the ladder,

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that either side could be used
to construct the other side.

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And then you would have two strands,

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two identical strands of the DNA.

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And so let's see what
that actually looks like.

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So let me get my pen tool out now,

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let me deselect this,
get the pen tool out.

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It's a new tool I'm using,

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so let me make sure I'm doing it right.

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Alright, so from this side,

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from this left side,

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or at least what we are
looking at as the left side,

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you can then construct another right side

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based on this information.

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A always pairs with T if
we're talking about DNA.

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So adenine pairs with
thymine just like that.

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Thymine pairs with adenine

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Let me do that a little bit neater.

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Thymine pairs with adenine,

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guanine pairs with cytosine,

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cytosine pairs with guanine,

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falling a little bit down here.

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And just like that I was able to construct

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a new right hand side
using that left hand side.

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So maybe I'll do the new sugar phosphate

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backbone in yellow.

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And we can do the same thing here

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using the original right hand side.

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So using the original right hand side,

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once again the T is paired with the A,

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let me do that in adenine's color.

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So we have an adenine and thymine,

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adenine and thymine,

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adenine and thymine.

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Thymine pairs with adenine,

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so thymine, adenine.

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Thymine, adenine.

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Guanine pairs with cytosine.

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And then cytosine pairs with guanine.

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So cytosine just like that.

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And so you can take half
of each of this ladder,

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and then you can use it to
construct the other half,

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and what you've essentially done is

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you've replicated the actual DNA.

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And this is actually a
kind of conceptual level

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of how replication is done

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before a cell divides and replicates,

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and the entire cell duplicates itself.

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So that's replication.

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So the next thing you're
probably thinking about,

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"Okay, well it's nice to be
able to replicate yourself

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"but that's kind of useless
if that information can't be

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"used to define the organism in some way

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"to express what's actually happening."

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And so let's think about how the genes

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in this DNA molecule
are actually expressed.

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So I'll write this as "expression".

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And actually that warrants
a little bit of a detour

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because you hear sometimes the words

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DNA and chromosome and gene

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used somewhat interchangeably,

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and they are clearly related,

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but it's worth knowing what is what.

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So when you're talking about DNA

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you're talking literally
about this molecule here

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that has this sugar phosphate base

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and it has the sequence of base pairs,

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it's got this double helix structure,

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and so this whole thing this
could be a DNA molecule.

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Now when you have a DNA molecule

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and it's packaged together
with other molecules

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and proteins and kind of
given a broader structure,

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then you're talking about a chromosome.

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And when you're talking about a gene,

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you're talking about a section of DNA

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that's used to express a certain trait.

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Or actually used to code for
a certain type of protein.

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So for example this could be,

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this whole thing could be a strand of DNA,

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but this part right over,
let's say in orange I'll do it,

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this part in orange right
over here could be one gene,

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it might define information for one gene,

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it could define a protein,

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this section right over here

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could be used to define another gene.

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And genes could be anywhere from

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several thousand base pairs long,

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all the way up into the millions.

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And as we'll see,

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the way that a gene is expressed,

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the way we get from the
information for that section of DNA

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into a protein which is
really how it's expressed,

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is through a related molecule to DNA,

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and that is RNA.

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Actually let me write this down.

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RNA.

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So RNA stands for ribonucleic acid.

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Ribonucleic acid, let me write that down.

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And so you might remember that DNA is

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deoxyribonucleic acid,

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so the sugar backbone in RNA

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is a very similar molecule,

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well now it's got its oxy,

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it's not deoxyribonucleic acid,

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it's ribonucleic acid.

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The R, let me make it clear
where the RNA come from,

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the R is right over there,

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then you have the nucleic, that's the n,

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and then it's a, acid.

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Same reason why we call
the DNA nucleic acid.

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So you have this RNA.

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So what role does this
play as we are trying

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to express the information in this DNA?

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Well the DNA,

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especially if we're talking
about cells with nucleii,

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the DNA sits there but
that information has to

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for the most part get
outside of the nucleus

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in order to be expressed.

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And one of the functions that RNA plays

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is to be that messenger,

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that messenger between
a certain section of DNA

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and kind of what goes on
outside of the nucleus,

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so that that can be translated
into an actual protein.

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So the step that you go from DNA to mRNA,

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messenger RNA,

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is called transcription.

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Let me write that down.

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And what happens in transcription,

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let's go back to looking at
one side of this DNA molecule.

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So let's say you have
that right over there,

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let me copy and paste it.

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So there we go, actually
I didn't wanna do that.

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I wanted the other side.

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So actually I think I'm on the
wrong, let me go back here.

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And so let me copy and then let me paste.

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There we go.

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So let's say you have
part of this DNA molecule,

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or you have 1/2 of it

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just like we did when we replicated it.

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But now we're not just trying
to duplicate the DNA molecule,

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we're actually trying to create

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a corresponding mRNA molecule.

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At least for that section of,

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at least for that gene.

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So this might be part of a gene

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Actually whoops, let me make
sure I'm using the right tool.

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This might be part of a
gene that is this section

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of our DNA molecule right over there.

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And so transcription is a
very similar conceputal idea,

00:09:23.550 --> 00:09:25.014
where we're now going to construct

00:09:25.014 --> 00:09:28.264
a strand of RNA and specifically mRNA

00:09:28.264 --> 00:09:29.516
'cause it's going to take that information

00:09:29.516 --> 00:09:32.001
outside of the nucleus.

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And so it's very similar

00:09:33.769 --> 00:09:35.929
except for when we're talking about RNA,

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adenine, instead of pairing with thymine,

00:09:38.113 --> 00:09:41.044
is now going to pair with uracil.

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So let me write this down,

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so now you're gonna have
adenine pairs not with thymine

00:09:45.617 --> 00:09:46.997
but uracil.

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DNA has uracil instead of the thymine.

00:09:49.344 --> 00:09:52.357
But you're still going to have
cytosine and guanine pairing.

00:09:52.672 --> 00:09:56.588
So for the RNA and in this case the mRNA

00:09:56.864 --> 00:09:59.152
that's going to leave the nucleus

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A is going to pair with U,

00:10:01.489 --> 00:10:03.568
U for uracil,

00:10:03.568 --> 00:10:06.167
so uracil, that's the
base we're talking about,

00:10:06.167 --> 00:10:07.933
let me write it down, uracil.

00:10:09.770 --> 00:10:12.704
Thymine is still going
to pair with adenine,

00:10:15.272 --> 00:10:16.452
just like that.

00:10:16.452 --> 00:10:18.932
Guanine is gonna pair with cytosine,

00:10:20.207 --> 00:10:25.207
and cytosine is going
to pair with guanine.

00:10:26.372 --> 00:10:27.724
And so when you do that,

00:10:27.724 --> 00:10:29.900
now these two characters can detach,

00:10:29.900 --> 00:10:32.379
and now you have a single strand of RNA

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and in this case messenger RNA,

00:10:33.908 --> 00:10:37.405
that has all the information

00:10:37.405 --> 00:10:41.210
on that section of DNA.

00:10:41.210 --> 00:10:44.863
And so now that thing
can leave the nucleus,

00:10:44.863 --> 00:10:46.712
go attach to a ribosome,

00:10:46.712 --> 00:10:48.983
and we'll talk more about
that in future videos

00:10:48.983 --> 00:10:50.440
exactly how that's happened,

00:10:50.543 --> 00:10:52.486
and then this code can be used

00:10:52.486 --> 00:10:55.242
to actually code for proteins.

00:10:55.242 --> 00:10:56.305
Now how does that happen?

00:10:56.305 --> 00:10:58.586
And that process is called translation.

00:11:01.985 --> 00:11:04.980
Which is really taking
this base pair sequence

00:11:04.980 --> 00:11:07.356
and turning it into an
amino acid sequence.

00:11:07.356 --> 00:11:10.754
Proteins are made up of
sequences of amino acids.

00:11:10.754 --> 00:11:11.907
So translation.

00:11:11.907 --> 00:11:15.190
So let's take our mRNA or this
little section of our mRNA,

00:11:15.996 --> 00:11:18.959
and actually let me draw it like this.

00:11:20.435 --> 00:11:23.668
Now let's see, I have it is U A C,

00:11:23.668 --> 00:11:28.498
so it's gonna be U A C then U U

00:11:28.498 --> 00:11:30.739
then A C G okay?

00:11:30.903 --> 00:11:33.095
And then we have an A,

00:11:33.095 --> 00:11:35.510
let me make sure I change
it to the right color.

00:11:35.510 --> 00:11:40.510
We have an A there, and
then we have this U U A,

00:11:41.771 --> 00:11:43.300
C G, alright,

00:11:43.300 --> 00:11:45.522
now let me put a C right over there,

00:11:45.522 --> 00:11:47.938
I'm just taking this and
I'm writing it horizontally.

00:11:47.938 --> 00:11:51.246
I have a C here, not a G, it's a C.

00:11:52.248 --> 00:11:54.660
And then finally I have a G.

00:11:54.660 --> 00:11:57.722
And of course it'll keep
going on and on and on.

00:11:57.722 --> 00:12:01.789
And what happens is
each sequence of three,

00:12:01.939 --> 00:12:03.517
and you have to be very
careful where it starts,

00:12:03.517 --> 00:12:05.761
and so this is in some ways
a delicate and surprising,

00:12:05.761 --> 00:12:08.228
but at the same time
surprisingly robust process,

00:12:08.228 --> 00:12:13.228
every three of these bases
code for a specific amino acid.

00:12:14.121 --> 00:12:16.638
And so three bases together,

00:12:16.638 --> 00:12:18.582
so these bases right over here,

00:12:18.582 --> 00:12:20.846
these I guess you could
say this three letter word

00:12:20.846 --> 00:12:22.190
or this three letter sequence,

00:12:22.190 --> 00:12:23.770
that's called a codon.

00:12:25.070 --> 00:12:28.117
And this is going to be the next codon.

00:12:29.536 --> 00:12:31.694
And we actually haven't drawn
the next codon after that

00:12:31.694 --> 00:12:34.922
'cause we need three bases
to get to the next codon.

00:12:35.733 --> 00:12:38.070
And how many possible codons do you have?

00:12:38.070 --> 00:12:40.062
Well you have one of four bases

00:12:40.062 --> 00:12:42.622
and you have them in
three different places,

00:12:42.622 --> 00:12:44.588
so you have four times four times four,

00:12:44.588 --> 00:12:47.750
possible codon words
I guess you could say.

00:12:47.750 --> 00:12:50.141
And four times four times four is 64.

00:12:50.447 --> 00:12:55.447
So you have 64 possible codons.

00:12:56.217 --> 00:12:58.901
Which is good because you
have 20 possible amino acids.

00:12:58.901 --> 00:13:01.309
So this is overkill and
allows codons to be used

00:13:01.309 --> 00:13:02.844
for other purposes as well.

00:13:02.844 --> 00:13:04.989
And they also, you might
have more than one codon

00:13:04.989 --> 00:13:07.076
coding for the same amino acid.

00:13:07.076 --> 00:13:08.553
So you have 64 possible codons

00:13:08.553 --> 00:13:11.430
that need to code for 20 amino acids.

00:13:11.477 --> 00:13:14.660
And so this codon right
over here with the ribosome,

00:13:14.660 --> 00:13:16.716
and we'll talk more
about how that happens,

00:13:16.716 --> 00:13:18.619
can code for

00:13:22.172 --> 00:13:25.038
amino acid 1.

00:13:25.038 --> 00:13:28.918
So let me just write it
here, this is amino acid 1.

00:13:28.918 --> 00:13:31.614
And actually this amino
acid is brought to here,

00:13:31.614 --> 00:13:34.725
they're actually matched
together by another type of RNA,

00:13:34.725 --> 00:13:37.117
this is mRNA we're talking
about right over here.

00:13:37.117 --> 00:13:41.897
This is mRNA, but there's
another type of RNA

00:13:41.907 --> 00:13:43.610
called tRNA

00:13:43.610 --> 00:13:47.034
that essentially brings these
two characters together.

00:13:47.034 --> 00:13:48.146
So the tRNA,

00:13:48.146 --> 00:13:49.480
and I'm just gonna, it's
got some structure here,

00:13:49.480 --> 00:13:51.013
I'm not drawing it completely right,

00:13:51.013 --> 00:13:52.706
but it's going to match right over here,

00:13:52.706 --> 00:13:57.706
where maybe it has an A, a
U, and a G right over here

00:13:58.770 --> 00:14:01.801
and on this end it was
attached to this amino acid,

00:14:01.801 --> 00:14:03.809
and so it matches them together.

00:14:03.809 --> 00:14:07.125
And then they're gonna have another tRNA

00:14:08.369 --> 00:14:11.464
that might attach to amino acid 2,

00:14:12.064 --> 00:14:13.674
which I will do in purple,

00:14:16.812 --> 00:14:19.429
and that just happens to coincide with,

00:14:19.429 --> 00:14:21.192
so it can complement right over here,

00:14:21.192 --> 00:14:22.406
so it attaches in the right place,

00:14:22.406 --> 00:14:25.075
so it's A A U right over here,

00:14:25.075 --> 00:14:26.468
this tRNA.

00:14:26.468 --> 00:14:29.796
And so it'll construct the
sequence of amino acids.

00:14:29.796 --> 00:14:31.965
And as you put these amino acids together,

00:14:31.965 --> 00:14:34.679
then you're actually
constructing a protein.

00:14:34.915 --> 00:14:38.011
So protein is essentially a bunch,

00:14:38.011 --> 00:14:40.554
a sequence of these
amino acids put together.

00:14:42.706 --> 00:14:46.239
And these proteins are
essentially the molecules

00:14:46.239 --> 00:14:49.288
that run life for the most part.

00:14:49.288 --> 00:14:51.086
Obviously you know if you eat an animal

00:14:51.086 --> 00:14:53.999
it's going to be made up of
fat and sugars and proteins,

00:14:53.999 --> 00:14:56.415
but the proteins are the
things that actually do a lot

00:14:56.415 --> 00:14:58.815
of the whether they're enzymes,
whether they're structural,

00:14:58.815 --> 00:15:00.903
the muscle is formed from proteins,

00:15:00.903 --> 00:15:01.782
these are the things,

00:15:01.782 --> 00:15:03.631
and I'm just drawing a
small segment of them,

00:15:03.631 --> 00:15:08.522
they could be thousands or
more of these amino acids long.

00:15:08.522 --> 00:15:11.583
And they kind of form these
incredibly complex shapes

00:15:11.583 --> 00:15:13.231
and they have all of these functions.

00:15:13.231 --> 00:15:15.807
This is what's kind of
doing the work of life.

00:15:15.807 --> 00:15:17.120
And this for the most part,

00:15:17.120 --> 00:15:21.334
and this is kind of how the
information for life is stored.


DNA

WEBVTT
Kind: captions
Language: en

00:00:00.466 --> 00:00:02.633
- [Voiceover] As long as
human beings have been around

00:00:02.633 --> 00:00:04.442
I could imagine that
they have noticed that

00:00:04.442 --> 00:00:07.400
offspring tend to have traits in common

00:00:07.400 --> 00:00:08.667
with the parent.

00:00:08.667 --> 00:00:10.233
For example, someone might have told you,

00:00:10.233 --> 00:00:12.100
"Hey, you walk kind of like your dad,"

00:00:12.100 --> 00:00:14.333
or, "Your smile is kind of like your mom,"

00:00:14.333 --> 00:00:18.464
or, "Your eyes are like one of your uncles

00:00:18.464 --> 00:00:20.189
"or your grandparents."

00:00:20.189 --> 00:00:21.866
And so there's always been this notion

00:00:21.866 --> 00:00:23.733
of inherited traits.

00:00:23.733 --> 00:00:27.366
But it wasn't until the
1800 that that started to be

00:00:27.366 --> 00:00:30.928
studied in a more scientific
way with Gregor Mendel

00:00:30.928 --> 00:00:32.767
the father of genetics.

00:00:32.767 --> 00:00:34.900
But even then, even Mendel

00:00:34.900 --> 00:00:38.233
who was starting to
understand the mechanisms

00:00:38.233 --> 00:00:41.179
or he was trying to understand
how inheritance happened,

00:00:41.179 --> 00:00:43.166
then you even could start to breed

00:00:43.166 --> 00:00:44.646
certain types of things.

00:00:44.646 --> 00:00:46.107
Even he didn't know exactly

00:00:46.107 --> 00:00:49.433
what was the molecular
basis for inheritance.

00:00:49.433 --> 00:00:52.100
And the answer to that
question wasn't figured out

00:00:52.100 --> 00:00:53.593
until fairly recent times,

00:00:53.593 --> 00:00:55.366
until the mid 20th century.

00:00:55.366 --> 00:00:58.933
Not until the structure of DNA

00:00:58.933 --> 00:01:01.633
was established by Watson and Crick

00:01:01.633 --> 00:01:03.592
and their work was based
on the work of many others

00:01:03.592 --> 00:01:05.679
especially folks like Rosalind Franklin

00:01:05.679 --> 00:01:07.925
who essentially provided
the bulk of the data

00:01:07.925 --> 00:01:09.533
for Watson and Crick's work,

00:01:09.533 --> 00:01:12.100
Maurice Wilkins and many,
many, many other folks.

00:01:12.100 --> 00:01:14.900
But it's really the structure of DNA

00:01:14.900 --> 00:01:18.371
that made people say,
"Hey, that looks like

00:01:18.371 --> 00:01:21.264
"the molecule that's
storing the information."

00:01:21.264 --> 00:01:24.100
Just to be clear, DNA
wasn't discovered in 1953.

00:01:24.100 --> 00:01:26.474
DNA was discovered in the mid 1800s.

00:01:26.474 --> 00:01:28.492
It was this kind of this molecule

00:01:28.492 --> 00:01:32.100
that was inside of nuclei of cells.

00:01:32.100 --> 00:01:33.740
And for some time people said,

00:01:33.740 --> 00:01:37.133
"Maybe this could be a
molecular basis of inheritance."

00:01:37.133 --> 00:01:38.734
You could imagine what you would need

00:01:38.734 --> 00:01:40.228
to be a molecular basis of inheritance.

00:01:40.228 --> 00:01:41.676
It would have to be a molecule

00:01:41.676 --> 00:01:44.347
or a series of molecules that
could contain information,

00:01:44.347 --> 00:01:45.825
that could be replicated,

00:01:45.825 --> 00:01:48.333
that could be expressed in some way.

00:01:48.333 --> 00:01:50.053
But it wasn't until 1953

00:01:50.053 --> 00:01:52.500
wherein this double helix structure

00:01:52.500 --> 00:01:53.625
of DNA was established.

00:01:53.625 --> 00:01:58.194
The people said, "Hey, this
looks like our molecule."

00:01:58.194 --> 00:02:01.133
So first, let's just talk
about the structure here

00:02:01.133 --> 00:02:03.763
and then actually we'll talk
about where this name, DNA,

00:02:03.763 --> 00:02:08.266
deoxyribonucleic acid comes from.

00:02:08.266 --> 00:02:09.800
And then we'll talk a little bit about

00:02:09.800 --> 00:02:13.167
why this structure lends itself well

00:02:13.167 --> 00:02:15.233
to something that stores information,

00:02:15.233 --> 00:02:17.463
that can replicate its information

00:02:17.463 --> 00:02:19.242
and that could express its information.

00:02:19.242 --> 00:02:22.069
We might go in depth on the
expression of information

00:02:22.069 --> 00:02:23.933
in future videos.

00:02:23.933 --> 00:02:25.215
So this structure right over here

00:02:25.215 --> 00:02:28.158
and this is a visual
depiction of a DNA molecule.

00:02:28.158 --> 00:02:30.166
You can view this as
kind of a twisted ladder.

00:02:30.166 --> 00:02:31.846
It has these two, I guess you could say

00:02:31.846 --> 00:02:33.800
sides of the ladder that are twister.

00:02:33.800 --> 00:02:35.966
That is one side right over there

00:02:35.966 --> 00:02:37.813
and then it is another side.

00:02:37.813 --> 00:02:40.466
There is another side right over here.

00:02:40.466 --> 00:02:43.566
And in between those two sides

00:02:43.566 --> 00:02:46.133
or connecting those two
sides of that twisted ladder

00:02:46.133 --> 00:02:48.012
you have these rungs.

00:02:48.012 --> 00:02:49.948
And these rungs are actually where

00:02:49.948 --> 00:02:53.133
the information, the
genetic information is

00:02:53.133 --> 00:02:55.366
I guess you could say stored in some way.

00:02:55.366 --> 00:02:59.266
Because these rungs it's a
sequence of different bases.

00:02:59.266 --> 00:03:01.066
And when I say bases,
you're gonna say wait.

00:03:01.066 --> 00:03:03.966
This says acid, why are you
saying bases right over here?

00:03:03.966 --> 00:03:07.033
Well, the word deoxyribonucleic acid

00:03:07.033 --> 00:03:09.067
comes from the fact that this backbone

00:03:09.067 --> 00:03:13.166
is made up of a combination
of sugar and phosphate.

00:03:13.166 --> 00:03:16.300
And the sugar that makes up the backbone

00:03:16.300 --> 00:03:18.261
is deoxyribose.

00:03:18.261 --> 00:03:21.100
So that's essentially the D in DNA.

00:03:21.100 --> 00:03:22.933
And then the phosphate group is acidic

00:03:22.933 --> 00:03:25.507
and that's now where you
get the acid part of it.

00:03:25.507 --> 00:03:27.092
And nucleic is, hey this was found

00:03:27.092 --> 00:03:28.647
in nuclei of cells.

00:03:28.647 --> 00:03:30.500
It is nucleic acid.

00:03:30.500 --> 00:03:33.500
Deoxyribonucleic acid.

00:03:35.607 --> 00:03:38.600
It is actually mildly acidic all in total

00:03:38.600 --> 00:03:41.600
but for every acid it
actually also has a base,

00:03:41.600 --> 00:03:44.900
and those bases form
the rung of the ladders.

00:03:44.900 --> 00:03:48.346
And actually each rung is a pair of bases

00:03:48.346 --> 00:03:50.694
and as I said, that's
where the information

00:03:50.694 --> 00:03:51.658
is actually stored.

00:03:51.658 --> 00:03:53.066
Well what am I talking about?

00:03:53.066 --> 00:03:55.666
Well let me talk about
the four different bases

00:03:55.666 --> 00:03:58.867
that make up the rungs of a DNA molecule.

00:03:58.867 --> 00:04:01.600
So, you have adenine.

00:04:03.733 --> 00:04:05.007
Adenine.

00:04:05.007 --> 00:04:08.511
And so for example, this
part right over here.

00:04:08.511 --> 00:04:12.600
This section of that
rung might be adenine.

00:04:12.600 --> 00:04:15.166
Maybe this right over here is adenine.

00:04:15.166 --> 00:04:16.365
This right over here.

00:04:16.365 --> 00:04:18.902
Remember, each of these
rungs are made up by

00:04:18.902 --> 00:04:20.799
it's a pair of bases.

00:04:20.799 --> 00:04:22.510
And that might be adenine.

00:04:22.510 --> 00:04:25.400
Maybe this is adenine

00:04:25.400 --> 00:04:26.625
and I could stop there,

00:04:26.625 --> 00:04:27.959
I mean I'll do a little more adenine.

00:04:27.959 --> 00:04:29.792
Maybe that's adenine right over there.

00:04:29.792 --> 00:04:34.400
And adenine always pairs
with the base thymine.

00:04:34.400 --> 00:04:35.423
So let me write that down.

00:04:35.423 --> 00:04:38.300
So adenine pairs with thymine.

00:04:39.534 --> 00:04:40.900
Thymine.

00:04:40.900 --> 00:04:42.767
So, if that's an adenine there

00:04:42.767 --> 00:04:44.866
then this is going to be a thymine.

00:04:44.866 --> 00:04:45.804
If this is an adenine

00:04:45.804 --> 00:04:47.600
then this is going to be a thymine.

00:04:47.600 --> 00:04:49.066
Or if I drew the thymine first,

00:04:49.066 --> 00:04:50.700
well say, okay it's gonna
pair with the adenine.

00:04:50.700 --> 00:04:53.365
So this is going to be a
thymine right over here.

00:04:53.365 --> 00:04:55.167
This is going to be a thymine.

00:04:55.167 --> 00:04:56.241
If I were to draw this,

00:04:56.241 --> 00:04:58.466
this would be a thymine right over here.

00:04:58.466 --> 00:05:00.012
Now the other two bases,

00:05:00.012 --> 00:05:02.546
you have cytosine which pairs with guanine

00:05:02.546 --> 00:05:04.833
or guanine that pairs with cytosine.

00:05:04.833 --> 00:05:08.027
So guanine and we're not gonna go into

00:05:08.027 --> 00:05:10.633
the molecular structure
of these bases just yet,

00:05:10.633 --> 00:05:12.760
although these are good names to know

00:05:12.760 --> 00:05:13.733
because they show up a lot

00:05:13.733 --> 00:05:15.533
and they really form kind of the code,

00:05:15.533 --> 00:05:17.023
your genetic code.

00:05:17.023 --> 00:05:18.776
Guanine.

00:05:18.776 --> 00:05:22.461
Guanine pairs with cytosine.

00:05:22.461 --> 00:05:25.679
Guanine and cytosine.

00:05:25.679 --> 00:05:28.033
Cytosine.

00:05:28.033 --> 00:05:29.733
So actually if this is,

00:05:29.733 --> 00:05:31.500
let's say there's some cytosine there,

00:05:31.500 --> 00:05:33.169
let's say cytosine right over here.

00:05:33.169 --> 00:05:36.537
Maybe this is a cytosine,
maybe this is cytosine,

00:05:36.537 --> 00:05:39.966
maybe this is cytosine, this is cytosine

00:05:39.966 --> 00:05:41.833
and maybe this is cytosine.

00:05:41.833 --> 00:05:44.555
Then it always pairs with the guanine.

00:05:44.555 --> 00:05:46.966
So, let's see, this is guanine then

00:05:46.966 --> 00:05:48.871
and this will be guanine.

00:05:48.871 --> 00:05:51.933
This is guanine, this is guanine.

00:05:51.933 --> 00:05:53.333
I actually didn't draw stuff here.

00:05:53.333 --> 00:05:56.000
This is guanine, I didn't
say what these could be

00:05:56.000 --> 00:05:58.919
but these would be maybe the pairs of

00:05:58.919 --> 00:06:00.733
they could be adenine-thymine pairs

00:06:00.733 --> 00:06:02.076
and it could be adenine on either side

00:06:02.076 --> 00:06:03.325
or the thymine on either side,

00:06:03.325 --> 00:06:05.230
and they could be made
of guanine-cytosine pairs

00:06:05.230 --> 00:06:07.800
where the guanine or the
cytosine is on the other side.

00:06:07.800 --> 00:06:09.263
Actually just to make it
a little bit more complete

00:06:09.263 --> 00:06:14.263
let me just color in the
rungs here as best as I can.

00:06:14.717 --> 00:06:16.166
So those are guanines

00:06:16.166 --> 00:06:18.000
so they're gonna pair with cytosine.

00:06:18.000 --> 00:06:20.471
Pair with cytosine, pair with cytosine.

00:06:20.471 --> 00:06:21.633
When you straw in this way

00:06:21.633 --> 00:06:24.233
you might start to see how
this is essentially a code,

00:06:24.233 --> 00:06:27.800
the order of which the bases are...

00:06:28.753 --> 00:06:31.367
I guess the order in which we have these

00:06:31.367 --> 00:06:34.927
or the sequence of these
bases essentially in code

00:06:34.927 --> 00:06:37.593
the information that make you, you,

00:06:37.593 --> 00:06:38.727
and you could be.

00:06:38.727 --> 00:06:40.467
Well how much of it is
nature versus nurture

00:06:40.467 --> 00:06:41.974
and when people say nature, you know,

00:06:41.974 --> 00:06:43.400
it's literally genetic,

00:06:43.400 --> 00:06:46.176
and that's an ongoing
debate, an ongoing debate

00:06:46.176 --> 00:06:49.876
but it does code for things
like your hair color.

00:06:50.538 --> 00:06:51.833
When you see that your smile

00:06:51.833 --> 00:06:53.767
is similar to your parents

00:06:53.767 --> 00:06:56.366
it is because that
information to a large degree

00:06:56.366 --> 00:06:57.633
is encoded genetically.

00:06:57.633 --> 00:07:00.300
It affects a lot of what makes you you

00:07:00.300 --> 00:07:02.207
and actually not even
just within a species

00:07:02.207 --> 00:07:05.242
but also across species.

00:07:05.242 --> 00:07:07.433
Humans have more genetic material

00:07:07.433 --> 00:07:08.933
in common with other humans

00:07:08.933 --> 00:07:10.569
than they do with say a plant.

00:07:10.569 --> 00:07:12.766
But all living creatures as we know them

00:07:12.766 --> 00:07:14.292
have genetic information.

00:07:14.292 --> 00:07:16.366
This is the basis by which they are

00:07:16.366 --> 00:07:19.348
passing down their actual traits.

00:07:19.348 --> 00:07:20.466
Now you might be saying

00:07:20.466 --> 00:07:22.233
well, how much genetic information

00:07:22.233 --> 00:07:24.600
does a human being have?

00:07:24.600 --> 00:07:27.266
And the number will either disappoint you

00:07:27.266 --> 00:07:30.066
or you might find it mind-boggling.

00:07:30.066 --> 00:07:33.634
The human genome and every species

00:07:33.634 --> 00:07:35.082
has a different number of base pairs

00:07:35.082 --> 00:07:37.070
to large degree correlated
with how complex they are

00:07:37.070 --> 00:07:38.333
although not always.

00:07:38.333 --> 00:07:43.333
But the human genome has 6,000,000.

00:07:43.366 --> 00:07:45.725
Sorry, not 6,000,000, 6,000,000,000.

00:07:45.725 --> 00:07:46.794
6,000,000 would be disappointing,

00:07:46.794 --> 00:07:48.300
even billion might be disappointing.

00:07:48.300 --> 00:07:50.900
6,000,000,000 base pairs.

00:07:50.900 --> 00:07:52.700
6,000,000,000.

00:07:52.700 --> 00:07:54.173
6,000,000,000 base pairs.

00:07:54.173 --> 00:07:56.119
And when you have your full
complement of chromosomes

00:07:56.119 --> 00:07:58.261
and this is in most of
the cells in your body

00:07:58.261 --> 00:08:01.496
and outside of your sex cells,

00:08:01.496 --> 00:08:03.900
the sperm or the egg cells.

00:08:03.900 --> 00:08:08.900
This is going to be spread
over 46 chromosomes.

00:08:09.000 --> 00:08:11.987
46 chromosomes or I guess you could say

00:08:11.987 --> 00:08:13.346
23 pair of chromosomes.

00:08:13.346 --> 00:08:15.915
If you divide 6,000,000,000 by 46

00:08:15.915 --> 00:08:18.366
you get a little over
on average 100,000,000.

00:08:18.366 --> 00:08:21.294
I think it's a 100 and something million

00:08:21.294 --> 00:08:23.676
base pairs per chromosome.

00:08:23.676 --> 00:08:24.912
And some chromosomes are longer,

00:08:24.912 --> 00:08:27.096
actually the longest are over 200,000,000

00:08:27.096 --> 00:08:28.546
and some might be shorter.

00:08:28.546 --> 00:08:30.033
That's just on average.

00:08:30.033 --> 00:08:32.622
Now this number might to some
of you might be exciting.

00:08:32.622 --> 00:08:34.952
You're like, "I thought
I was a simple creature.

00:08:34.952 --> 00:08:37.033
"I didn't know I was this complex."

00:08:37.033 --> 00:08:38.727
6,000,000,000, that's a lot of base pairs.

00:08:38.727 --> 00:08:40.479
That feels like a lot of information.

00:08:40.479 --> 00:08:43.166
For others of you it
might not feel so great.

00:08:43.166 --> 00:08:44.581
You might say, "Hey, wait I could store

00:08:44.581 --> 00:08:46.912
"this much information
on a modern thumb drive

00:08:46.912 --> 00:08:47.900
"or on a hard disk.

00:08:47.900 --> 00:08:51.333
"I thought I was more unique than that."

00:08:51.333 --> 00:08:52.912
And of course we all
are special and unique.

00:08:52.912 --> 00:08:54.415
You're gonna say 6,000,000,000 base pairs.

00:08:54.415 --> 00:08:55.327
I thought I was, you know,

00:08:55.327 --> 00:08:57.533
I was infinitely complex
and whatever else.

00:08:57.533 --> 00:08:58.900
There's some arguments for that

00:08:58.900 --> 00:09:01.067
along some other directions,

00:09:01.067 --> 00:09:05.392
but this is the approximate
length I guess you could say

00:09:05.392 --> 00:09:10.000
or the approximate size of
the actual human genome.

00:09:10.000 --> 00:09:11.296
And when we talk about chromosomes

00:09:11.296 --> 00:09:15.150
and we'll talk about
chromosomes in much more depth,

00:09:15.150 --> 00:09:17.800
imagine taking this zoomed in thing

00:09:17.800 --> 00:09:19.600
that you have right over here

00:09:19.600 --> 00:09:21.216
and you know, over here, I
don't know how many we have,

00:09:21.216 --> 00:09:22.471
Like one, two, three, four, five,

00:09:22.471 --> 00:09:23.948
six, seven, eight, nine, 10,

00:09:23.948 --> 00:09:27.033
11, 12, 13, 14, 15, 16, 17, 18, 19.

00:09:27.033 --> 00:09:29.266
We have about 20 base pairs depicted here.

00:09:29.266 --> 00:09:33.101
Imagine if you had about
200,000,000 of these base pairs

00:09:33.101 --> 00:09:34.496
and then you were to take this thing

00:09:34.496 --> 00:09:36.266
and you were to kind of coil it up

00:09:36.266 --> 00:09:40.600
into that thing is a chromosome.

00:09:40.600 --> 00:09:42.294
It is a chromosome and
you're saying, "Wait,

00:09:42.294 --> 00:09:44.207
"I have that much information in

00:09:44.207 --> 00:09:45.927
"most of the cells of my body.

00:09:45.927 --> 00:09:48.761
"This thing must be incredible compact."

00:09:48.761 --> 00:09:50.533
And if you said that I would say,

00:09:50.533 --> 00:09:51.966
"Yes, you are correct."

00:09:51.966 --> 00:09:56.966
This, the radius, the
radius of the DNA molecule

00:09:57.133 --> 00:09:59.594
is on the order of one nanometer.

00:09:59.594 --> 00:10:04.066
One nanometer which is
a billionth of a meter.

00:10:04.066 --> 00:10:05.866
So you can start to assess

00:10:05.866 --> 00:10:07.107
kind of the scale of this thing.

00:10:07.107 --> 00:10:09.100
This is a very dense way

00:10:09.100 --> 00:10:12.266
to actually store information.

00:10:12.266 --> 00:10:13.754
But just to have an appreciation of

00:10:13.754 --> 00:10:15.800
and you might have seen
it when I was coloring in

00:10:15.800 --> 00:10:18.166
on why the structure lends itself

00:10:18.166 --> 00:10:20.666
to being able to replicate the information

00:10:20.666 --> 00:10:23.782
or even to be able to translate
or express the information.

00:10:23.782 --> 00:10:26.266
Let's think about if you
were to take this ladder

00:10:26.266 --> 00:10:28.392
and you were to just kind
of split all the base pairs.

00:10:28.392 --> 00:10:30.500
So, you just have 1/2 of them.

00:10:30.500 --> 00:10:32.367
So you essentially have
half of the ladder.

00:10:32.367 --> 00:10:34.400
And so if you only have
half of the ladder,

00:10:34.400 --> 00:10:37.009
you're able to construct the
other half of the ladder.

00:10:37.009 --> 00:10:39.100
Let's take an example, let's say

00:10:39.100 --> 00:10:41.958
and I'll just use the
first letter to abbreviate

00:10:41.958 --> 00:10:43.276
for each of these bases.

00:10:43.276 --> 00:10:44.186
Let's say you have some...

00:10:44.186 --> 00:10:45.507
So let's say this is one of the,

00:10:45.507 --> 00:10:48.094
this is the sugar phosphate
backbone right over here.

00:10:48.094 --> 00:10:50.389
So this could be one of the sides.

00:10:50.389 --> 00:10:51.833
Let's say there's some adenine.

00:10:51.833 --> 00:10:53.819
Actually we do in the right color.

00:10:54.466 --> 00:10:56.900
So you got some adenine, adenine.

00:10:56.900 --> 00:10:59.000
Maybe some adenine right over here

00:10:59.000 --> 00:11:00.666
and maybe there's an adenine there.

00:11:00.666 --> 00:11:05.066
And maybe you have some thymine, thymine,

00:11:05.066 --> 00:11:07.266
maybe thymine right over here

00:11:07.266 --> 00:11:11.033
and then you have some guanine,

00:11:11.033 --> 00:11:13.412
guanine, guanine.

00:11:13.412 --> 00:11:16.000
And then let's say you have some cytosine

00:11:16.000 --> 00:11:17.834
and you have some cytosine.

00:11:17.834 --> 00:11:22.633
So with just half of this
ladder I guess you could say,

00:11:22.633 --> 00:11:24.176
you're able to construct the other half,

00:11:24.176 --> 00:11:26.500
and this is actually how DNA replicates.

00:11:26.500 --> 00:11:28.500
This ladder splits and then each of those

00:11:28.500 --> 00:11:29.809
two halves of that ladder

00:11:29.809 --> 00:11:32.748
are able to construct
versions of the other half,

00:11:32.748 --> 00:11:33.861
or versions of the other half

00:11:33.861 --> 00:11:36.000
are able to constructed on top of that,

00:11:36.000 --> 00:11:37.258
on top of that half.

00:11:37.258 --> 00:11:38.666
So how does that happen?

00:11:38.666 --> 00:11:41.633
Well, it's based on how these bases pair.

00:11:41.633 --> 00:11:43.389
Adenine always pairs with thymine

00:11:43.389 --> 00:11:44.816
if we're talking about DNA.

00:11:44.816 --> 00:11:46.266
So if you have an A there,

00:11:46.266 --> 00:11:48.769
you're gonna have a T on
this end, T on this end.

00:11:48.769 --> 00:11:51.966
T's right all over here,
T right over there.

00:11:51.966 --> 00:11:53.200
If you have a T on that end

00:11:53.200 --> 00:11:54.995
you're gonna have an A right over there.

00:11:54.995 --> 00:11:56.992
A, A.

00:11:56.992 --> 00:11:59.592
If you have a G, a guanine on this side,

00:11:59.592 --> 00:12:01.833
you're gonna have a
cytosine on the other side.

00:12:01.833 --> 00:12:04.101
Cytosine, cytosine, cytosine.

00:12:04.101 --> 00:12:05.466
And if you have a cytosine

00:12:05.466 --> 00:12:08.000
you're gonna have a
guanine on the other side.

00:12:08.000 --> 00:12:09.740
Hopefully that gives you an appreciation

00:12:09.740 --> 00:12:12.066
of how DNA can replicate itself.

00:12:12.066 --> 00:12:14.866
And as we'll see also how
this information can be

00:12:14.866 --> 00:12:17.662
translated to other forms
of either related molecules

00:12:17.676 --> 00:12:20.056
but eventually to proteins.

00:12:20.056 --> 00:12:22.060
And just to kind of round out this video,

00:12:22.060 --> 00:12:23.307
to get a real visual sense

00:12:23.307 --> 00:12:24.729
what the DNA molecule looks like

00:12:24.729 --> 00:12:27.167
or I guess a different
visual depiction from this.

00:12:27.167 --> 00:12:31.600
I found this animated gif

00:12:31.600 --> 00:12:33.600
that, you know, if you
haven't fully digested

00:12:33.600 --> 00:12:36.467
what a double helix
looks like, this is it.

00:12:36.467 --> 00:12:37.992
And you see here, you see your

00:12:37.992 --> 00:12:39.866
sugar phosphate bases here.

00:12:39.866 --> 00:12:42.063
You see kind of the sugars and phosphate,

00:12:42.063 --> 00:12:43.433
the sugars and the phosphates

00:12:43.433 --> 00:12:45.601
alternating along this backbone,

00:12:45.601 --> 00:12:48.830
and then the rungs of the
ladder are these base pairs.

00:12:48.830 --> 00:12:50.066
So this is one of the bases,

00:12:50.066 --> 00:12:51.256
that's the corresponding,

00:12:51.256 --> 00:12:53.394
that's this corresponding,
I guess you can say partner.

00:12:53.394 --> 00:12:56.471
And you can see that along
all the way up and down

00:12:56.471 --> 00:12:58.433
in this molecule.

00:12:58.433 --> 00:12:59.766
Very exciting.


Constant angular momentum when no net torque

WEBVTT
Kind: captions
Language: en

00:00:00.300 --> 00:00:01.334
- [Voiceover] So right over here

00:00:01.334 --> 00:00:02.994
like I've done in previous videos,

00:00:02.994 --> 00:00:05.078
we have a diagram of a mass.

00:00:05.078 --> 00:00:06.981
We really should conceptualize
it as a point mass

00:00:06.981 --> 00:00:08.417
although it doesn't look like a point,

00:00:08.417 --> 00:00:09.950
it looks like a circle.

00:00:09.950 --> 00:00:11.458
But imagine a point mass here

00:00:11.458 --> 00:00:13.976
and it's tethered to something.

00:00:13.976 --> 00:00:16.862
It's kind of it's tied
to a massless string,

00:00:16.862 --> 00:00:19.969
a theoretical massless
string right over here.

00:00:19.969 --> 00:00:21.401
Where functionally a mass of string

00:00:21.401 --> 00:00:22.433
and it's kind of nailed down.

00:00:22.433 --> 00:00:24.733
And let's say it's on
a frictionless surface

00:00:24.733 --> 00:00:28.409
and let's say it has some velocity.

00:00:28.409 --> 00:00:32.500
And right here we have the
magnitude of its velocity

00:00:32.500 --> 00:00:35.533
in the direction that is perpendicular

00:00:35.533 --> 00:00:39.953
to the wire that is holding it,

00:00:39.953 --> 00:00:41.767
or I guess you can say perpendicular

00:00:41.767 --> 00:00:45.466
to the radial direction.

00:00:45.466 --> 00:00:47.802
Now based on that, we've had a definition

00:00:47.802 --> 00:00:49.097
for angular momentum.

00:00:49.097 --> 00:00:50.800
The magnitude of angular momentum

00:00:50.800 --> 00:00:53.466
is going to be equal to the mass,

00:00:53.466 --> 00:00:58.134
times this velocity, times the radius.

00:00:58.134 --> 00:00:59.433
And you could also view that

00:00:59.433 --> 00:01:01.433
and this is kind of always
kind of tying the connections

00:01:01.433 --> 00:01:04.011
between you know, translational notions

00:01:04.011 --> 00:01:05.527
and rotational notions.

00:01:05.527 --> 00:01:06.801
We can see that angular momentum

00:01:06.801 --> 00:01:08.058
could be the same thing.

00:01:08.058 --> 00:01:09.833
Well, the mass times its velocity

00:01:09.833 --> 00:01:13.100
you could do that as the
translational momentum row

00:01:13.100 --> 00:01:15.392
in the magnitude of translational momentum

00:01:15.392 --> 00:01:17.900
in this direction times r.

00:01:17.900 --> 00:01:19.566
So once again, we took
the translational idea,

00:01:19.566 --> 00:01:21.000
multiplied it by r

00:01:21.000 --> 00:01:22.493
and we're getting the rotational idea,

00:01:22.493 --> 00:01:25.466
the angular momentum versus
just the translational one.

00:01:25.466 --> 00:01:26.500
And we can also think about it

00:01:26.500 --> 00:01:29.066
in terms of angular velocity.

00:01:29.066 --> 00:01:30.666
Now this comes straight out of the idea

00:01:30.666 --> 00:01:34.533
that this v is going
to be equal to omega r.

00:01:34.533 --> 00:01:35.725
So you do that substitution,

00:01:35.725 --> 00:01:37.633
you get this right over here.

00:01:37.633 --> 00:01:39.802
Now, in previous videos we said okay.

00:01:39.802 --> 00:01:42.166
Like based on this and based on the idea

00:01:42.166 --> 00:01:44.266
that if torque is held constant

00:01:44.266 --> 00:01:46.233
then this does not change.

00:01:46.233 --> 00:01:49.367
You can describe or you could predict

00:01:49.367 --> 00:01:51.286
the type of behavior, explain the behavior

00:01:51.286 --> 00:01:52.223
that you might see.

00:01:52.223 --> 00:01:54.166
The figure skating competition

00:01:54.166 --> 00:01:57.223
where if someone pulls their
arms in while they're spinning

00:01:57.223 --> 00:01:59.700
and they're not, you know,
applying anymore torque to spin,

00:01:59.700 --> 00:02:01.433
and if they pull their arms in,

00:02:01.433 --> 00:02:03.100
well this thing is going to be constant

00:02:03.100 --> 00:02:05.100
because there's no torque being applied.

00:02:05.100 --> 00:02:07.566
Well, their mass isn't going to change

00:02:07.566 --> 00:02:10.800
so they'll just spin faster.

00:02:10.800 --> 00:02:11.700
When you do the opposite,

00:02:11.700 --> 00:02:13.433
the opposite would be happening.

00:02:13.433 --> 00:02:14.780
But you might have been left

00:02:14.780 --> 00:02:16.933
a little bit unsatisfied
when we first talked about it

00:02:16.933 --> 00:02:17.792
because I just told you that.

00:02:17.792 --> 00:02:19.166
I said, hey look, if torque is,

00:02:19.166 --> 00:02:21.176
if there's no net torque

00:02:21.176 --> 00:02:23.127
then angular momentum is constant

00:02:23.127 --> 00:02:25.200
and then you have this thing happening.

00:02:25.200 --> 00:02:26.704
But let's dig a little bit deeper

00:02:26.704 --> 00:02:27.840
and look at the math of it.

00:02:27.840 --> 00:02:30.600
So you feel good that
that is actually the case.

00:02:30.600 --> 00:02:34.096
So let's go back, let's go
to the definition of torque.

00:02:34.096 --> 00:02:35.473
And so the magnitude of torque,

00:02:35.473 --> 00:02:38.300
I'll focus on magnitudes in this video.

00:02:38.300 --> 00:02:41.594
The magnitude of torque
is going to be equal to,

00:02:41.594 --> 00:02:45.766
it's going to be equal to
the magnitude of the force

00:02:45.766 --> 00:02:50.209
that is in this perpendicular
direction, times r.

00:02:50.779 --> 00:02:52.434
Times r.

00:02:52.434 --> 00:02:54.833
Now what is this, this force?

00:02:54.833 --> 00:02:57.200
Well, this is just going to be equal to

00:02:57.200 --> 00:02:58.919
the mass force, f equals ma.

00:02:58.919 --> 00:03:01.501
So this is going to be mass times

00:03:01.501 --> 00:03:03.901
the acceleration in this direction

00:03:03.901 --> 00:03:05.900
which we could view as,

00:03:05.900 --> 00:03:08.767
which we could view as the change

00:03:08.767 --> 00:03:12.924
in this velocity over time,

00:03:12.924 --> 00:03:14.366
and we're talking about magnitudes.

00:03:14.366 --> 00:03:15.833
I guess you could say, it's through

00:03:15.833 --> 00:03:18.866
the magnitude of velocity
in that direction.

00:03:18.866 --> 00:03:22.384
And then of course we have times r.

00:03:22.384 --> 00:03:24.033
Times r.

00:03:24.033 --> 00:03:26.900
Now if we multiplied both
sides of this times delta t,

00:03:26.900 --> 00:03:31.000
we get and actually we do
tau in a different color.

00:03:31.000 --> 00:03:32.400
We do torque in green.

00:03:32.400 --> 00:03:35.766
We get torque times delta t.

00:03:35.766 --> 00:03:39.800
Torque times delta t is equal to,

00:03:39.800 --> 00:03:44.800
is equal to mass times delta v.

00:03:46.866 --> 00:03:50.656
Delta v in that perpendicular
direction times r.

00:03:50.656 --> 00:03:53.166
Well, what's this thing going to be?

00:03:53.166 --> 00:03:54.733
What's this?

00:03:54.733 --> 00:03:57.215
Well, that's just change
in angular momentum.

00:03:57.215 --> 00:04:01.567
So this is just going to be
change in angular momentum.

00:04:01.567 --> 00:04:03.133
And there's a complete analogy

00:04:03.133 --> 00:04:04.766
to what you might remember

00:04:04.766 --> 00:04:06.600
from kind of the translational world.

00:04:06.600 --> 00:04:08.866
The translational world
you have this notion,

00:04:08.866 --> 00:04:10.533
if you take your force

00:04:10.533 --> 00:04:11.833
and you multiply it times

00:04:11.833 --> 00:04:13.766
how long you're applying the force,

00:04:13.766 --> 00:04:16.025
should do this in a different color.

00:04:16.025 --> 00:04:19.783
So we multiply it by how long
you are applying the force.

00:04:19.783 --> 00:04:23.673
So this quantity we often call is impulse.

00:04:24.196 --> 00:04:25.366
Impulse.

00:04:25.366 --> 00:04:26.633
That's going to be equal to

00:04:26.633 --> 00:04:30.033
your change in translational momentum.

00:04:30.033 --> 00:04:32.040
Your change in translational momentum.

00:04:32.040 --> 00:04:32.979
And if you have no force

00:04:32.979 --> 00:04:34.607
then you're not gonna have
any change in momentum

00:04:34.607 --> 00:04:36.496
or you're gonna have your
conversation of momentum,

00:04:36.496 --> 00:04:37.766
or it's not gonna change,

00:04:37.766 --> 00:04:39.133
it's just going to be conserved.

00:04:39.133 --> 00:04:40.350
And then you can do all sorts of neat,

00:04:40.350 --> 00:04:42.400
you know, predicting
where your ball might go

00:04:42.400 --> 00:04:43.733
or whatever else.

00:04:43.733 --> 00:04:45.500
We have the same analogy here.

00:04:45.500 --> 00:04:48.866
The analog for force
in the rotational world

00:04:48.866 --> 00:04:51.700
is torque, it's obviously this force times

00:04:51.700 --> 00:04:55.866
the kind of radial, times
that radial distance.

00:04:55.866 --> 00:04:57.800
But if you take torque times

00:04:57.800 --> 00:04:59.400
how long you're applying that torque,

00:04:59.400 --> 00:05:02.625
that's going to be your
change in angular momentum.

00:05:02.625 --> 00:05:04.446
So if you're not applying any torque,

00:05:04.446 --> 00:05:06.310
if your torque is zero,

00:05:06.310 --> 00:05:08.307
if your torque is equal to zero,

00:05:08.307 --> 00:05:11.596
well that means that your delta L is zero.

00:05:11.596 --> 00:05:13.163
Your angular momentum is not changing

00:05:13.163 --> 00:05:17.466
or you could say your
angular momentum is constant.

00:05:17.466 --> 00:05:19.100
So if you don't apply any torque,

00:05:19.100 --> 00:05:21.279
like once this figure
skater is already spinning

00:05:21.279 --> 00:05:23.934
and he or she, she's
not pushing to get more,

00:05:23.934 --> 00:05:25.535
to spin so she's not applying

00:05:25.535 --> 00:05:27.166
or he's not applying more torque,

00:05:27.166 --> 00:05:29.540
well then, they're angular
momentum's going to be constant

00:05:29.540 --> 00:05:33.466
but they can change their rate of spinning

00:05:33.466 --> 00:05:36.483
by changing r, by changing how far

00:05:36.483 --> 00:05:37.858
in or out r is,

00:05:37.858 --> 00:05:39.200
or how far enough the masses are.

00:05:39.200 --> 00:05:40.733
And obviously I said in the last video,

00:05:40.733 --> 00:05:43.245
a figure skater is a much
more complicated system

00:05:43.245 --> 00:05:46.235
than a point mass tethered to, you know,

00:05:46.235 --> 00:05:48.600
tethered to a rope.

00:05:48.600 --> 00:05:49.743
You could view a figure skater

00:05:49.743 --> 00:05:51.725
as kind of being modeled
by a bunch of point masses

00:05:51.725 --> 00:05:53.900
but hopefully this gives you the idea.


Angular momentum

WEBVTT
Kind: captions
Language: en

00:00:00.521 --> 00:00:03.417
If we have some mass, m,

00:00:03.417 --> 00:00:07.379
and it is moving with some velocity,

00:00:07.379 --> 00:00:11.506
let's say the magnitude of
that velocity we say is v,

00:00:12.065 --> 00:00:15.456
we know that this object
right over here has momentum.

00:00:15.456 --> 00:00:17.441
Translational momentum.

00:00:17.441 --> 00:00:19.913
And that momentum, and we
use the Greek letter rho

00:00:19.913 --> 00:00:22.005
to represent momentum.

00:00:22.072 --> 00:00:25.400
Translational momentum
is defined as being equal

00:00:25.953 --> 00:00:30.649
to the mass times the velocity.

00:00:32.491 --> 00:00:34.155
This is all a review, we have other videos

00:00:34.155 --> 00:00:36.435
where we talk about
translationial momentum,

00:00:36.435 --> 00:00:38.691
and one way to think about it is,

00:00:38.691 --> 00:00:42.921
"Well how hard is it to stop this thing?"

00:00:43.093 --> 00:00:45.669
Literally in everyday language you think,

00:00:45.669 --> 00:00:47.805
"Well how much momentum
does something have?

00:00:47.805 --> 00:00:50.938
"The more momentum this has
the harder it's going to,

00:00:50.954 --> 00:00:54.247
"the harder it is to stop it in some way."

00:00:54.773 --> 00:00:56.812
And so we know if we wanna get

00:00:56.812 --> 00:00:58.476
a little bit more mathematical,

00:00:58.476 --> 00:01:01.100
that if we wanna change momentum,

00:01:01.100 --> 00:01:03.668
we have to apply force
for some amount of time.

00:01:03.668 --> 00:01:05.979
And so the magnitude of our force

00:01:08.086 --> 00:01:11.678
times the duration of the
time that we apply it for,

00:01:12.056 --> 00:01:15.151
force times time and
this is called impulse.

00:01:15.448 --> 00:01:18.039
And this is once again, all review.

00:01:18.039 --> 00:01:20.338
This is equal to change in momentum.

00:01:22.429 --> 00:01:24.496
Let me do this in that yellow color.

00:01:24.496 --> 00:01:28.374
That is equal to change in momentum.

00:01:28.987 --> 00:01:30.209
So if you don't have any impulse,

00:01:30.209 --> 00:01:32.212
especially if you don't have any net force

00:01:32.212 --> 00:01:33.491
acting on an object,

00:01:33.491 --> 00:01:35.793
its momentum is going to be constant.

00:01:35.793 --> 00:01:38.260
You have a conservation of momentum.

00:01:38.260 --> 00:01:39.863
And we use that idea in all sorts of

00:01:39.863 --> 00:01:43.076
interesting physics
applications in the world,

00:01:43.076 --> 00:01:45.236
and especially a lot of
cases using billiard balls

00:01:45.236 --> 00:01:47.020
and whatever else.

00:01:47.020 --> 00:01:49.132
So now let's try to take a similar idea,

00:01:49.132 --> 00:01:51.579
but go into the rotational world.

00:01:51.579 --> 00:01:53.707
So let's imagine you have a mass,

00:01:53.707 --> 00:01:56.091
for the sake of this we're
gonna assume it's a point mass.

00:01:56.967 --> 00:01:59.111
So you have a mass there.

00:01:59.111 --> 00:02:01.358
And let's just say it's attached by,

00:02:01.358 --> 00:02:03.510
essentially a massless wire,

00:02:05.093 --> 00:02:08.312
to you know, it's just nailed down

00:02:08.312 --> 00:02:09.364
right over here.

00:02:09.364 --> 00:02:10.668
And so this right over here would be

00:02:10.668 --> 00:02:11.948
its center of rotation,

00:02:11.948 --> 00:02:13.611
and so you could imagine
if someone applied

00:02:13.611 --> 00:02:15.396
a torque to this mass,

00:02:15.396 --> 00:02:18.371
this mass could start
rotating in a circle.

00:02:18.371 --> 00:02:20.211
And you can just assume that maybe

00:02:20.211 --> 00:02:21.814
it's sitting on a, you know the screen,

00:02:21.814 --> 00:02:24.125
this is kind of a frictionless surface,

00:02:24.125 --> 00:02:25.587
there's no air resistance.

00:02:25.587 --> 00:02:28.227
And so then it will, if
you apply a torque here,

00:02:28.227 --> 00:02:30.699
it will start rotating.

00:02:30.699 --> 00:02:31.915
And so you could think about,

00:02:31.915 --> 00:02:33.004
"Well there might be an idea,

00:02:33.004 --> 00:02:34.546
"just as momentum is this idea of,

00:02:34.546 --> 00:02:37.687
"well how hard is it to stop something?"

00:02:38.410 --> 00:02:39.473
You might say, "Well how?"

00:02:39.473 --> 00:02:42.682
And this is, stop translating
something from moving.

00:02:42.682 --> 00:02:44.881
You might think, "Well
maybe there's a similar idea

00:02:44.881 --> 00:02:46.474
"of how hard is it for something,

00:02:46.474 --> 00:02:50.013
"or how hard is it to
stop rotating something?"

00:02:50.409 --> 00:02:53.506
And you could imagine that
that idea has been defined

00:02:53.506 --> 00:02:56.157
and it has been defined
as angular momentum.

00:02:56.625 --> 00:02:58.010
So let me make this clear,

00:02:58.010 --> 00:03:00.763
this right over here is momentum.

00:03:04.870 --> 00:03:08.154
And over here we'll talk
about angular momentum.

00:03:16.314 --> 00:03:18.482
And actually both momentum
and angular momentum

00:03:18.482 --> 00:03:19.757
are vector quantities.

00:03:19.757 --> 00:03:21.930
So here I just wrote
kind of the magnitudes

00:03:21.930 --> 00:03:23.930
of velocity and momentum.

00:03:23.930 --> 00:03:26.722
But momentum is a vector
and it could be defined,

00:03:26.722 --> 00:03:29.874
the momentum vector could be
defined as equal to the mass

00:03:29.874 --> 00:03:32.113
which is a scalar quantity
times the velocty.

00:03:32.542 --> 00:03:34.894
Times the velocity vector.

00:03:35.335 --> 00:03:37.545
Now the same thing is
true for angular momentum,

00:03:37.545 --> 00:03:39.743
but I'm gonna stay focused on

00:03:40.634 --> 00:03:43.586
the magnitude of angular momentum.

00:03:43.586 --> 00:03:45.866
Angular momentum can have
direction as you can imagine

00:03:45.866 --> 00:03:47.849
you could rotate in two different ways,

00:03:47.849 --> 00:03:49.075
but that gets a little
bit more complicated

00:03:49.075 --> 00:03:51.449
when you start thinking about
taking the products of vectors

00:03:51.449 --> 00:03:53.377
because as you may already know

00:03:53.377 --> 00:03:54.921
or you may see in the future,

00:03:54.921 --> 00:03:56.962
there's different ways of
taking products of vectors.

00:03:56.962 --> 00:03:59.090
But just to get the intuition
of angular momentum,

00:03:59.090 --> 00:04:01.017
I'll focus on the magnitudes.

00:04:01.017 --> 00:04:03.323
So angular momentum is defined

00:04:03.323 --> 00:04:05.346
and the letter used is L.

00:04:05.346 --> 00:04:07.105
I did a lot of research
to try to figure out

00:04:07.105 --> 00:04:09.537
why it is called L, and I
could not find a good reason.

00:04:09.537 --> 00:04:13.337
So in the message board below
if anyone has a good reason

00:04:14.290 --> 00:04:17.159
I would like to know

00:04:17.159 --> 00:04:20.584
why angular momentum is called L.

00:04:20.584 --> 00:04:22.238
A lot of the best arguments I saw

00:04:22.238 --> 00:04:23.445
is that almost everything else was,

00:04:23.445 --> 00:04:25.246
all the other letters were used up

00:04:25.246 --> 00:04:27.333
for other ideas in physics.

00:04:27.333 --> 00:04:30.061
But anyway, angular momentum is defined,

00:04:30.061 --> 00:04:32.821
and it's defined very similarly.

00:04:32.821 --> 00:04:35.240
Just as kind of torque
is the thing that can

00:04:35.240 --> 00:04:37.064
change how something rotates,

00:04:37.064 --> 00:04:39.734
and force is the way
that something changes

00:04:39.734 --> 00:04:41.400
how something translates it,

00:04:41.400 --> 00:04:44.673
and torque is force times distance

00:04:44.673 --> 00:04:47.465
from the center of rotation,

00:04:47.465 --> 00:04:49.945
everything in kind of the rotational world

00:04:49.945 --> 00:04:52.329
is defined in a similar way.

00:04:52.329 --> 00:04:54.625
You kind of take the analogue
in the translational world,

00:04:54.625 --> 00:04:56.704
and you multiply it times the distance

00:04:56.704 --> 00:04:58.633
from your center of rotation.

00:04:58.633 --> 00:05:01.297
So angular momentum is defined as

00:05:03.557 --> 00:05:06.898
mass times velocity

00:05:09.540 --> 00:05:13.484
times distance from the center of rotation

00:05:13.878 --> 00:05:16.940
so let's call this distance
right over here, r.

00:05:16.940 --> 00:05:19.223
r for radius 'cause you could imagine

00:05:19.223 --> 00:05:20.492
if this was traveling in a circle

00:05:20.492 --> 00:05:22.380
that would be the radius of the circle.

00:05:22.380 --> 00:05:24.041
m, v, r.

00:05:24.148 --> 00:05:26.028
Actually let me be a little
bit more careful here.

00:05:26.028 --> 00:05:28.452
It's the magnitude of the velocity

00:05:28.452 --> 00:05:30.837
that is perpendicular to the radius.

00:05:30.837 --> 00:05:33.716
Sometimes it might be called
the tangential velocity.

00:05:33.716 --> 00:05:35.124
So this symbol right over here,

00:05:35.124 --> 00:05:37.227
this is the magnitude of the velocity

00:05:37.227 --> 00:05:38.996
that is perpendicular to the radius.

00:05:38.996 --> 00:05:43.580
So it would be that
magnitude right over here.

00:05:43.735 --> 00:05:48.170
This is what we define
as angular momentum.

00:05:48.958 --> 00:05:50.238
Now what I will tell you here is,

00:05:50.238 --> 00:05:52.591
just as in the absence of a net force,

00:05:52.591 --> 00:05:54.538
momentum is constant.

00:05:55.079 --> 00:05:57.101
We know, and I haven't
shown it to you yet,

00:05:57.101 --> 00:05:59.453
I haven't proven it to
you yet mathematically,

00:05:59.453 --> 00:06:01.845
but in the absence of torque,

00:06:01.845 --> 00:06:03.925
so if torque is equal to zero,

00:06:03.925 --> 00:06:06.171
we'll do torque in pink.

00:06:06.534 --> 00:06:09.194
If torque is equal to zero,

00:06:09.194 --> 00:06:11.565
if there's no net torque going on here,

00:06:11.565 --> 00:06:15.069
if the magnitude of
torque is equal to zero,

00:06:15.069 --> 00:06:19.065
then we will have no change.

00:06:22.981 --> 00:06:26.236
No change in angular momentum.

00:06:26.236 --> 00:06:29.412
And we will look at that
mathematically in a few seconds.

00:06:29.412 --> 00:06:30.760
But just from this

00:06:30.760 --> 00:06:33.214
there's a very interesting
thing that arises.

00:06:33.214 --> 00:06:35.062
And something that you might have observed

00:06:35.062 --> 00:06:37.254
at even the Olympics or in other things.

00:06:37.254 --> 00:06:39.164
And this is the idea that you can,

00:06:39.164 --> 00:06:41.857
by changing your radius,

00:06:42.208 --> 00:06:44.874
you could actually change
your tangential velocity.

00:06:44.874 --> 00:06:46.340
And as we've seen in previous videos,

00:06:46.340 --> 00:06:49.579
tangential velocity is closely related to

00:06:49.579 --> 00:06:52.013
angular velocity.

00:06:52.030 --> 00:06:53.806
So let's explore that a little bit.

00:06:53.806 --> 00:06:57.146
So when we write it in the world where,

00:06:57.146 --> 00:06:59.198
well actually you see
it straight out of this,

00:06:59.198 --> 00:07:02.650
if L is constant, if r went down,

00:07:02.925 --> 00:07:04.116
so let me write this down.

00:07:04.116 --> 00:07:05.924
So let me rewrite it over here.

00:07:05.924 --> 00:07:08.196
So L, whoops.

00:07:11.042 --> 00:07:16.042
L is equal to mass times
tangential velocity,

00:07:17.184 --> 00:07:19.185
or actually well yeah,
tangential velocity,

00:07:19.185 --> 00:07:22.445
or the velocity that's
perpendicular to the radius,

00:07:22.929 --> 00:07:24.620
times the radius.

00:07:24.880 --> 00:07:26.066
Now what happens,

00:07:26.066 --> 00:07:27.865
if we assume that this is constant,

00:07:30.463 --> 00:07:32.345
if we assume that there's no torque,

00:07:32.345 --> 00:07:33.618
so we're in this world.

00:07:33.618 --> 00:07:35.930
So this over here is going to be constant.

00:07:39.037 --> 00:07:42.544
So what happens if we were to reduce r?

00:07:42.612 --> 00:07:46.055
Somehow this wire started
to reel in a little bit

00:07:46.164 --> 00:07:47.405
or started to wrap around here,

00:07:47.405 --> 00:07:49.115
and that's actually a reasonable thing,

00:07:49.115 --> 00:07:51.392
you could imagine as it rotates
it starts to wrap around

00:07:51.392 --> 00:07:53.587
this thing so the wire gets shorter.

00:07:54.215 --> 00:07:56.350
So if r goes down,

00:07:57.746 --> 00:08:00.234
and this is constant, the
mass isn't going to change,

00:08:00.234 --> 00:08:02.160
Well if L is constant,
mass isn't changing,

00:08:02.160 --> 00:08:04.521
r is going down, tangential velocity,

00:08:04.521 --> 00:08:06.181
or the velocity that's
perpendicular to the radius

00:08:06.181 --> 00:08:07.980
is going to go up.

00:08:13.262 --> 00:08:14.833
And if we wanna think about it,

00:08:14.833 --> 00:08:17.505
we can think about it in
terms of angular velocity,

00:08:17.505 --> 00:08:20.545
we know that angular velocity,

00:08:20.545 --> 00:08:22.588
which we would measure
in radians per second,

00:08:22.588 --> 00:08:24.846
we would use the symbol omega,

00:08:24.846 --> 00:08:25.990
omega is defined,

00:08:25.990 --> 00:08:27.934
and we go into much more
depth in this in other videos,

00:08:27.934 --> 00:08:31.154
as tangential velocity,

00:08:33.260 --> 00:08:35.405
the magnitude of the velocity that is

00:08:35.405 --> 00:08:37.056
perpendicular to the radius,

00:08:37.056 --> 00:08:38.576
divided by the radius.

00:08:40.809 --> 00:08:44.318
Or if you solve for tangential velocity,

00:08:44.327 --> 00:08:47.894
you get v is equal to

00:08:48.570 --> 00:08:50.517
is equal to omega r.

00:08:56.882 --> 00:08:59.342
And so if you substitute back into this,

00:08:59.342 --> 00:09:02.767
really this definition
for angular momentum,

00:09:04.996 --> 00:09:07.108
you get angular momentum

00:09:07.108 --> 00:09:11.725
is equal to mass times this times r.

00:09:12.879 --> 00:09:16.067
So mass times, I'm just
substituting for velocity here,

00:09:16.386 --> 00:09:18.478
times omega r,

00:09:20.153 --> 00:09:22.087
times r.

00:09:22.087 --> 00:09:26.621
Which of course is just omega r squared.

00:09:27.108 --> 00:09:29.528
So once again we do the same exercise.

00:09:29.528 --> 00:09:31.304
If our radius goes down,

00:09:31.304 --> 00:09:33.001
what happens to our angular velocity?

00:09:33.001 --> 00:09:34.153
Remember we could measure this in

00:09:34.153 --> 00:09:36.449
angles per second or radians per second,

00:09:36.449 --> 00:09:38.688
well if this is constant,

00:09:38.688 --> 00:09:40.896
remember we're assuming
that there's no net torque

00:09:40.896 --> 00:09:42.194
being applied to the system,

00:09:42.194 --> 00:09:45.521
so we're still in this
world right over here.

00:09:45.713 --> 00:09:47.864
If we assume that this
thing isn't changing,

00:09:47.864 --> 00:09:49.777
but the radius were to change,

00:09:49.777 --> 00:09:52.022
what's going to happen to omega?

00:09:52.022 --> 00:09:54.150
Well omega is going to go,

00:09:54.150 --> 00:09:56.190
omega is going to go up.

00:09:56.190 --> 00:09:58.817
Now likewise, if the radius got longer,

00:10:01.416 --> 00:10:03.025
So the radius got longer,

00:10:03.025 --> 00:10:04.589
what's going to happen to omega?

00:10:04.589 --> 00:10:06.217
Omega is going to go,

00:10:06.217 --> 00:10:08.169
omega is going to go down.

00:10:08.169 --> 00:10:10.305
So if you reduce the radius

00:10:10.305 --> 00:10:12.313
you're going to start spinning faster

00:10:12.313 --> 00:10:13.929
if you increase that radius,

00:10:13.929 --> 00:10:15.903
you're gonna start spinning slower.

00:10:15.903 --> 00:10:17.184
And you have seen this,

00:10:17.184 --> 00:10:18.774
or I think there's a high likelihood

00:10:18.774 --> 00:10:19.878
that you have seen this

00:10:19.878 --> 00:10:23.160
probably at the Olympics when
you have seen figure skaters.

00:10:23.160 --> 00:10:24.866
Where they might start spinning

00:10:24.866 --> 00:10:26.377
and they have their arms out.

00:10:26.377 --> 00:10:27.498
So when their arms are out

00:10:27.498 --> 00:10:29.218
you could say that their
radius is further out.

00:10:29.218 --> 00:10:30.413
And obviously a figure skater is

00:10:30.413 --> 00:10:33.514
a much more complex
system than a point mass.

00:10:33.514 --> 00:10:34.686
You could imagine a figure skater is

00:10:34.686 --> 00:10:36.641
a bunch of point masses.

00:10:37.656 --> 00:10:39.303
Well you could just model a figure skater

00:10:39.303 --> 00:10:41.105
as a huge number of point masses

00:10:41.105 --> 00:10:41.895
at different radii,

00:10:41.895 --> 00:10:44.311
and you would wanna sum
up their angular momentum,

00:10:44.311 --> 00:10:47.428
but the essence of what is happening is

00:10:47.428 --> 00:10:49.605
is when her arm is out

00:10:49.605 --> 00:10:52.509
the average radius when you're calculating

00:10:52.509 --> 00:10:55.874
all of the point masses in
her arms and all the rest,

00:10:55.874 --> 00:10:58.066
the average radius is higher.

00:10:58.066 --> 00:10:59.938
And then when she pulls them in,

00:10:59.938 --> 00:11:02.238
when she pulls them in
that radius goes down,

00:11:02.238 --> 00:11:05.730
and her angular velocity goes up.

00:11:05.851 --> 00:11:07.424
And you see that. They start spinning,

00:11:07.424 --> 00:11:08.957
and then without applying any torque,

00:11:08.957 --> 00:11:10.277
when they pull their arms in

00:11:10.277 --> 00:11:11.805
they start spinning faster.

00:11:11.805 --> 00:11:13.070
And then if they push their arms out,

00:11:13.070 --> 00:11:14.837
once again without applying any torque,

00:11:14.837 --> 00:11:16.802
they start spinning slower.


Average height of a building's floor

WEBVTT
Kind: captions
Language: en

00:00:00.782 --> 00:00:02.791
- The new headquarters of Khan Academy

00:00:02.791 --> 00:00:05.263
is at 314 Math Avenue.

00:00:05.263 --> 00:00:07.005
It has 200 windows

00:00:07.005 --> 00:00:08.862
and has seven stories.

00:00:08.862 --> 00:00:11.799
The parking lot can fit 90 cars.

00:00:11.799 --> 00:00:15.051
The building itself is 63 feet tall.

00:00:15.051 --> 00:00:17.639
How tall is each story?

00:00:17.639 --> 00:00:19.763
So, I encourage you to pause this video

00:00:19.763 --> 00:00:22.967
and try this on your own.

00:00:22.967 --> 00:00:24.140
So let's try to answer it.

00:00:24.140 --> 00:00:27.425
They're asking us how tall is each story?

00:00:27.425 --> 00:00:29.062
So, what information do we need?

00:00:29.062 --> 00:00:32.045
Well, we definitely
don't need the address.

00:00:32.045 --> 00:00:34.878
We don't care how many windows it has.

00:00:34.878 --> 00:00:37.142
Now, the number of
stories seems interesting,

00:00:37.142 --> 00:00:38.187
especially because they tell us

00:00:38.187 --> 00:00:39.638
the total number of feet

00:00:39.638 --> 00:00:41.240
or the total height of the building.

00:00:41.240 --> 00:00:42.401
For example, they tell us

00:00:42.401 --> 00:00:44.444
that the building is 63 feet tall.

00:00:44.444 --> 00:00:46.417
So, this height right over here,

00:00:46.417 --> 00:00:50.422
the building's height is 63 feet tall

00:00:50.422 --> 00:00:52.837
and they tell us that
it has seven stories.

00:00:52.837 --> 00:00:54.346
Seven stories.

00:00:54.346 --> 00:00:58.235
So, one, two, three, four,

00:00:58.235 --> 00:01:01.126
five, six and seven.

00:01:01.126 --> 00:01:03.018
So it has seven stories.

00:01:03.018 --> 00:01:06.814
So if we divide 63 by seven,

00:01:06.814 --> 00:01:09.821
we should figure out
how tall each story is.

00:01:09.821 --> 00:01:10.576
So let's do that.

00:01:10.576 --> 00:01:13.339
We're going to divide 63 feet

00:01:13.339 --> 00:01:14.836
divided by,

00:01:14.836 --> 00:01:17.738
divided by seven stories

00:01:17.738 --> 00:01:18.841
and this is going to tell us

00:01:18.841 --> 00:01:21.279
how tall each story is.

00:01:21.279 --> 00:01:25.342
So that's going to be
equal to question mark.

00:01:25.342 --> 00:01:27.873
Now, 63 divided by seven

00:01:27.873 --> 00:01:29.533
be equal to question mark.

00:01:29.533 --> 00:01:30.938
This is another way of saying

00:01:30.938 --> 00:01:32.935
that seven times question mark

00:01:32.935 --> 00:01:34.641
is going to be equal to 63.

00:01:34.641 --> 00:01:35.895
Let me write that down.

00:01:35.895 --> 00:01:37.638
So this is another way of saying

00:01:37.638 --> 00:01:41.258
that 63 is equal to,

00:01:41.258 --> 00:01:43.580
is equal to seven,

00:01:43.580 --> 00:01:46.413
seven times,

00:01:46.413 --> 00:01:48.711
times question mark.

00:01:48.711 --> 00:01:50.557
Times question mark.

00:01:50.557 --> 00:01:51.614
So, if we can figure out

00:01:51.614 --> 00:01:53.517
what do we have to multiply seven by

00:01:53.517 --> 00:01:54.597
to get to 63,

00:01:54.597 --> 00:01:57.894
then we know what 63 divided by seven is.

00:01:57.894 --> 00:01:58.718
And to do that,

00:01:58.718 --> 00:02:01.516
I'm just going to skip count by seven.

00:02:01.516 --> 00:02:04.012
So, let's start with seven.

00:02:04.012 --> 00:02:06.496
So seven times one is seven.

00:02:06.496 --> 00:02:07.878
Seven, so let me just write this.

00:02:07.878 --> 00:02:09.573
Seven times one is seven.

00:02:09.573 --> 00:02:12.510
Seven times two is 14.

00:02:12.510 --> 00:02:16.492
Seven times three is 21.

00:02:16.492 --> 00:02:19.615
Seven times four is 28.

00:02:19.615 --> 00:02:22.331
Notice I'm just adding by seven each time.

00:02:22.331 --> 00:02:25.489
Seven times five is 35.

00:02:25.489 --> 00:02:29.053
Seven times six is 42.

00:02:29.053 --> 00:02:32.733
Seven times seven is 49.

00:02:32.733 --> 00:02:36.807
Seven times eight is 56.

00:02:36.807 --> 00:02:38.096
Just adding seven.

00:02:38.096 --> 00:02:41.637
Seven times nine is 63.

00:02:41.637 --> 00:02:44.934
So we see, seven times nine is 63.

00:02:44.934 --> 00:02:48.486
So the question mark
must be equal to nine.

00:02:48.486 --> 00:02:52.596
Question mark must be equal to nine.

00:02:52.596 --> 00:02:55.951
So we can write that 63 divided by seven,

00:02:55.951 --> 00:03:00.734
63, 63 divided by seven,

00:03:00.734 --> 00:03:01.709
let me do the same colors

00:03:01.709 --> 00:03:03.566
that I just used,

00:03:03.566 --> 00:03:08.566
63 divided by seven is equal to nine.

00:03:08.906 --> 00:03:11.228
Divided by seven is equal to nine.

00:03:11.228 --> 00:03:12.029
And let's,

00:03:12.029 --> 00:03:12.830
let's think about that.

00:03:12.830 --> 00:03:14.873
We're saying that if we take 63 feet

00:03:14.873 --> 00:03:16.766
and divide it into seven equal stories,

00:03:16.766 --> 00:03:19.563
that each story is going
to be nine feet on average.

00:03:19.563 --> 00:03:21.409
Does that make sense?

00:03:21.409 --> 00:03:23.046
So, does it make sense

00:03:23.046 --> 00:03:25.090
that each of these,

00:03:25.090 --> 00:03:28.723
each of these stories are
going to be nine feet?

00:03:28.723 --> 00:03:30.046
Well, we have seven of them,

00:03:30.046 --> 00:03:31.033
so it should be,

00:03:31.033 --> 00:03:33.123
just the first story should be nine feet.

00:03:33.123 --> 00:03:34.330
By the time we get to the second story,

00:03:34.330 --> 00:03:35.863
we should be at 18 feet.

00:03:35.863 --> 00:03:37.267
I'm adding by nine now.

00:03:37.267 --> 00:03:39.183
Third story, the top of the third story

00:03:39.183 --> 00:03:40.889
should be 27 feet.

00:03:40.889 --> 00:03:45.649
Top of the fourth story
is going to be 36 feet.

00:03:45.649 --> 00:03:49.747
Top of the fifth story
is going to be 45 feet.

00:03:49.747 --> 00:03:54.747
Top of the sixth story
is going to be 54 feet.

00:03:54.948 --> 00:03:57.444
And then the top of the seventh story,

00:03:57.444 --> 00:03:58.883
which is also the top of the building,

00:03:58.883 --> 00:04:01.286
is going to be 63 feet.

00:04:01.286 --> 00:04:03.945
So, if each floor is nine feet high,

00:04:03.945 --> 00:04:05.849
you just have to keep adding nine

00:04:05.849 --> 00:04:07.126
every time you add a floor

00:04:07.126 --> 00:04:08.461
and you see if you do that,

00:04:08.461 --> 00:04:10.039
if you have seven floors

00:04:10.039 --> 00:04:12.245
you're going to get to 63 feet.

00:04:12.245 --> 00:04:13.267
So it completely makes sense,

00:04:13.267 --> 00:04:17.719
each story is nine feet tall.


Blueberries for friends

WEBVTT
Kind: captions
Language: en

00:00:00.436 --> 00:00:04.021
- Kali is having a picnic
for her six friends.

00:00:04.021 --> 00:00:06.842
The oldest friend,
Vikram, is 10 years old.

00:00:06.842 --> 00:00:09.907
The youngest, Diya, is six years old.

00:00:09.907 --> 00:00:12.020
She has a total of 48 blueberries

00:00:12.020 --> 00:00:13.808
and wants to split them evenly

00:00:13.808 --> 00:00:15.480
between her friends.

00:00:15.480 --> 00:00:18.928
How many blueberries does each friend get?

00:00:18.928 --> 00:00:20.019
And I encourage you to now,

00:00:20.019 --> 00:00:21.307
pause this video

00:00:21.307 --> 00:00:22.688
and try to figure it out on your own.

00:00:22.688 --> 00:00:26.763
How many blueberries does each friend get?

00:00:26.763 --> 00:00:28.226
Let's think about this a little bit.

00:00:28.226 --> 00:00:30.606
So she has six friends.

00:00:30.606 --> 00:00:31.684
She has six friends

00:00:31.684 --> 00:00:33.438
and she wants them all

00:00:33.438 --> 00:00:35.587
to be able to get the same amount.

00:00:35.587 --> 00:00:38.721
So, she wants to split
the 48 blueberries evenly

00:00:38.721 --> 00:00:39.939
amongst her six friends.

00:00:39.939 --> 00:00:42.145
The ages of her friends don't matter.

00:00:42.145 --> 00:00:44.689
So, she's going to take
the 48 blueberries.

00:00:44.689 --> 00:00:46.661
She's going to take the 48 blueberries

00:00:46.661 --> 00:00:48.565
and divide it,

00:00:48.565 --> 00:00:50.237
and divide it

00:00:50.237 --> 00:00:51.305
by six.

00:00:51.305 --> 00:00:53.882
She wants to divide it into six groups.

00:00:53.882 --> 00:00:57.806
So she wants to divide it into six groups.

00:00:57.806 --> 00:01:00.337
48 divided by 6.

00:01:00.337 --> 00:01:01.713
And so this,

00:01:01.713 --> 00:01:03.065
so question mark,

00:01:03.065 --> 00:01:06.060
is going to be equal to
the number of blueberries

00:01:06.060 --> 00:01:08.834
that each friend gets.

00:01:08.834 --> 00:01:11.922
So 48 divided by six is
equal to question mark,

00:01:11.922 --> 00:01:13.954
is the same thing as saying

00:01:13.954 --> 00:01:16.044
that 48,

00:01:16.044 --> 00:01:18.621
48 is equal to,

00:01:18.621 --> 00:01:23.044
is equal to question mark times six,

00:01:23.044 --> 00:01:24.623
times six.

00:01:24.623 --> 00:01:25.760
So if we could figure out

00:01:25.760 --> 00:01:28.117
what number we can multiply by six

00:01:28.117 --> 00:01:29.813
to get 48,

00:01:29.813 --> 00:01:32.598
then we know what 48 divided by six

00:01:32.598 --> 00:01:33.921
actually is.

00:01:33.921 --> 00:01:35.361
For example, this question mark,

00:01:35.361 --> 00:01:37.416
this is the number of
blueberries per friend.

00:01:37.416 --> 00:01:41.653
The number of blueberries
per friend times six friends,

00:01:41.653 --> 00:01:43.777
well that should tell us the
total number of blueberries,

00:01:43.777 --> 00:01:45.542
which is 48.

00:01:45.542 --> 00:01:47.562
So what is this number?

00:01:47.562 --> 00:01:48.560
Well, let's think about,

00:01:48.560 --> 00:01:49.512
let's just think about

00:01:49.512 --> 00:01:51.857
all of the multiples of six.

00:01:51.857 --> 00:01:56.177
So, six times one is equal to six.

00:01:56.177 --> 00:01:59.357
Six times two is equal to 12.

00:01:59.357 --> 00:02:02.178
And really we're just
increasing by six each time.

00:02:02.178 --> 00:02:04.534
We're just increasing by six.

00:02:04.534 --> 00:02:07.878
Six times three is equal to 18.

00:02:07.878 --> 00:02:10.954
Six times four is equal to 24.

00:02:10.954 --> 00:02:15.099
Six times five is equal to 30.

00:02:15.099 --> 00:02:18.697
Six times six is equal to 36.

00:02:18.697 --> 00:02:21.495
Six times seven is equal to 42.

00:02:21.495 --> 00:02:23.573
Notice we're just adding six every time.

00:02:23.573 --> 00:02:27.834
Six times eight is equal to 48.

00:02:27.834 --> 00:02:29.993
Is equal to 48.

00:02:29.993 --> 00:02:32.350
So we now know that question mark,

00:02:32.350 --> 00:02:35.948
we now know that the
question mark must be eight.

00:02:35.948 --> 00:02:36.889
Six times eight

00:02:36.889 --> 00:02:38.793
and eight times six is the same thing.

00:02:38.793 --> 00:02:40.155
So this is going to be equal

00:02:40.155 --> 00:02:42.716
to six times question mark.

00:02:42.716 --> 00:02:46.408
Six times question mark

00:02:46.408 --> 00:02:47.569
and now we learned

00:02:47.569 --> 00:02:50.332
that question mark is equal to 48.

00:02:50.332 --> 00:02:53.246
Sorry, question mark is equal to eight.

00:02:53.246 --> 00:02:54.407
So, each of her friends

00:02:54.407 --> 00:02:56.473
are going to get eight blueberries.

00:02:56.473 --> 00:02:57.588
So this is, right over here,

00:02:57.588 --> 00:03:02.588
48 divided by six is equal
to eight blueberries.

00:03:03.973 --> 00:03:05.807
Now, let's verify that.

00:03:05.807 --> 00:03:08.233
We have 48 blueberries right over here.

00:03:08.233 --> 00:03:10.474
Lets divide them into six groups

00:03:10.474 --> 00:03:13.852
where each group is going
to have eight blueberries.

00:03:13.852 --> 00:03:15.024
So let me do my best.

00:03:15.024 --> 00:03:17.385
So let's see, this is one, two,

00:03:17.385 --> 00:03:22.385
three, four, five, six, seven, eight.

00:03:22.930 --> 00:03:25.426
So, that's a group of eight blueberries.

00:03:25.426 --> 00:03:28.630
See, here's another group
of eight blueberries,

00:03:28.630 --> 00:03:30.627
right over here.

00:03:30.627 --> 00:03:33.610
And there's another
group, right over here,

00:03:33.610 --> 00:03:35.944
of eight blueberries.

00:03:35.944 --> 00:03:37.929
And then, here's our fourth group

00:03:37.929 --> 00:03:40.193
of eight blueberries.

00:03:40.193 --> 00:03:40.912
And now, let's see,

00:03:40.912 --> 00:03:43.052
we can make a fifth group

00:03:43.052 --> 00:03:45.544
of eight blueberries.

00:03:45.544 --> 00:03:47.425
Fifth group of eight blueberries.

00:03:47.425 --> 00:03:48.390
And then, finally,

00:03:48.390 --> 00:03:50.722
here is our sixth group.

00:03:50.722 --> 00:03:51.987
Here is our sixth group

00:03:51.987 --> 00:03:54.031
of eight blueberries.

00:03:54.031 --> 00:03:54.729
So notice,

00:03:54.729 --> 00:03:56.921
we have six groups of eight blueberries.

00:03:56.921 --> 00:03:58.349
Each of her six friends

00:03:58.349 --> 00:04:00.160
could take one of these groups

00:04:00.160 --> 00:04:01.873
of eight blueberries.


Liters of soda for the party

WEBVTT
Kind: captions
Language: en

00:00:01.085 --> 00:00:05.866
So we're asked, "how many liters of
soda do we have for the party?"

00:00:05.896 --> 00:00:08.337
And they give us all of this other
information.

00:00:08.403 --> 00:00:12.907
I encourage you to pause this video
and think about which of this information

00:00:12.907 --> 00:00:17.049
you actually need to answer this first
question and then try to answer the question:

00:00:17.049 --> 00:00:20.879
"How many liters of soda do we have
for the party?" So pause now.

00:00:21.209 --> 00:00:23.501
Let's look at this information:

00:00:23.501 --> 00:00:29.159
"20 people are coming to the party."
This doesn't let us know how many liters we actually have.

00:00:29.205 --> 00:00:31.358
So we know we can ignore this.

00:00:31.446 --> 00:00:38.779
"We have purchased 5 bottles of soda for the party."
Well, this seems useful - we're going to have 5 bottles of soda.

00:00:38.837 --> 00:00:54.442
So that's 1... 2... 3.... 4.... and 5 bottles of soda.
That's this piece of information right over here.

00:00:54.523 --> 00:00:59.694
If only we now knew how much soda is in each bottle.

00:00:59.856 --> 00:01:04.373
"The party will last for 3 hours." This has nothing
to do with how many liters of soda we have.

00:01:04.447 --> 00:01:12.785
"Each bottle has 2 liters of soda." This
is interesting.

00:01:12.791 --> 00:01:18.719
This is 2 liters... this is 2 liters... this is 2 liters...
this is 2 liters... and that is 2 liters.

00:01:18.729 --> 00:01:24.227
If we wanted to figure out the total number
of liters of soda we have,

00:01:24.277 --> 00:01:31.919
We have 5 bottles, and each of them are
2 liters each. So we have 5 times 2

00:01:32.049 --> 00:01:34.423
And what is that equal to?

00:01:34.449 --> 00:01:40.926
5 times 2 is the same thing as
2 plus 2 plus 2 plus 2 plus 2

00:01:41.258 --> 00:01:50.527
You have five 2's added together.
Let me write this down...

00:01:50.597 --> 00:01:56.988
Which is equal to: 2, 4, 6, 8, 10.
5 times 2 is 10.

00:01:57.245 --> 00:02:01.542
We have 10 liters of soda for the party.
We're able to answer it without even looking

00:02:01.627 --> 00:02:06.027
at this last one. This last one tells us how
many bottles of soda we had for the picnic last week.

00:02:06.198 --> 00:02:10.967
which doesn't seem related at all
to our current party.


Unknowns with multiplication and division

WEBVTT
Kind: captions
Language: en

00:00:00.937 --> 00:00:05.124
- I have six equations here,
where there is an unknown.

00:00:05.124 --> 00:00:08.549
What I want you to do, is
pause the video right now

00:00:08.549 --> 00:00:11.346
and try to figure out
what that unknown is.

00:00:11.346 --> 00:00:14.009
So, in this first one,
the unknown is a blank.

00:00:14.009 --> 00:00:16.467
What is this blank? What
is this question mark?

00:00:16.467 --> 00:00:17.686
What is this smiley face?

00:00:17.686 --> 00:00:20.704
What does this letter A need
to be in terms of a number?

00:00:20.704 --> 00:00:22.543
What is B? What is this star?

00:00:22.543 --> 00:00:25.478
So, pause the video now.

00:00:25.478 --> 00:00:27.054
So, let's think through each of them.

00:00:27.054 --> 00:00:31.187
This says three times
something is equal to 12.

00:00:31.187 --> 00:00:32.592
So, let's think about
what we have to multiply

00:00:32.592 --> 00:00:35.053
by three to get to 12.

00:00:35.053 --> 00:00:39.255
So, three times one is three,
three times two is six.

00:00:39.255 --> 00:00:44.219
Three times three is nine,
three times four is 12.

00:00:44.959 --> 00:00:47.126
Three times four is 12, so we could say

00:00:47.126 --> 00:00:50.499
that the blank needs to be equal to four.

00:00:50.499 --> 00:00:53.204
Three times four is 12.

00:00:53.204 --> 00:00:54.591
Now, let's work on this one.

00:00:54.591 --> 00:00:57.470
Something divided by, so question mark

00:00:57.470 --> 00:01:01.789
divided by four is equal to six.

00:01:01.789 --> 00:01:04.846
Well, this is the same thing as saying

00:01:04.846 --> 00:01:09.846
that question mark is
equal to four times six,

00:01:10.662 --> 00:01:13.204
or you could say six times
four, they're the same.

00:01:13.204 --> 00:01:15.305
It is equal to six times four,

00:01:15.305 --> 00:01:19.789
which is the same thing as four times six.

00:01:19.789 --> 00:01:22.344
So, what is six times four?

00:01:22.344 --> 00:01:26.003
Well six times one is six,
six times two is twelve,

00:01:26.003 --> 00:01:31.003
six times three is eighteen,
six time four is 24.

00:01:31.477 --> 00:01:34.089
So, question mark, so this is equal to 24,

00:01:34.089 --> 00:01:37.769
so question mark must be equal to 24.

00:01:37.769 --> 00:01:39.266
Write that down, question mark,

00:01:39.266 --> 00:01:42.401
in this case, is equal to 24.

00:01:42.401 --> 00:01:47.265
Now, here I have 54 is equal
to nine times smiley face.

00:01:47.265 --> 00:01:49.928
So, nine times what is equal to 54?

00:01:49.928 --> 00:01:51.314
Well, let's just skip count with nine

00:01:51.314 --> 00:01:53.113
and try to figure that out.

00:01:53.113 --> 00:01:56.492
Nine times one is nine.
Nine times two is 18.

00:01:56.492 --> 00:01:59.816
Nine times three is 27,
notice I'm just adding nine

00:01:59.816 --> 00:02:03.551
each time, nine times four is 36.

00:02:03.551 --> 00:02:08.551
Nine times five is 45.
Nine times six is 54.

00:02:10.265 --> 00:02:13.384
This is 54 is nine times six.

00:02:13.384 --> 00:02:16.430
Nine times six is equal to 54.

00:02:16.430 --> 00:02:19.238
So, we now know that the smiley face,

00:02:19.238 --> 00:02:23.623
so smiley face must be equal to six.

00:02:23.623 --> 00:02:25.610
If we replace the smiley face with a six,

00:02:25.610 --> 00:02:27.262
then this equation is true.

00:02:27.262 --> 00:02:31.501
54 is equal to nine times six.

00:02:31.501 --> 00:02:33.243
Let's work on this one up here.

00:02:33.243 --> 00:02:38.194
Nine is equal to A divided by eight.

00:02:38.194 --> 00:02:41.461
Well, this is the same thing
as saying that if A divided by

00:02:41.461 --> 00:02:43.977
eight is equal to nine, well that means

00:02:43.977 --> 00:02:47.390
that nine times eight must be equal to A.

00:02:47.390 --> 00:02:52.390
Nine times eight must be equal to A.

00:02:52.869 --> 00:02:56.327
If I divide A into eight
groups and I have nine

00:02:56.327 --> 00:02:59.962
in each group, that means
if I have nine in a group

00:02:59.962 --> 00:03:04.064
times eight groups, I must have
the total number of things.

00:03:04.064 --> 00:03:06.057
So, what is nine times eight?

00:03:06.057 --> 00:03:08.843
Well, nine times one is nine,
in fact we already did a lot

00:03:08.843 --> 00:03:10.546
of our nine times tables down here,

00:03:10.546 --> 00:03:12.120
we could just keep going.

00:03:12.120 --> 00:03:16.900
Nine times six was 54,
nine times seven is 63.

00:03:16.900 --> 00:03:21.900
Nine times eight is 72,
so nine times eight,

00:03:22.939 --> 00:03:25.755
nine times eight is equal to 72.

00:03:25.755 --> 00:03:30.755
So, we can say that A is equal to 72

00:03:30.793 --> 00:03:34.157
and if A is equal to 72,
then this equation becomes

00:03:34.157 --> 00:03:38.359
nine is equal to 72 divided by eight,

00:03:38.359 --> 00:03:39.971
which is absolutely true.

00:03:39.971 --> 00:03:44.971
72 divided by eight is nine,
nine times eight is 72.

00:03:44.973 --> 00:03:48.995
B is equal to 20 divided by five.

00:03:48.995 --> 00:03:51.297
Well, what's 20 divided by 5?

00:03:51.297 --> 00:03:52.920
Well, there's a couple of
ways you could think about it.

00:03:52.920 --> 00:03:55.091
You could literally view this
as the same thing as saying

00:03:55.091 --> 00:03:59.245
that five times B is equal to 20.

00:03:59.245 --> 00:04:01.996
So, five times what is equal to 20?

00:04:01.996 --> 00:04:05.317
Five times one is five,
five times two is 10.

00:04:05.317 --> 00:04:10.313
Five times three is fifteen,
five times four is 20.

00:04:10.543 --> 00:04:14.348
Five times four is equal
to 20, so that tells us

00:04:14.348 --> 00:04:18.225
that B, B must be equal to four.

00:04:18.225 --> 00:04:22.346
B is equal to four, so we could write four

00:04:22.346 --> 00:04:26.946
is equal to 20 divided by
five, which is absolutely true.

00:04:26.946 --> 00:04:28.939
If 20 divided by five is equal to four,

00:04:28.939 --> 00:04:32.027
four is equal to 20 divided by five.

00:04:32.027 --> 00:04:33.789
Now, we have one last one.

00:04:33.789 --> 00:04:38.789
We have star times two is
equal to four, is equal to 14.

00:04:39.497 --> 00:04:42.620
So, what times two is equal to 14?

00:04:42.620 --> 00:04:45.279
Well, let's just look at
our two, alright, our two,

00:04:45.279 --> 00:04:46.881
our multiples of two.

00:04:46.881 --> 00:04:51.181
So, let's see if two times
one is two, four, six, eight,

00:04:51.181 --> 00:04:55.461
10, 12, 14, so how did, how many times

00:04:55.461 --> 00:04:57.601
did we have to multiply two to get to 14?

00:04:57.601 --> 00:05:02.534
So, this is one, two, three,
four, five, six, seven.

00:05:02.534 --> 00:05:07.212
Two times seven is 14, so
if I wrote seven times two

00:05:07.212 --> 00:05:10.794
is equal to 14, this is absolutely true.

00:05:10.794 --> 00:05:14.219
So, star must be equal to seven.

00:05:14.219 --> 00:05:17.301
Star is equal to seven.