Upload
sage-mews
View
215
Download
1
Tags:
Embed Size (px)
Citation preview
Upcoming Classes
Thursday, Sept. 20th
Energy and the First Law
Assignment due:
* Homework #3 (Flip-book)
Tuesday, Sept. 25th
Entropy and the Second LawAssignment 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, ChristopherFor 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.
Mass is a measure of inertia for linear motion.
Rotational inertia is similar concept for rotation.
Inertia
M m
Gold brick Normal brick
Difficult to move Easy to move
x x
Wood Bat Plastic Pee-wee Bat
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
Rotate
Leadweights
Easyto
Rotate
Hardto
Rotate
Check Yourself
Which dancer has greater rotational inertia?
Axis of Rotation
A B
Dancer B since the leg is extended, putting mass further from the axis of rotation.
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
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 >60ºFor a 5’ 10” dancer; times slightly less for shorter dancers, more for taller
Rates at which an off-balanced dancer falls over, standing with arms and legs to the side.
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.
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)
Torque
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
BLever ArmLever 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.
Push onFloor
ReactionForce
LeverArm
Feet apart Feet together
Movie: Fouetté Turns
Torque for Fouetté Turns
Push onFloor
ReactionForce
LeverArm
Lower heel to the floor
Push off while swinging right leg
Lift heel and return to point
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
SlowRotation
FASTRotation
LARGE Inertia Small Inertia
Angular momentum is constant since(Rotational Inertia) x (Angular Velocity) remains constant.
Demo: Flip the Wheel
Counter-ClockwiseRotation
Counter-ClockwiseRotation
ClockwiseRotation
Similar tocollisions
Fouetté Turns, Revisited
1
2
3
4
5
6
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
Movie: Fouetté Turns
Fouetté Turns, Analyzed
1
2
3
4
5
6
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.
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
Jump! Turn Land
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.
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)