Slow sock on Lubricon VI - Physics, Engineering Video Lecture - Aeronautical Engineering

This is a picture of
the planet Lubricon-VI.
And Lubricon-VI is a
very special planet
because it's made up of
a yet to be discovered
element called Lubrica.
And Lubrica is special
because if anything glides
across the surface
of Lubrica, it
will experience
absolutely no friction.
So if this right over here
is a sheet of Lubrica--
we're looking at
it from the side.
And if we have a brick on top of
it, maybe gliding on top of it
like that, it experiences
absolutely no friction.
Now, the other things we
know about Lubricon-VI
is it's drifting in deep
space and it does not
have an atmosphere.
In fact, it is a complete
vacuum outside of it.
It's in such deep space,
such a remote part of space,
that there aren't even a few
hydrogen atoms right over here.
It is a complete,
absolute vacuum.
And it's also an ancient planet.
The star that it
used to orbit around
has long since died away.
So it's just this lonely
planet drifting in deep space
without an atmosphere.
The other thing we
know about Lubricon-VI
is that it is a perfect sphere.
It is a perfect, perfect sphere.
Now, my question to you.
For some bizarre
reason there happens
to be, on the surface
of Lubricon-VI--
so this right over here is
the surface of Lubricon-VI.
There happens to be a sock that
is frozen in a block of ice.
So this is my sock and its
frozen in this block of ice.
And it happens to be traveling
at 1 kilometer per hour
in that direction.
If we were to look at it
from this kind of macro scale
when we're looking
at the planet,
let's say then that
is the frozen sock,
and it is traveling
along the equator.
It is traveling along the
equator of Lubricon-VI.
So my question to you,
given all of the assumptions
we made that it has
absolutely no atmosphere,
it's a perfect
sphere, and Lubrica
has absolutely no
friction regardless
of what's traveling
on top of it-- what
will happen to this
frozen sock over time?
To answer that question,
we need to think about all
of the forces that
are acting on this,
I guess, frozen block
of ice and sock.
And first of all, let's
think about these forces that
are acting in the radial
direction, inward or outward,
of the center of the planet.
Well, this planet has a mass.
And so you have an inward force
towards the planet's center
of mass.
And so you have the
force of gravity
acting on this
block going radially
inward to the center
of the planet.
So I'll draw it like this.
So we have our force of gravity.
We have our force of gravity
going radially inward,
just like that.
But then we know that
the block is not just
spiraling towards the
center of the earth.
We have the surface here.
It's not going to go through
the surface of Lubrica.
We can also assume that
Lubrica is a very, very, very
strong material.
And so you also
have a normal force.
You also have a
normal force that
is keeping the
block from spiraling
towards the center of the earth.
So this is a normal force.
And one thing we'll
think about now,
and we'll address it
directly in another tutorial,
is whether this normal force is
equal to the force of gravity.
We'll think about that
in a future video.
But these are all
the forces that
are acting in the
radial direction,
either inward towards the
center of the planet or outward.
But if we think about in
the tangential direction,
along the surface of the
planet, there are no net forces.
And because there
are no net forces
in this tangential
direction right over here,
this block will not either
accelerate nor decelerate.
There is no air friction.
Or I should say air
resistance, which is really
just friction with the particles
if you had an atmosphere.
It's a complete vacuum,
so there's nothing there.
There is no friction with
the surface of the planet.
So there's no
friction there, which
could have been a force in
the tangential direction.
So there's absolutely no forces
in the tangential direction.
So this block of
ice will actually
continue to travel at
one kilometer per hour
for all of eternity.
So it'll just continue
to do it given
the assumptions that
we've just made.