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)