dear mojing
hi it's me austin blah blah blah and i'm
back again you cannot keep me down and
you can
not keep me away at this point you're
starting to become like my pokemon an
infinite well of content fuel for me
[Laughter]
anyway this week we're doing an episode
on something i thought of while i was in
the shower because that's where
all the best ideas come from and it's
stupid and dumb and fun and awesome and
we're gonna learn things about angular
velocity centripetal force gravity and
all kinds of fun things that have to do
with it if by chance you're a
trigonometry teacher and you're trying
to show your class that trig
is awesome instead of tedious this
is the video for you although i do have
to warn you nightmare fuel
like this
does show up in any case the topic i
came up with today that is
stupid and silly is this what
are the consequences of an incredibly
fast
day night cycle in minecraft
for those of you who don't know the date
night cycle in minecraft is
20 minutes long 20 minutes
the designers do this presumably for the
same reason lots of games do this to
make it so you can experience
the full gamut of daylight and night
time in a single playthrough without
having to play for like 12 hours but it
turns out this can have some pretty
amazing consequences once you start to
dig
into the implications of what this
actually means and to get to the heart
of this
let's start simple what is
a day you see we think of a day as being
one 365th of a rotation around the sun
but a cpg
grey points out in this amazing video
about
leap years one day is actually one full
rotation of the earth along its central
axis when it makes one full
360 degree rotation that is one day it
just so happens that the earth spins at
a rate that's
roughly equivalent to 1 365th of a
rotation
around the sun it's this rotation that
makes the sun
appear to rise in the east and set in
the west
in reality the sun is barely moving in
relationship to us but the rotation
of the planet is constantly
repositioning
us in relationship to it on the planet
so sunrise to sunrise that is a
full day on any planet it's this
connection to spinning speed that makes
our problem way more fascinating than it
might seem
at first glance all planets have
different spinning speeds the earth's
takes 24 hours while jupiter
the largest planet spins over twice as
fast as
us at 10 hours per 360 degree rotation
now in order to know the full
consequences of a planet that rotates
once per 20 minutes we gotta know
how big our planet is plus i do have to
address something that comes up
literally
every single freaking time i do
a video on minecraft because people
don't bother
to read the freaking wiki before making
a comment
the minecraft world size is finite
not infinite period there's a world
boundary that appears at coordinates 29
999 984 and what always happens when i
mention this border is that people go
but
austin you can clearly see stuff past
that and
okay you know what screw you i'm gonna
go
past this barrier and using both
teleportation and ender pearls you can
get past the world border and you know
what happens
there's another invisible border at
coordinate
30 million and if if if
if you could somehow get past this
invisible wall you would immediately
fall through the floor into the abyss
and you die because none of these blocks
can be
interacted with at all they functionally
don't
exist they might as well be the sky
painted on the wall at the end of the
truman show so stop
telling me the minecraft world is
infinite
it is not it is at most
60 million blocks by 60 million blocks
or 3.6 quadrillion square meters since
one side of a block is a meter period
[Music]
using the power of math specifically the
square root of the area divided by 4 pi
we can project this surface area onto a
sphere
and figure out its radius which we'll
need for a couple of things
one is to figure out the effects of this
rotational energy and another
to find the density which will become
relevant later the radius of the
minecraft
planet is 16.9 million meters or over
10 000 miles for context this makes the
minecraft world over two and a half
times wider than the earth
yikes next we need to find out the
angular velocity of a sphere that's
rotating around a central axis that's
rotating once
every 20 minutes that's .05 rotations
per minute or
31 radians per minute which drops down
five to .00523 five radians per second
that is our angular velocity now a human
being standing on the surface of the
earth is actually rotating around the
axis of the earth along with it i think
that makes sense right uh with an rpm of
.0006947 and a radius of 6.3 million
meters a person at the equator is
rotating around the center of the earth
at 362 meters per second or over
1 000 miles per hour interestingly
enough this spinning does
create centrifugal force on us as we
stand on the earth as we're
constantly changing velocity thankfully
the earth is much much stronger than
this force
as even at the equator where your
tangential velocity is at its highest
you will only experience
.0336 meters per second per second force
from centrifugal force making you feel
0.34 percent less gravity than you would
at the north or south poles where spin
is minimal this is the same force that
allows you to swing a bucket upside down
over your head as long as you're
spinning it fast enough the constant
change of direction and speed caused by
the rotation around a single point your
shoulder will create a force opposing
the center of rotation
and it can relatively easily be more
powerful than gravity this is also how
halo rings work this is called
centrifugal force and yes i do hear you
back there nitpicking my use of
centripetal and centrifugal but screw
you they're mostly fake names anyway for
an amalgamation of other forces anyway
so get off my back man
i bring all of this up because
oh boy a planet bigger than the earth
spinning
faster than the earth is going to create
some absolutely
nuts forces the tangential velocity you
experience on the earth is a little over
the speed of sound but the tangential
speeds you'll be experiencing on a
minecraft planet
at the equator would be over 88 000
meters per second
that's 10 times faster than the speed of
the halo rings using this formula we can
figure out the acceleration created by
this constant change of velocity which
is
get this 463.85
meters per second per second of
acceleration through the centrifugal
force
holy crap given that gravity on the
minecraft planet is 32.4 meters per
second squared measured by
you know falling this is over 14
minecraft g's of force holy crap this
means that either a
we'd be flying off the planet's surface
immediately at almost and this is not an
exaggeration
200 000 miles per hour
or the planet is actually massive enough
to create enough gravitational pull to
counteract the centrifugal force that is
pulling you upward and away from the
planet's surface
this presents some problems though with
just
32.4 meters per second squared of
minecraft's gravity our minecraft world
would have to be as massive
as 23 earths which you know with it
being as big as it is shouldn't be a
surprise but if it's managing to pull
32.4 meters per second per second of
gravity
after the 463.8 meters per second
squared of centrifugal forces canceled
out
that means it would have a total
gravitational pull of 496.28 meters per
second squared over
15 minecraft g's meaning it would have
to have a mass
of 356 earths that is bigger than
jupiter
furthermore all this mass is shoved into
a space dramatically smaller than
jupiter's the minecraft world which have
a density of over one hundred thousand
kilograms
per cubic meter that's as dense as the
core of the freaking sun which
you know i guess maybe that's why
bedrock is impossible to break outside
of creative mode but
if we accept this as possible this makes
the minecraft world
kinda habitable if a bit far-fetched
with this day night cycle like if we
accept that this clearly
impossible planet could actually exist
there's
way way more to be wary of because if
if all of this is true it means that
there is in theory
a very small band of habitability around
the center
of the world and if you go outside of
that you are
toast okay so remember earlier when i
said at the equator you technically
weigh point three four percent less than
you worth of poles that is because as
you travel
north the radius around which you're
spinning around the center of the earth
becomes
much much smaller meaning your
tangential velocity drops which means
you experience
less change of velocity therefore less
centrifugal force as you can see
here if we drop these numbers down but
it gets even
worse remember centrifugal force is
experienced perpendicular to the axis of
rotation meaning when you're at the
equator the centrifugal force you
experience due to the rotation of the
earth is directly
opposite to gravity but the further
north you go it starts to pull
at an angle to gravity that's because
gravity pulls you toward a point
at the center of the earth but the
centrifugal force pulls you
away from the axis of rotation which
runs along the entire
length of the globe meaning the further
up you go
not only is the spin getting less strong
it's also less directly opposed to
gravity meaning
the centrifugal force drops off
exponentially
not linearly if we're only calculating
the sums of acceleration
at the equator we can easily just
subtract the centrifugal force from
gravity but if we want to calculate it
at any other point we have to use
this mess which does look scary but it's
actually just the pythagorean theorem at
minecraft's poles centrifugal force
falls to zero and you would experience
the full
50 earth g's of gravity even if we take
into account the likelihood
that steve and alex can survive stronger
g-forces than us at around the 10 degree
latitude mark they'd be
experiencing over three minecraft g's
meaning that the average earthling
instead of weighing around
70 kilos would weigh 210 kilos or
450 pounds this is pretty much the limit
of what is a
habitable zone this would kind of be
like if humans could only live
on this narrow strip of earth or risk
being crushed to death by gravity
kind of amazingly though since minecraft
is so big
it would actually take you an extremely
long time to reach this border it's over
1500 kilometers north or south which
traveling at the fastest method in the
game means it'd take over 13
hours of rocket-fueled flight to reach
you can cut this down to a little over
90 minutes if you use the nether but
still
that's a long long time to travel you'd
likely
never get this far in a single game of
minecraft unless you dedicated your
entire play
time to traveling directly north or
directly south but aside from this
the storms on the planet would be out of
this world the rotation of planets is
what causes things like hurricanes and
things like the red spot on jupiter this
planet spinning around at 88 000 meters
per second would create the most
destructive
storms you have ever seen and past this
10 degree boundary that's only 3 000
kilometers wide the world would get
really flat like gravity would just be
too strong
for things like hills to stay formed
they just get pulled down
instantly you know in fact i'm pretty
sure that something this massive
spinning this fast couldn't even
hold the shape of a sphere but you know
that's a story for a different time so
there you have it we did it minecraft
is impossible who would have thought
that a game that's about building stuff
with square blocks would be unrealistic
this also arguably goes for every other
game with a truncated day night cycle i
think that means that like uh world of
warcraft and the modern pokemon games
are the only safe places to live i don't
have anything
sassy to say or anything to yell about
this was just a really really fun math
problem for me to work out oh
and if you are a trig teacher trying to
make this into a fun
exercise in your class here is all the
formulas i used albeit rearranged and
simplified whenever possible to
save my editor all of it was centered
around using the arc length to reverse
engineer angles and gravity but you can
do all this work with all these tools
and these known numbers
have fun sincerely austin
you