You might have heard of the Orange Bowl.
Possibly you've heard of the Rose Bowl.
I'm guessing you've heard of the Super Bowl.
All of those pale in comparison to our upcoming
competition, the Nerd Bowl!
Soon the sportiest of our lab are gonna
go head-to-head with the most proficient ellipsoid tossers at Sandia National
Laboratories, Facebook
and Stanford Linear Accelerator.
(We call them the slackers.)
Now, to minimize bruised knees, hurt feelings and chronic traumatic
encephalopathy, we're going to proceed with flag football rules for the Nerd
Bowl, where tackling is replaced by removing flags from around your
opponent's waistband.
I'm open! I'm open!
In honor of this competition, today on Learning with Leland we're gonna dig
into the physics governing footballs as they soar through the air. To help me
with this effort is Livermore's
chief football trajectory initializer Jason Laurea.
One of the wonderful things about physics is that seemingly complicated
behavior can often be boiled down into a few simple governing principles.
For our first data point,
let's look at a soon-to-be game-winning toss by
Livermore's quarterback, Jason.
Alright Jason, here's the situation:
It's fourth down, bottom of the ninth,
overtime.
You've got one quiver left in your bow.
Let that baby fly.
You got it.
For our second data point, we're gonna have a less
conventional trajectory thrown by someone a little less athletic than Jason.
Now to protect the innocent, the identity of this person will be hidden.
To help our anonymous thrower along, we're gonna give them some
personal protective equipment.
Ready for action!
(grunts)
Let's watch now our two trajectories side by side.
At first glance, they look
completely different. One is extremely complicated, wobbling and rotating as it
gets to its destination. The other is a very smooth arc. An instant after the
football has been released, there are several forces acting on it.
There's air resistance, which in this case we'll say is small, and of course there's
the force of gravity pulling it down.
The football is made up of billions of tiny
atoms distributed across its ellipsoid shape. We might think that to calculate
its trajectory we need to take into account forces acting on each of these
individual points. That might be a monstrous calculation requiring the
world's largest supercomputers, although we have those here on site, we don't use
them to calculate football trajectories. Instead, a very simple property known as
the center of mass helps us calculate exactly what's going to happen to the
football very easily.
The center of mass on a football is going to be right at
the center of the ball. There's no material there, but that's really the
average position of all of the material making up the football.
That was an awkward toss.
To know where that center of mass is going to go, we just look at the total force
acting everywhere else and pretend it's only acting at that one point.
Let's look at the two trajectories again, this time paying
close attention to the center-of-mass.
What we see is that the center of mass behaves exactly the same
in the two cases. It's experiencing a uniform acceleration in the Earth's
gravitational field, makes this upside-down U shape that we call a
parabola. From that point, we can consider their different rotations to be a
separate piece of the motion. Once we decompose the motion into these two
pieces, it actually becomes very straight forward.
Step one, we pretend all the mass is located at the center of mass. We know
how that behaves due to constant acceleration. Step two, we can add on the
rotational motion based on its initial conditions. This idea of the center of
mass simplifies the problem, and these two dynamics don't seem so complicated
after all.
Good luck at the Nerd Bowl, Lawrence Livermore National Lab!
This has been Learning with Leland.
Oh that was a good one!