Upcoming Deadlines

1
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

2
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.
3
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.
4
Extra Credit Opportunity
Attend the Game Developers 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

5
Homework Assignment 5

• In this assignment youll 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.

6
Homework Assignment 5
Original Video Reference
7
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 youve landed.
• After tracking your motion, upload the screen
  image from Tracker to your blog into a post
  called "Video analysis of path of action".

8
Homework Assignment 5
Straight Line
Parabolic Path of Action
Parabolic Curve
9
Homework Assignment 5

• Finally, rewind your video to the first frame of
  your jump and from the "File" menu select "Record
  -gt 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.

10
Homework Assignment 5
Video Reference with Tracking
11
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)

12
Survey Question

• So far the pace of the class has been
• Too fast
• A little fast
• About right
• A little slow
• Too slow

13
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)
14
Motion Graph of a Ball Drop
D)
Height
Frames
15
Arcs in Animation
16
Disneys 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.
17
Disneys 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.
We have already discussed several of these
principles of animation, specifically
18
Disneys 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.
Today we will discuss arcs and how they relate to
animated motion.
19
Arcs of Motion
Motion usually follows an arc, which may be
simple, like a circle, or very complex and
irregular.
20
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
21
Circular Arcs
Circular arcs are common since motion is often
around a fixed pivot point, such as a joint.
22
Speed in Circular Motion

• Rotational Speed Revolutions per second
• Tangential Speed Total distance per second

Same Rotational Speed Different Tangential Speeds
23
Throwing Arm
The longer the throwing arm, the greater the
tangential speed so the farther it can throw.
Tangential Speed
x2
Sling lengthens the arm at almost no cost in the
weight.
Doubling the speedquadruples the range!
24
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

Slow in
Uniform
Slow out
25
Non-Uniform Circular Motion
Two common types of motion on circular arcs that
have non-uniform timing and spacing are
Exponential Spacing
Pendulum Spacing
ExampleTipping over
ExampleStride inwalking
26
Tipping Over
Tipping over is a common example of motion on a
circular arc. Two ways to tip over
X
X
Center tipped past point of contact
Center past an edge
27
Tipping Rotation
A brick rotates about a point as it tipsthat
point is the center of a circular arc.
X
X
X
X
Friction tends to keep the brick from sliding
until it loses contact with the table.
28
Exponential Spacing
1
Constant acceleration (Odd Rule)
1
3
Release
2
5
3
7
1
4
Release
2
3
Exponential Spacing
4
As the slope of the incline increases, the
acceleration itself accelerates.
29
Rolling off a Tipping Point
2
3
4
1
5
6
7
Peak
8
Slowing out from a tipping point is very slow
initially, but then accelerates rapidly.
30
Video Reference of Tipping Brick
http//www.youtube.com/watch?votYAYMZ4iGg
31
Anticipation Exponential Spacing
Also notice motion blur near top of brick, which
has large tangential speed.
Texture of the timing as the brick tips over
creates anticipation, which you want at the start
of a scene
32
Pendulum Spacing
A pendulums path of action is also a circular
arc but the spacing is very different from the
exponential spacing of tipping over.
33
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.
34
Pencil Test Example
http//www.youtube.com/watch?vxuoJdNGxffU
35
Motion Graph for Pendulum
The motion graph (angle vs. frame) shows that the
timing is mostly textured (curves the most) at
the apexes.
7
SLOW, again
1
Angle
SLOW
SLOW, again
FAST
FAST
4
Ball goes fastest around the bottom but the speed
is almost constant.
SLOW
Frame
36
Uniform Rotation in Perspective
The timing for uniform rotation has texture when
seen in perspective.
Rotation from key 1 to 5 in background takes
twice as long as from 6 to 8 in foreground.
37
Swinging in Perspective
Visually the timing has even more texture when
the swing occurs in perspective.
38
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 byRichard Williams
39
Who Framed Roger Rabbit? (1988)
http//www.youtube.com/watch?vsLNqtU-gYPc
40
Demo Dont Flinch

• Pendulum swings back and forth yet it doesnt hit
  your face.

41
Bowling Ball Pendulum
http//www.youtube.com/watch?vUNsD15GjWWE
Click
This video clip lets you experience what its
like to do this demo.
42
Spirals
A spiral is just a circular arc with a radius
thats either increasing (spiral out) or
decreasing (spiral in).
Concept art fromPirates of the Caribbean 3
43
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
44
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
45
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
46
Demo Skaters Spin
FAST Rotation
Slow Rotation
Exert a force to pull hand weights toward my
body, causing a big increase in rotational and
tangential speeds
47
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
itstillspinsfasterand faster.
Spiral In
Coin Vortex
48
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!
49
How Does the Brick Fall?
1
Does the brick rotate and then fall down the side
of the table?
X
X
2
X
3
No! The brick does not fall this way.
X
4
50
Video Reference of Tipping Brick
http//www.youtube.com/watch?votYAYMZ4iGg
51
Forces on the Tipping Brick
The table pushes on the brick upward and towards
the right. Gravity pulls downward
X
X
Center of the brick shifts down and towards the
right.
If no table
52
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.
X
X
X
Once it loses contact with the table, only the
force of gravity accelerates the brick.
53
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
54
Class Demo Bucket Overhead

• I will put a bucket full of water over my head
  without getting wet. How?

Centrifugal Force
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
55
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?vp4YxdXw9evc
56
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)
57
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.
58
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
59
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.
GAP
60
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
61
2001 A Space Odyssey (1968)
62
Simple Spinning
1
A falling brick may turn by simple spinning
around its center.
1
2
Arbitrary
3
3
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.
5
4
7
63
Tumbling
1
A falling brick may also turn by a more
complicated tumbling motion.
1
2
Arbitrary
3
3
There is no simple way to describe tumbling.
However, the bricks center still follows the
same parabolic path of action.
5
4
7
64
Tennis Racket Theorem
SPIN
When an object turns about its long or its short
axis, it tends to spin. When an object turns
about its middle axis, it may tumble.
TUMBLE
SPIN
65
Irregular Objects
SPIN
SPIN
TUMBLE
TUMBLE
SPIN
SPIN
66
Spin or Tumble?
A

• Rotation around two of these axes is
  spinning.The axis of rotation that tumbles is
• Head-to-toe axis
• Side-to-side axis
• Front-to-back axis

B
C
67
Spin or Tumble?
B) Side-to-side axis
B
Rotating along this axis typically results in
irregular tumbling. Spinning is possible but
requires more control than along the other two
axes.
68
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.
69
Next LectureCreating Action

• By Wednesday of next week
• Complete the 5th homework
• (Video analysis of Path of Action)

Please return the clickers!