FIRST TRANSPARENCY • Marching Onto Stage
Ladies and Gentleman - students of all ages:
Welcome to “Out Juggling In My Class JUG:123(A)”
A celebration of my thirty seven years of
teaching science and mathematics.
That you are here for this
Annual 200X CELEBRATION
means you are outstanding.
We all enjoy a parade!
Right?
SECOND TRANSPARENCY • Physics of WMT
My students inspired this parade graphic.
When I march and toss an object, the flight path looks
like a two dimensional parabola to me.
Perhaps y = 16 - x²/4.
But you see a different parabola.
As I march approximately "pi" mph, you may see
the parabola y = 16 - x²/20.
But I'm ahead of my story with these equations, SO ...
Let me step back and tell you about
"The Principle Of Maximal Aging".
Within the same Earth Time Interval tossed
objects age longer when further from earth.
Also, tossed objects age longer at slower velocities.
Physicist John A. Wheeler* demonstrated a parabolic
relation of height versus time for a tossed object
as shown in this graphic:
THIRD TRANSPARENCY • The Principle Of Maximal Aging
The top green curve has the advantage of aging
longer due to a longer height interval.
The bottom blue curve has the advantage of aging
longer due to slower velocities getting there.
The best balance for longer aging is the
middle red geodesic parabola. YES !
Free fall height equaling a constant times time squared
results from maximizing the object's aging.
We know what that's like - as teenagers we all maximized
our clock age by years / not just nano-ticks of spacetime!
Let's simulate a Gregorian chant to remember this concept:
CHANT Teenagers can be louader than that!
Think back to those days and try again.
CHANT
Good For You!
All Right?
Now, how does the geometry of a tossed
object also take a parabolic pattern?
Galileo answered this question by indicating
that the horizontal component of
this motion fits a linear model.
x = rate * time
"The Principle Of Maximal Aging" - Get higher but go slower.
Poster
FOURTH TRANSPARENCY • Chanting the distance formula
Try Chanting:
CHANT x distance equals rate times time!
How about that: ( WOW )
When we replace time with a fraction of
horizontal distance, t = x/rate, then
the geometry of a parabola triumphs again.
Consider:
y = constant t²
y = constant (x/rate)²
y = (constant/rate²) x²
y = konstant x²
Wheeler's Principle Of Maximal Aging
and Galileo's Horizontal Linear Motion Model
combine to give parabolic flight paths.
Wonderful - but we are not teenagers and time,
- AH - yes time, well, - I won't go there now!
BUT - - your chanting sounds really good!
From your response, I can tell that
you are outstanding in your field.
In a few minutes I'll have you
out standing in the aisles.
I mean standing out in the
aisles for a little fun.
PROP - SHEET OF PAPER or plastic ball
• JUG:004A Basic Numbers Script
Copyright © 1991 through © 2001
with all rights reserved by
William V. Thayer, PedLog