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Upcoming Classes Thursday, Sept. 20 th Energy and the First Law Assignment due: * Homework #3 (Flip-book) Tuesday, Sept. 25 th Entropy and the Second Law Assignment due: * Read Exploiting Heat, The New Way Things Work, D. Macaulay, Pages

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Upcoming Deadlines Thursday, September 27 th First Set of Oral Presentations First term paper (if not giving presentation) Thursday, October 11 th Outline of second oral presentation or written paper

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Oral Presentations The following persons will give oral presentations on Thursday, September 27 th : Batres, Adan Boyd, Heidi Chen, Emily Kwiatkowski, Dajon Lebedeff, Christopher Lipton, Christopher For everyone else, your first term paper is due on that date.

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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. 16 th Guardians of the Secret, Jackson Pollock, 1943

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Extra Credit: San Jose Ballet See a performance of San Jose Ballet in San Jose Center for Performing Arts (Nov. 15 th – 18 th ). Turn in your ticket receipt. Worth one homework assignment or three quiz/participation credits. Ramon Moreno in CARMINA BURANA

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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. 20 th. I will hand out tickets at the door from 6:30 to 6:50pm; dont be late to the performance! Worth two quiz/participation extra credits.

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Quiz Answer the following question from todays 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

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Motion & Dance (II) Rotation and Turns

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Rotational Motion In physics we distinguish two types of motion for objects: Translational Motion (change of location) Rotational Motion (change of orientation) Weve mostly discussed translational motion; today we consider rotation.

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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

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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

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Demo: Inertia Sticks Two metal pipes of the same mass Rotate Lead weights Easy to Rotate Hard to Rotate

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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.

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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.

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Rate of Falling Over Start½º1º2º4º ½ second1.0º2.1º4.1º8.2º 1 second3.7º7.5º15º30º 1½ sec.14º29º57º>60º For 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.

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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.

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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

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Demo: Long Legs Long legs have greater rotational inertia than short legs so long legged animals have a slow walking stride.

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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

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Lever Arm Lever arm is perpendicular distance from axis of rotation to the direction of the force.

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Check Yourself In which case are you exerting more torque? Case A, because lever arm is longer. A B Lever Arm almost zero

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Movie: Pirouette

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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 on Floor Reaction Force Lever Arm Feet apart Feet together

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Movie: Fouetté Turns

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Torque for Fouetté Turns Push on Floor Reaction Force Lever Arm 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

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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.

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Demo: Skaters Spin By moving their outstretched arms and legs inward an ice skater can decrease their bodys rotational inertia. By conservation of angular momentum, they increase their angular velocity (spin faster)

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Demo: Skaters Spin Slow Rotation FAST Rotation LARGE Inertia Small Inertia Angular momentum is constant since (Rotational Inertia) x (Angular Velocity) remains constant.

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Demo: Flip the Wheel Counter- Clockwise Rotation Counter- Clockwise Rotation Clockwise Rotation Similar to collisions

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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

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Movie: Fouetté Turns

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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.

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Demo: Mid-Air Twist Stand up and clear space around you. When I say Jump!, jump. In mid-air Ill 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?

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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 youve 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.

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Demo: Drop the Cat

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Demo: Drop the Cat (cont.) Cat lands on its feet by clever use of angular momentum conservation

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Special Guest: Adam Pintek

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Next Lecture Energy & First Law Remember: Assignment due: Homework #3 (Flip-book)

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