Transcript Uniform Motion - artphysics123

Upcoming
Deadlines
Pick up a clicker, find
the right channel, and
enter Student ID
Fifth Homework (Video Analysis of a Jump)
Due Wednesday, Feb. 24th (Next week)
15 points (10 points if late)
Sixth Homework (Stop-motion Animation)
Due Wednesday, March 3rd (In two weeks)
20 points (if late, 10 points)
Bonus prize of 20 extra points to top three.
For full schedule, visit course website:
ArtPhysics123.pbworks.com
Activating your Clicker
* Turn on your clicker.
* Enter the channel number or letter for
joining this class. Hit Enter/Send key.
* Clicker should read AP123S258
* Type in your student ID; hit Enter/Send.
Clicker is now ready to use; leave it on.
Hit any key to wake
the clicker from
sleep mode.
Extra Credit Opportunity
Go to any event at Cinequest Film
Festival in downtown San Jose.
Turn in proof of attendance
(receipt, photos, etc.) for
5 points of extra credit.
Extra Credit Opportunity
Attend the Game Developer’s
Conference in San Francisco,
on Saturday, March 13th
Student registration is $75 (ouch)
Turn in your receipt for 10 points
of extra credit.
For info: www.gdconf.com
Homework Assignment #5
In this assignment you’ll again use Tracker
software to analyze the motion of a moving
object from video reference.
First, shoot some reference of yourself
doing a running jump.
Position your camera so that you're in frame
the entire time that you're in the air.
Stage the jump to be in profile.
Shoot at least 5 takes, even if they are more
or less the same.
Homework Assignment #5
Original Video Reference
Homework Assignment #5
Import your video reference into the Tracker
software (as in previous homework).
Track the center of your waistline or beltline,
which is approximately the location of your
center of gravity.
Marking your position from the time you leave
the ground until you’ve landed.
After tracking your motion, upload the screen
image from Tracker to your blog into a post
called "Video analysis of path of action".
Homework Assignment #5
Straight Line
Parabolic
Path of Action
Parabolic Curve
Homework Assignment #5
Finally, rewind your video to the first frame
of your jump and from the "File" menu
select "Record -> Quicktime Movie".
Hit the play button and allow the clip to play
until the end of your jump. Next, in the
"Capturing Quicktime MOV" window click
"Save As" to save the recording.
Homework Assignment #5
Video Reference with Tracking
Homework Assignment #5
Check that your saved Quicktime movie has
the track showing the path of action then
put both clips (original and with tracking) in
your blog post using YouTube or Vimeo.
This assignment is due by 8am on
Wednesday, Feb. 24th (week from today).
15 points (10 points if late)
Survey Question
So far the pace of the class has been:
A)Too fast
B)A little fast
C)About right
D)A little slow
E)Too slow
Review Question
The motion graph for a ball drop,
going from the apex until the ball
just touches the ground, looks like:
A)
B)
C)
D)
Motion Graph of a Ball Drop
Height
D)
Frames
Arcs in Animation
Disney’s Principles of Animation
In their classic book, Disney
Animation – The Illusion of Life, Frank
Thomas and Olie Johnston list a set of
basic principles for animation.
1.
2.
3.
4.
5.
Squash & Stretch
Timing
Anticipation
Staging
Follow Through
& Overlapping Action
6. Straight Ahead &
Pose-to-Pose Action
7. Slow In and Slow Out
8. Arcs
9. Exaggeration
10. Secondary Action
11. Appeal
Disney’s Principles of Animation
In their classic book, Disney
Animation
The Illusion
of discussed
Life, Frank
We– have
already
Thomasseveral
and Olieof
Johnston
list a set of
these principles
basic principles
for animation.
of animation,
specifically:
1.
2.
3.
4.
5.
Squash & Stretch
Timing
Anticipation
Staging
Follow Through
& Overlapping Action
6. Straight Ahead &
Pose-to-Pose Action
7. Slow In and Slow Out
8. Arcs
9. Exaggeration
10. Secondary Action
11. Appeal
Disney’s Principles of Animation
In their classic book, Disney
Animation
– The
Illusion
of Life,arcs
Frank
Today
we
will discuss
Thomasand
and how
Olie they
Johnston
list to
a set of
relate
basic principles
formotion.
animation.
animated
1.
2.
3.
4.
5.
Squash & Stretch
Timing
Anticipation
Staging
Follow Through
& Overlapping Action
6. Straight Ahead &
Pose-to-Pose Action
7. Slow In and Slow Out
8. Arcs
9. Exaggeration
10. Secondary Action
11. Appeal
Arcs of Motion
Motion usually follows an
arc, which may be simple,
like a circle, or very
complex and irregular.
Importance of Arcs
Disney animation legends Frank
Thomas and Olie Johnston write:
One of the major problems
for the inbetweeners is
that it is much more
difficult to make a
drawing on an arc.
Drawings made as straight
inbetweens completely kill
the essence of the action.
Right
Wrong
Circular Arcs
Circular arcs are common since
motion is often around a fixed
pivot point, such as a joint.
Speed in Circular Motion
Rotational Speed: Revolutions per second
Tangential Speed: Total distance per second
Same Rotational Speed
Different Tangential Speeds
Throwing Arm
The longer the
throwing arm,
the greater the
tangential speed
so the farther it
can throw.
Sling lengthens
the arm at almost
no cost in the
weight.
Doubling the speed
quadruples the range!
Timing on Circular Arcs
A circular arc is a simple path of action but
the timing may be complex and textured.
In this golf swing the
motion:
• Slows out (accelerates)
to hit the ball
• Uniform after the hit
• Slows in as the swing
finishes follow-through
Non-Uniform Circular Motion
Two common types of motion on circular arcs that
have non-uniform timing and spacing are:
Exponential Spacing
Example:
Tipping over
Pendulum Spacing
Example:
Stride in
walking
Tipping Over
Tipping over is a common example of motion
on a circular arc. Two ways to tip over:
X
Center tipped past
point of contact
Center past an edge
Tipping Rotation
A brick rotates about a point as it tips;
that point is the center of a circular arc.
X
Friction tends to keep the brick from sliding
until it loses contact with the table.
Exponential Spacing
Release
1
1
Constant acceleration (Odd Rule)
3
2
5
3
1
Release
7
4
2
3
Exponential Spacing
4
As the slope of the incline increases,
the acceleration itself accelerates.
Rolling off a Tipping Point
1 2 3 4
5
6
7
Peak
8
Slowing out from a tipping point is very slow
initially, but then accelerates rapidly.
Video Reference of Tipping Brick
http://www.youtube.com/watch?v=otYAYMZ4iGg
Anticipation & Exponential Spacing
Texture of the
timing as the brick
tips over creates
anticipation, which
you want at the
start of a scene
Also notice motion
blur near top of
brick, which has
large tangential
speed.
Pendulum Spacing
A pendulum’s path of action is also a circular arc
but the spacing is very different from the
exponential spacing of tipping over.
Spacing & Timing in Swinging
A pendulum will slow in and out as it
swings back and forth, the same as a
ball rolling in a half-pipe.
Most of the texture in the timing is at the
endpoints; the timing is even in the center.
Pencil Test Example
http://www.youtube.com/watch?v=xuoJdNGxffU
Motion Graph for Pendulum
#7
#1
Angle
The motion graph (angle vs. frame) shows
that the timing is mostly textured
(curves the most) at the apexes.
#4
Ball goes fastest around
the bottom but the speed
is almost constant.
Frame
Uniform Rotation in Perspective
The timing for uniform rotation has
texture when seen in perspective.
Half orbit
Quarter
orbit
Rotation from key #1 to #5 in background takes
twice as long as from #6 to #8 in foreground.
Swinging in Perspective
Visually the timing
has even more
texture when the
swing occurs in
perspective.
Who Framed Roger Rabbit? (1988)
The opening sequence in
Who Framed Roger
Rabbit? makes great use
of the textured timing
of arcs in perspective.
Animation by
Richard Williams
Who Framed Roger Rabbit? (1988)
http://www.youtube.com/watch?v=sLNqtU-gYPc
Demo: Don’t Flinch
Pendulum swings back and forth yet it
doesn’t hit your face.
Bowling Ball Pendulum
http://www.youtube.com/watch?v=UNsD15GjWWE
Click
This video clip lets you
experience what it’s
like to do this demo.
Spirals
A spiral is just a circular arc with a radius
that’s either increasing (spiral out) or
decreasing (spiral in).
Concept art from
Pirates of the Caribbean 3
Rotational Speed in Spirals
If the radius decreases without pulling
the object inward then the rotational
speed increases (due to shrinking radius)
but the tangential speed stays constant.
Spacings along
the curve stay
constant.
Spiral In
Demo: Interrupted Pendulum
An “interrupt” bar changes the
radius of the arc for a pendulum.
Tangential speed
does not increase
due to the pendulum
whipping around the
interrupt bar.
Energy is not
increased by the
interrupt bar so ball
swings back to the
same spot.
Bar
Rotation in Spirals (cont.)
If the radius decreases by pulling the
object inward then the rotational speed
increases due to shrinking radius and due
to an increase in the tangential speed.
Spacings along
the curve get
bigger and
bigger.
Spiral In
Demo: Skater’s Spin
Slow
Rotation
FAST
Rotation
Exert a force to pull hand weights toward my body,
causing a big increase in rotational and tangential speeds
Rotation in Spirals (cont.)
If the tangential speed decreases (say by
friction) but inward force constant then
the rotational speed still increases.
Spacings along
the curve get
shorter
yet it
still
spins
faster
and faster.
Spiral In
Coin Vortex
Rotation in a Spirals
In summary, typically as an object rotates
in a spiral, the rotation speed increases as
the radius decreases.
So as radius goes down,
the r.p.m.s go up.
However the spacings
may get longer, or
shorter, or stay constant!
How Does the Brick Fall?
Does the brick
rotate and then fall
down the side of
the table?
1
2
3
No! The brick does
4
not fall this way.
X
Video Reference of Tipping Brick
http://www.youtube.com/watch?v=otYAYMZ4iGg
Forces on the Tipping Brick
The table pushes on
the brick upward and
towards the right.
Gravity pulls downward
Center of the brick shifts
down and towards the right.
If no table…
Pushing Off by the Table
The table pushes away
on the brick, which
causes the brick to
move away from the
table as it falls.
Once it loses contact
with the table, only
the force of gravity
accelerates the brick.
Centrifugal Force
Insect inside a can rotating in a circle
When we move on an
arc, it seems to us
as if there is an
outward force,
pushing us away
from the center of
the circle.
Physicists call this
apparent force the
centrifugal force.
What we see
What the
insect feels
Class Demo: Bucket Overhead
I will put a bucket full of
water over my head without
getting wet. How?
By rotating it fast enough.
The water stays in the bucked
as if pressed into it by a
centrifugal force.
You experience
centrifugal force on
taking a sharp turn
Centrifugal
Force
Wile E. Coyote & Loop-D-Loop
Watch carefully as Wile E. Coyote travels
in a circle around a natural arch bridge.
From “Beep Beep” (1952)
http://www.youtube.com/watch?v=p4YxdXw9evc
Wile E. Coyote & Loop-D-Loop
In reality, it is impossible
to travel upside-down, as
Wile E. Coyote does in this
scene. True or False?
“Beep Beep” (1952)
Wile E. Coyote & Loop-D-Loop
False.
If his speed is high enough then he
stays in contact with the arch, just
like the water in the spinning bucket.
Demo: Loop-the-Loop
If the speed of
the ball is large
then not only
does it stay on
the track, the
ball even pushes
outward and
against the rail.
Release
Velocity
Demo: Loop-the-Loop
Ball could even
circle a loop
with a gap, if
the speed was
just right so
gravity was
equal to the
centrifugal
force.
Release
Velocity
GAP
Simulated Gravity
Centrifugal force could be
used to simulate gravity in
a space station.
With the appropriate
rotational speed a person
on the outer rim would
feel as if they stood on
the surface of Earth.
Scientifically accurate in
the movie 2001: A Space
Odyssey (1968)
Rotation
2001: A Space Odyssey (1968)
Simple Spinning
A falling brick may
turn byArbitrary
simple
spinning around its
center.
1
1
2
In simple spinning, the angle
rotates at a constant rate.
A brick tipped 45º as it loses contact
with the table will fall spinning about
30º every two frames.
3
3
5
4
7
Tumbling
A falling brick may
Arbitrary
also turn
by a more
complicated
tumbling motion.
1
1
2
There is no simple way to
describe tumbling. However, the
brick’s center still follows the
same parabolic path of action.
3
3
5
4
7
Tennis Racket Theorem
SPIN
When an object
turns about its
middle axis, it may
tumble.
SPIN
TUMBLE
When an object
turns about its
long or its short
axis, it tends to
spin.
Irregular Objects
SPIN
TUMBLE
SPIN
SPIN
Spin or Tumble?
Rotation around two of
these axes is spinning.
The axis of rotation
that tumbles is:
A) Head-to-toe axis
B) Side-to-side axis
C) Front-to-back axis
A
B
C
Spin or Tumble?
B) Side-to-side axis
Rotating along this
axis typically results
in irregular tumbling.
Spinning is possible
but requires more
control than along the
other two axes.
B
Rolling & Slipping
1
2
3
4
5
6
7
ROLLING
Rolling ball turns one revolution when it
travels a distance equal to three times
its diameter (actually 3.1416 diameter)
1
2
3
4
5
SLIPPING
Slipping and rolling are both uniform in spacing and rotation.
Next Lecture
Creating Action
By Wednesday of next week:
Complete the 5th homework
(Video analysis of Path of Action)
Please return the clickers!