Transcript Slide 1

Upcoming Classes
Thursday, Sept. 20th
Energy and the First Law
Assignment due:
* Homework #3 (Flip-book)
Tuesday, Sept. 25th
Entropy and the Second Law
Assignment due:
* Read “Exploiting Heat”, The New Way Things Work,
D. Macaulay, Pages 142-157
Upcoming Deadlines
Thursday, September 27th
First Set of Oral Presentations
First term paper (if not giving presentation)
Thursday, October 11th
Outline of second oral presentation or
written paper
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
Answer the following question from today’s reading
assignment:
A bottle opener is an example of a:
a) Wedge
b) Inclined Plane
c) First Class Lever
d) Second Class Lever
e) Pulley
Motion &
Dance (II)
Rotation
and Turns
Rotational Motion
In physics we distinguish two types of motion
for objects:
• Translational Motion (change of location)
• Rotational Motion (change of orientation)
We’ve mostly discussed translational motion;
today we consider rotation.
Inertia
Mass is a measure of inertia for linear motion.
Gold brick
Normal brick
M
m
Difficult to move
Easy to move
Rotational inertia is similar concept for rotation.
Wood Bat
x
Plastic Pee-wee Bat
x
Difficult to Rotate
Easy to Rotate
Rotational Inertia
Rotational inertia depends on
• Total mass of the object
• Distribution of the mass
Farther the mass is from the axis of rotation, the
larger the rotational inertia.
Rotational inertia goes as (mass) x (distance)2
Demo: Inertia Sticks
Two metal pipes of the same mass
Easy
to
Rotate
Rotate
Hard
to
Rotate
Lead
weights
Check Yourself
Which dancer has greater rotational inertia?
Dancer B since the
leg is extended,
putting mass further
from the axis of
rotation.
Axis of Rotation
A
B
Demo: Drop the Stick
Two meter sticks stand
upright against a wall; one
has a hunk of clay on the
end.
Which stick will swing down
and hit the floor first?
The one without the hunk of
clay.
Why?
Clay increases rotational
inertia, which slows the
rotation.
Rate of Falling Over
Rates at which an off-balanced dancer falls
over, standing with arms and legs to the side.
Start
½º
1º
2º
4º
½ second 1.0º 2.1º 4.1º 8.2º
1 second
3.7º 7.5º 15º 30º
1½ sec.
14º 29º
57º >60º
For a 5’ 10” dancer; times slightly less for shorter dancers, more for taller
Balance & Rotational Inertia
By stretching arms and legs out a dancer
increases rotational inertia.
If unbalanced
the dancer will
fall more
slowly than
when arms
and legs are at
the side.
Balance Beam
You tend to hold your arms
out when on a balance
beam for two reasons:
• Increase your rotational
inertia so as to slow your
rate of tipping over.
• Allow rapid changes of
your center of gravity, to
regain balance
Demo: Long Legs
Long legs have greater
rotational inertia than
short legs so long
legged animals have
a slow walking stride.
Torque
When a force causes a rotation, we identify this as
a torque.
Torque depends on
• Magnitude of Force
• Direction of Force
• Lever Arm
(Torque) = (Force) x (Lever Arm)
Lever Arm
Lever arm is perpendicular distance
from axis of rotation to the direction of
the force.
Check Yourself
In which case are you exerting more torque?
Case A, because lever arm is longer.
A
Lever Arm
B
Lever Arm
almost zero
Movie: Pirouette
Torque for a Pirouette
The farther the distance between the feet,
the greater the lever arm so the greater
the torque for creating the rotation.
Reaction
Force
Push on
Floor
Lever
Arm
Feet apart
Feet together
Movie: Fouetté Turns
Torque for Fouetté Turns
Push off while swinging right leg
Lower heel to the floor
Lift heel and return to point
Reaction
Force
Push on
Floor
Lever
Arm
The torque first creates a
rotation of the arm & leg, then
whole body rotates together
Angular Momentum
There are two types of momentum
(Linear Momentum) = (Mass) x (Velocity)
and
(Angular Momentum) =
(Rotational Inertia) x (Rotational Velocity)
Principle of conservation for both types.
Demo: Skater’s Spin
By moving their
outstretched arms and
legs inward an ice
skater can decrease
their body’s rotational
inertia.
By conservation of
angular momentum,
they increase their
angular velocity (spin
faster)
Demo: Skater’s Spin
LARGE Inertia
Slow
Rotation
Small Inertia
FAST
Rotation
Angular momentum is constant since
(Rotational Inertia) x (Angular Velocity) remains constant.
Demo: Flip the Wheel
CounterClockwise
Rotation
CounterClockwise
Rotation
Clockwise
Rotation
Similar to
collisions
Fouetté Turns, Revisited
Sequence of the turn:
#1 Push off with left foot
#2 Right arm & leg turn,
Torso stationary
#3 Right arm & leg turn,
Torso stationary
#4 Right turns,
Torso stationary
#5 Arm & leg come back,
Rapid turn of the torso
#6 Torso continues
rotating with momentum,
Prepare to push off again
1
6
2
5
3
4
Movie: Fouetté Turns
Fouetté Turns, Analyzed
The torque from pushing
off gives angular
momentum to the right
arm and leg, which rotate
freely from #1 to #4.
Then the right arm and leg
are made to rotate back in
the opposite direction.
By conservation of angular
momentum, the torso
recoils and rotates in the
original direction.
1
6
2
5
3
4
Demo: Mid-Air Twist
Stand up and clear
space around you.
When I say “Jump!”,
jump.
In mid-air I’ll point left
or right and I want
you to try to turn so
you land facing that
direction.
Jump!
Turn
Land
How can you rotate in mid-air without pushing off of anything?
Demo: Mid-Air Twist
As you turn your legs 90 degrees, your
arms and torso rotate in the opposite
direction. Sticking your arms out as you
turn helps by increasing the rotational
inertia of your upper body.
A large rotation of your legs is exactly
cancelled by a small rotation of your
outspread arms and torso.
Your rotation stops as soon as you stop
rotating your upper body but by that time
you’ve landed with your feet turned to the
side. Once on the ground you can push
off on the ground to restore your arms
and torso to a normal stance.
Jump!
Turn
Land
Demo: Drop the Cat
www.abc.net.au/science
Demo: Drop the Cat (cont.)
Cat lands on its feet by clever use of
angular momentum conservation
Special Guest: Adam Pintek
Next Lecture
Energy & First Law
Remember:
Assignment due:
Homework #3 (Flip-book)