Man it is a rainy, lazy day here in Los Angeles and I am tirey-wheeled.
That’s okay.
I can keep it together and stay awake and
you should too because this is episode two
of the Learning Lounge.
Today we are going to talk about the Spoke
Blur Effect, something I learned about recently
and have since become dangerously obsessed
with.
When I’m driving on the road, I find myself
watching not the road ahead of me but the
tires of the cars near me, just to see the
effect happen.
Now if you have ever seen a rolling wheel,
whether by itself, or as part of a car, or
bike or sandwich, you may have noticed that
no matter what direction the wheel is rolling
in, the spokes at the bottom are clearer,
less blurry than those at the top.
Next time you see a rolling wheel pay attention
because this effect is everywhere but why
does it happen?
Wow the rain is really coming down right now
but that’s not going to stop me.
I get inside your brain rain or shine.
Now look, when things move quickly they can become blurry like the spokes on this wheel
while the wheel is turning.
Right now, the spokes are blurry everywhere all over the wheel but when the wheel rolls,
the bottom region is at all times less blurry
than the top.
I can make the most clearly distinguishable
be on the top, the right, the left, or anywhere
in between.
Look closely and follow the region with the
clearest spokes and note that region’s location
relative to the direction I’m translation
the wheel.
Now from your frame of reference, at rest
with me and this room, every part of a rotating
disc that’s not the very center of rotation
is accelerating it’s velocity.
That is it’s speed and direction at any
given moment of time is different than it
was the moment before.
For example, the point represented by this
red dot may at one moment be traveling due
left.
Then a bit left and up.
Then due up.
A bit up and right.
Due right.
Down and right.
Due down.
A bit down and left and over and over again.
The speed of its motion is what causes it
to be blurry.
If I rotate the disc fast enough, before the
camera or my eye can resolve a clear image
of the dot and the region it’s in it will
have moved somewhere else.
The blur inducing motion doesn’t have to
be from rotation.
I could also just translate the disc back
and forth fast enough to fuzzify it.
But what if I did both?
What if I rotated the disc while simultaneously
translating it.
Well then the motion from both of those transformations
would combine.
If during some brief amount of time a part
of the wheel rotates two centimeters to the
left but translates two centimeters to the
right it’s position after that interval
will be the same as before.
It will have been motionless for us and motionless
means not blurry.
And as it turns out this is exactly what happens
during rolling.
Pure rolling is a special combination of rotation
and translation in which a rotating thing
translates across a surface such that the
point where the rotating thing contacts the
surface is instantaneously motionless relative
to the surface.
I mean if that wasn’t true.
If the instantaneous contact point had some
velocity that was non-zero relative to the
road while touching it the wheel wouldn’t
be purely rolling.
It would be sliding as well.
If a wheel is rolling at any given moment
parts of the bottom of the wheel are moving
down or up with a little backwards motion
due to rotation which is opposite the forward
translational motion of the wheel and it’s
vehicle.
The point at the very bottom of the wheel
is in fact only moving directly opposite the
forward motion of the vehicle and with the
same speed so the two velocities cancel out
making it relative to the road or you standing
on the road watching instantaneously motionless.
So if you are not sliding, no matter how fast
your speedometer says you’re going, the
part of your tire that happens to be at any
specific instant in time touching the road
isn’t moving across the road at all.
On the other hand parts of the top half of
the wheel all have a horizontal velocity in
the same direction of the car.
The car’s forward motion and their rotational
forward motion combine into a velocity faster
than what your car’s speedometer says.
In fact again when not sliding, only purely
rolling, during the brief moment that a part
of your tire is at the top it is flying past
the road at twice the speed of your car.
Let’s look at this effect again.
While a spoke is in a position where the horizontal
component of its velocity due to rotation
and translation are in the same direction
they combine into a faster overall velocity
so it becomes blurrier but while the spoke
is in a position where its horizontal velocity
due to rotation is in the opposite direction
as its horizontal velocity due to translation
it moves more slowly relative to us watching
and therefore is more clear, less blurry.
It’s very spinteresting.
Ahh it almost sounded like the rain was gonna
die down just in time for us to be done.
Well anyway point is we have arrived at a
life hack.
That’s right the next time you are pulled
over for speeding by the police remind the
officer that while yeah sure maybe your vehicle
was traveling faster than the law allows at
every moment during your journey the point
of your tire that was in contact with the
road was not speeding at all.
In fact it was completely motionless.
If you bring that up you are sure to still
be fined but you will be much more annoying
and as always thanks for watching
