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Upcoming Classes
Thursday, Sept. 13th
Motion and Dance, Part 2
Assignment due:
* Read “Motions without Turns”, Physics and the Art of Dance,
K. Laws, Pages 36-51
* First draft of first oral presentation or written paper
Tuesday, Sept. 18th
Dance at the Nexus
Assignment due:
* Read “The Mechanics of Movement”, The New Way Things
Work, D. Macaulay, Pages 8-27
Upcoming Deadlines
Thursday, September 13th
First draft of your first term paper or your
oral presentation
Thursday, September 27th
First Set of Oral Presentations
First term paper (if not giving presentation)
Oral Presentations
The following persons will give oral presentations
on Thursday, September 27th :
• Batres, Adan
• Boyd, Heidi
• Chen, Emily
• Kwiatkowski, Dajon
• Lebedeff, Christopher
• Lipton, Christopher
For everyone else, your first term paper is due on
that date.
Extra Credit: SF Museum of Art
Visit San Francisco Museum of Modern Art and
see Abstract Expressionist paintings.
Turn in your ticket receipt ($7 for students). Worth
one homework assignment; deadline is Oct. 16th
Guardians of the Secret, Jackson Pollock, 1943
Extra Credit: San Jose Ballet
See a performance of San Jose Ballet in San Jose
Center for Performing Arts (Nov. 15th – 18th ).
Turn in your ticket receipt. Worth one homework
assignment or three quiz/participation credits.
Ramon Moreno in CARMINA BURANA
Extra Credit: Cypress Quartet
SJSU Celebrates 150th with Cypress String
Quartet Event Fusing Precision Playing with
World-Class Technology
SJSU Music Concert Hall, 7 p.m. Thur., Sept. 20th.
I will hand out tickets at the door
from 6:30 to 6:50pm; don’t be late
to the performance! Worth two
quiz/participation extra credits.
Quiz
Put your name on a sheet of paper and
answer the following questions from
today’s reading assignment:
What is a Grand Jeté?
What is the Grand Jeté
“Floating” Illusion?
Motion & Dance (I)
Balance
and
Motion
without
Turns
Dance
Dance is artistic motion of the human body.
Athletics
Ballet
Break
Dancing
Acrobats
(Cirque du
Soleil)
Tommie Smith & John Carlos
Mexico City 1968 Olympics
Newton’s Laws of Motion
Physical motion is governed by Newton’s
three laws of motion:
1. Principle of Inertia
2. Force = Mass x Acceleration
3. Action & Reaction
Sir Isaac Newton
(1643 – 1727)
We’ll see how these laws apply to dance.
Newton’s First Law of Motion
An object moves with constant, uniform
motion until acted on by a force.
No force
FORCE
First Law (Full Version)
An object at rest remains at rest &
an object in motion remains
in uniform motion*,
unless a force acts on the object.
*Moving in a straight line with constant speed.
First Law is also known as principle of inertia.
Demo: Tablecloth Pull
Flower
Vase
Yank quickly
Tablecloth
Due to the vase’s inertia it remains at rest since almost no force acts
on the vase if one pulls quickly & straight.
Demo: Riding Light Rail
When a moving train
stops, you continue
moving forward.
When the stopped
train starts moving
again, you remain
stationary and are
thrown backwards.
In both cases, it’s
due to your inertia.
Follow-through & Inertia
Follow-through is a
good example of the
principle of inertia.
An object won’t move
until a force acts on it
so long hair trails
behind as head turns.
Hair then remains in
motion even after the
head stops turning.
Net Force
When several forces act on an object, the
forces add together.
Sum of forces called net force or total force
3 Newtons
5 Newtons
8 Newtons
BRICK
same as
The Newton is metric unit of force (about 1/5 pound).
Equilibrium Rule
If an object is at rest then the net force must
be zero. Similarly if in uniform motion.
Zero Newtons
(No Force)
3 Newtons
3 Newtons
BRICK
same as
When this happens we say that forces “balance.”
Support Force
Solid surfaces exert a force, called a support
force, on objects pressed against them.
100 Newton
Gold Brick
100 Newton
Support force
Downward force (weight)
balanced by upward force
(support).
How much is the
net force on the brick?
Friction Force
Origin of friction is molecular interaction between
solid surfaces.
Friction is complicated.
Friction depends on
support force and on
properties of the surface.
Basic properties of
friction first established
by Leonardo da Vinci.
Forces on a Dancer
Newton’s First Law of Motion states that a
stationary object (not moving) remains
stationary if the net force on it is zero.
For a dancer, the three main forces are:
• Gravity (Downward)
• Support of the floor (Upward)
• Frictional force of the floor (Horizontal)
Center of Gravity
Average position of
an object’s weight
distribution is called
the center of gravity
(CG).
Force of gravity acts
on an object as if
pulling straight
down at the CG.
Center
of
Gravity
Stability & Balance
Object is stable if CG is above the base.
STABLE
BASE
Axis
BASE
Weight
Support
CG
Support
Weight
CG
Axis
UNSTABLE
Demo: Find your Center
Your CG is
roughly in the
center of your
body.
Varies with
orientation.
CG
STABLE
CG
UNSTABLE
Demo: Balanced Bird
Where is the bird’s center of gravity?
Point of support is the tip of the beak. Center of gravity must be directly
above or below that point. Wings are weighted so CG is below the beak.
Balance & Dance
The force of gravity and the
support force of the floor can
balance only when a
dancer’s center of gravity is
located above the base of
support.
Center of Gravity
located above the
dancer’s toe
Base of Support with a Partner
Two dancers, together, can
form a larger base of
support.
The center of gravity is
roughly located in between
the two dancers, as shown.
x
Center of
Gravity
What happens if he shifts his
front foot back?
What if he shifts his back
foot forward?
x
Ballet Barre
The ballet barre also
extends the base of
support, with the hand
acting as a “third foot.”
Hand
Base of
Support
Toe
Foot
Motion & Center of Gravity
Arbitrary
4
1
3
5
3
2
6
The center of gravity follows
a parabolic trajectory which is
the same for all objects.
5
1
7
A spinning object turns about
its center of gravity as it flies
through the air.
General tumbling motion (e.g., throw a
chair) is very complicated!
Note: If axe is about 10” long then 4 frames between keys.
7
Movie: Grand Jeté
Jumps & Center of Gravity
While a dancer is in the air (not in contact with the
floor) the only force on the dancer is gravity and the
trajectory of the center of gravity is a parabolic arc.
If the dancer jumps a lesser height
then the time in the air decreases
During a two foot
vertical jump a
dancer is in the air
for slightly less than
¾ of a second.
If the dancer’s
horizontal speed is
10 feet per second
then the CG travels
about 7.1 feet
during the jump.
CG
CG
Shifting the Center of Gravity
By raising their arms and legs, dancers can
raise the location of their center of gravity (CG).
CG
Near hips
CG
Lower torso
Grand Jeté Floating Illusion
Shifting the CG upward, the distance the dancer’s head
rises is reduced, giving illusion of floating longer.
Time in the air is 25% longer
than a similar leap where the
CG rises only 1.3 feet
Grand Jeté Floating Illusion
Illusion of floating is enhance by the fact that during the
peak of the jump the vertical motion is the slowest.
Newton’s Second Law of Motion
Acceleration occurs when an object’s
velocity changes, such as speeding up or
slowing down.
Acceleration depends on Force and Mass.
(Net Force)
(Acceleration) =
(Mass)
Acceleration is always in the direction of the
net Force acting on an object.
Newton’s Second Law (Part 1)
The greater the force on acting on an object,
the greater the acceleration of that object.
Newton’s Second Law (Part 2)
The greater the mass of an object, the less it
accelerates when acted on by the same force.
Demo: Spool
Pull on string wrapped
around a spool. Force is to
the right. In what direction
does the spool move?
Spool moves?
Spool moves?
Pull
Pull
Demo: Tricycle
Pull on tricycle pedal with a string.
Which direction does the tricycle move?
Pedal in bottom position
Pedal in top position
Bike moves?
Bike moves?
Pull
Pull
Newton’s Third Law of Motion
Whenever an object exerts First Object
(Hammer)
a force on a second
object, the second object Second Object
(Nail)
exerts a force of equal
magnitude in the
opposite direction on the
first object.
Action and Reaction
Common expression of 3rd Law is,
To every action there’s an equal and opposite
reaction.
What’s an “action”?
A force exerted by one object on second object.
How can reaction be “equal” and “opposite”?
Equal in magnitude but opposite in direction.
Demo: Mutual Attraction
What happens when:
• Mr. A pulls, Mr. B holds.
• Mr. A holds, Mr. B pulls.
• Mr. A & Mr. B both pull.
Mr. A
Mr. B has more
mass than Mr. A
Mr. B
Demo: Mutual Attraction (cont.)
If only Mr. A pulls on Mr. B then Mr. B accelerates.
Reaction force of equal magnitude so Mr. A also moves.
Who moves faster? Mr. A, Mr. B, or the same?
Mr. A
Reaction
Action
Mr. B
Mr. B has more
mass than Mr. A
Mr. A goes faster (greater acceleration) since his mass is less.
Demo: Mutual Attraction (cont.)
When both guys pull then there are two action forces and
two reaction forces.
If both pull with same force, how much greater is the
acceleration than when only one pulls?
Mr. A
Reaction
Action
Action
Mr. B
Reaction
Twice the force so twice the acceleration (by 2nd Law)
Demo: Mutual Repulsion
Similar demonstration is
to have Mr. A and Mr. B
push away instead of
pull together.
Same results; if Mr. A
pushes and Mr. B holds
then both move apart.
Mr. B
Mr. A
Reaction
Action
Standing on skateboards
IMPORTANT!!!
Action force & reaction force
NEVER balance each
other because they act on
different objects!
Repeat this to yourself over and over again
Walking, Running & Jumping
What forces accelerate us into motion when
we walk, run, or jump?
Forces on a Dancer
For a dancer, the three main forces are:
• Gravity (Downward)
• Support of the floor (Upward)
• Frictional force of the floor (Horizontal)
Only these forces can accelerate the dancer.
Gravity is constant but the force exerted by
the floor can increase in reaction to the
dancer exerting a force on the floor.
Walking Forward
When weight is on back foot it acts by pushing
back on the floor. Reaction is the friction of the
floor, which pushes your body forward
X (CG)
Action
Reaction
If there were no friction
then dancer would fall
straight down and
could not walk forward
Jumping
Jumping is done by pushing
downward on the ground
(action) so the ground
pushes upward on you
(reaction).
How high you jump depends
on the force and on the
distance over which you
apply that force.
Can only push while in contact
with the ground so squatting
helps by increasing distance.
Swinging Arms and Jumping
You swing your arms upward as you jump to
increase the force pushing down on the ground.
Try jumping and swinging your arms upward after
you leave the ground; you won’t jump as high.
Work & Force
The work done on an object is defined as
(Work done) = (Net Force) x (Distance)
The greater the work done, the greater the
change in the object’s velocity.
Pushing Off on a Jump
Notice the orientation of the foot on the
ground, which is pushing off on a jump
Push-Off with Turnout
The angle of flex is small
so the distance over
which the foot exerts a
force is small.
Jump will not be very high.
Distance
Push-Off without Turnout
The angle of flex is larger
so the distance over
which the foot exerts a
force is larger.
Jump will be higher.
Distance
Next Lecture
Motion & Dance (II)
Remember:
Assignment due: First draft or outline
of term paper or oral presentation