sy16_oct29_07hc

sy16_oct29_07hc - Physics 207 Lecture 16 Oct 29 Physics...

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Physics 207: Lecture 16, Pg 1 Physics 207, Physics 207, Lecture 16, Oct. 29 Lecture 16, Oct. 29 Agenda: Chapter 13 Agenda: Chapter 13 Center of Mass Center of Mass Torque Torque Moment of Inertia Moment of Inertia Rotational Energy Rotational Energy Rotational Momentum Rotational Momentum Assignment: Assignment: Wednesday is an exam review session, Exam will be Wednesday is an exam review session, Exam will be held in rooms B102 & held in rooms B102 & B130 in Van Vleck at 7:15 PM MP Homework 7, Ch. 11, 5 problems, MP Homework 7, Ch. 11, 5 problems, NOTE: Due Wednesday at 4 PM NOTE: Due Wednesday at 4 PM MP Homework 7A, Ch. 13, 5 problems, available soon MP Homework 7A, Ch. 13, 5 problems, available soon

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Physics 207: Lecture 16, Pg 2 Chap. 13: Rotational Dynamics Chap. 13: Rotational Dynamics Up until now rotation has been only in terms of circular motion with a c = v 2 / R and | a T | = d| v | / dt Rotation is common in the world around us. Many ideas developed for translational motion are transferable.
Physics 207: Lecture 16, Pg 3 Conservation of angular momentum has consequences How does one describe rotation (magnitude and direction)?

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Physics 207: Lecture 16, Pg 4 Rotational Dynamics: A child’s toy, a physics Rotational Dynamics: A child’s toy, a physics playground or a student’s nightmare playground or a student’s nightmare A merry-go-round is spinning and we run and jump on it. What does it do? We are standing on the rim and our “friends” spin it faster. What happens to us? We are standing on the rim a walk towards the center. Does anything change?
Physics 207: Lecture 16, Pg 5 Rotational Variables Rotational Variables Rotation about a fixed axis: Consider a disk rotating about an axis through its center:] How do we describe the motion: (Analogous to the linear case ) ϖ θ R (rad/s) 2 Tangential v T dt d = = = π θ ϖ dt dx = v

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Physics 207: Lecture 16, Pg 6 Rotational Variables. .. Rotational Variables. .. Recall: At a point a distance R away from the axis of rotation, the tangential motion: x = θ R v = ϖ R a = α R ϖ α R v = ϖ R x θ rad) in position (angular 2 1 rad/s) in elocity (angular v ) rad/s in accelation (angular constant 2 0 0 0 2 t t t α θ + + = + = =
Physics 207: Lecture 16, Pg 7 Summary Summary (with comparison to 1-D kinematics) (with comparison to 1-D kinematics) Angular Linear constant = α ϖ=ϖ 0 + α t θ θ ϖ α = + + 0 0 2 1 2 t t constant = a at + = 0 v v 2 0 0 2 1 v at t x x + + = And for a point at a distance R from the rotation axis: x = R θ v = ϖ R a = α R

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Physics 207: Lecture 16, Pg 8 Lecture 15, Lecture 15, Exercise 5 Exercise 5 Rotational Definitions Rotational Definitions A. The wheel is spinning counter-clockwise and slowing down. B. The wheel is spinning counter-clockwise and speeding up. C. The wheel is spinning clockwise and slowing down. D. The wheel is spinning clockwise and speeding up A friend at a party (perhaps a little tipsy) sees a disk spinning and says “Ooh, look! There’s a wheel with a negative ϖ and positive α !” Which of the following is a true statement about the wheel?
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sy16_oct29_07hc - Physics 207 Lecture 16 Oct 29 Physics...

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