Lecture 28

Lecture 28 - Last Meeting Physics 231 General University...

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Physics 231 General University Physics Lecture 28 Lecture 9 1 Last Meeting ± Angular Momentum ² Definition ² Relation to Torque ² Precession Lecture 9 2 Today ± Angular Momentum ² Rigid Body ² Conservation of Angular Momentum Lecture 9 3 Dictionary x θ v ω a α m I F p L Translation Rotation τ Lecture 9 4 Rotation about a Fixed Axis ± Demo: Conical Pendulum ± Discussion: Conical Pendulum ± Figure: Angular Momentum of a System Rotating about a Symmetry Axis Lecture 9 5

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Lecture 9 6 Rotation of a Rigid Body: Dynamics , z ext netz dL d I dt ω τ == , ext netz I α = ± Compare to , ext netz z Fm a = Note: fixed axis! Lecture 9 7 Angular Momentum of a Rotating Rigid Object ² Each particle of the object rotates in the xy plane about the z axis with an angular speed of ² The angular momentum of an individual particle is L i = m i r i 2 ² L and ω are directed along the z axis Lecture 9 8 Angular Momentum of a Rotating Rigid Object (cont.) ² To find the angular momentum of the entire object, add the angular momenta of all the individual particles ² This also gives the rotational form of Newton’s Second Law 2 zi i i ii LLm r I = ∑∑ ext z dL d II dt dt == = Lecture 9 9 Angular Momentum of a Bowling Ball ² The momentum of inertia of the ball is 2/5 MR 2 ² The angular momentum of the ball is L z = I ²
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Lecture 28 - Last Meeting Physics 231 General University...

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