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Unformatted text preview: Page 1 Physics 207 Lecture 12 Physics 207: Lecture 16, Pg 1 Physics 207, Physics 207, Lecture 16, Oct. 29 Lecture 16, Oct. 29 Agenda: Chapter 13 Agenda: Chapter 13 c Center of Mass Center of Mass c Torque Torque c Moment of Inertia Moment of Inertia c Rotational Energy Rotational Energy c Rotational Momentum Rotational Momentum Assignment: Assignment: c 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 c 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 c MP Homework 7A, Ch. 13, 5 problems, available soon MP Homework 7A, Ch. 13, 5 problems, available soon Physics 207: Lecture 16, Pg 2 Chap. 13: Rotational Dynamics Chap. 13: Rotational Dynamics c Up until now rotation has been only in terms of circular motion with a c = v 2 / R and | a T | = d| v | / dt c Rotation is common in the world around us. c Many ideas developed for translational motion are transferable. Physics 207: Lecture 16, Pg 3 Conservation of angular momentum has consequences Conservation of angular momentum has consequences How does one describe rotation (magnitude and direction)? Physics 207: Lecture 16, Pg 4 Rotational Dynamics: A child Rotational Dynamics: A child s toy, a physics s toy, a physics playground or a student playground or a student s nightmare s nightmare c A merry-go-round is spinning and we run and jump on it. What does it do? c We are standing on the rim and our friends spin it faster. What happens to us? c We are standing on the rim a walk towards the center. Does anything change? Physics 207: Lecture 16, Pg 5 Rotational Variables Rotational Variables c Rotation about a fixed axis: x Consider a disk rotating about an axis through its center:] c How do we describe the motion: (Analogous to the linear case ) R (rad/s) 2 Tangential v T dt d = = = dt dx = v Physics 207: Lecture 16, Pg 6 Rotational Variables... Rotational Variables... c Recall: At a point a distance R away from the axis of rotation, the tangential motion: x x = R x v = R x a = R R v = R x rad) in position (angular 2 1 rad/s) in elocity (angular v ) rad/s in accelation (angular constant 2 2 t t t + + = + = = Page 2 Physics 207 Lecture 12 Physics 207: Lecture 16, Pg 7 Summary Summary (with comparison to 1 (with comparison to 1-D kinematics) D kinematics) Angular Linear constant = = + t = + + 2 1 2 t t constant = a at + = v v 2 2 1 v at t x x + + = And for a point at a distance R from the rotation axis: x = R v = R a = R Physics 207: Lecture 16, Pg 9 Lecture 15, Lecture 15, Exercise 5 Exercise 5 Rotational Definitions Rotational Definitions c A goofy friend sees a disk spinning and says Ooh, look! Theres a wheel with a negative and with antiparallel and ! c Which of the following is a true statement about the...
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