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Unformatted text preview: Chapter 13 Chapter 13 Angular Momentum Angular Momentum Rotational Dynamics Rotational Dynamics r v r 2 d dt ngular Velocity and Acceleration as ngular Velocity and Acceleration as ectors ectors (a) An increase in angular speed alone means that Dw is parallel to w . (b) A decrease in angular speed alone means that Dw is antiparallel to w. (c) If w only changes direction, then for small Dw the angular acceleration is perpendicular to w . A change in the direction of the angular velocity without a change in angular speed is analogous to the radial acceleration for circular motion. Remember angular velocity and angular acceleration are vectors! Angular Momentum and Torque Angular Momentum and Torque Angular momentum is defined as L r p By analogy with Newtons 2 nd for linear motion we stated that: d L dt Now consider a system of particles for which the total angular momentum is: L i L i i r i p i Taking the time derivative of the angular momentum yields: d L dt i d r i dt p i r i d p i dt i r i F i d L dt i i net The analogy is complete! The analogy is complete! Note when there is no Note when there is no external torque, angular external torque, angular momentum is conserved! momentum is conserved! xample: Conservation of Angular Momentum xample: Conservation of Angular Momentum The lower disk has a mass M 1 and a radius R 1 , while the upper disk has a mass M 2 and a radius R 2 . The lower disk as a initial angular frequency of w i . The upper disk drops freely down and frictional forces act to bring the two disks to the same angular speed. (a) What is the final angular speed, w f ? n the absence of any external torque, angular momentum is conserved....
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 Spring '08
 Hicks
 Acceleration, Angular Momentum, Momentum

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