Chapter 11

Chapter 11 - Announcements Practice Exams are posted on...

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Announcements Practice Exams are posted on WileyPlus Exam #2, Monday, July 6 in class. It will cover ch. 7-11

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Chapter 11: rolling Reminders: • We considered: rigid bodies with stationary axis of rotation • rotational variables: θϖ= d θ /dt α= d 2 θ /dt 2 = d ϖ /dt • point at distance r from axis: v = ϖ r, a t = α r, a r = v 2 /r= ϖ 2 r • moment of inertia • parallel-axis theorem: • kinetic energy • Torque (signs!) • torque and angular acceleration 2 i i I m r = 2 1 2 K I ϖ = 2 , where R is distance between P and c.m. P com I I MR = + F axis r φ sin Fr τ φ = I α =
Smooth Rolling Smooth rolling, if a wheel does not slip at the point of contact cm cm s R v R a R θ ϖ α = = = θ so, because arc length s is the same as linear distance moved forward, s s

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Rolling: two equivalent views Two motions combined: • rotation about center • forward motion Two motions combined: • rotation about point of contact cm v R ϖ = same ϖ! ϖ! v cm
rolling without slipping: translation + rotation II cm R v ϖ = v cm pure translation + pure rotation 0 2 cm v rolling As seen by an observer at rest: = v cm

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Role of friction in rolling: 3 cases 1. no acceleration: in ideal world, no frictional force (pure slipping) 3. acceleration caused by friction! F 2. no acceleration: in ideal world, no frictional force (rolling) a cm v cm v cm (slowing down!) In this case, ! cm IF thereis no slipp R g a in α = v cm
Rolling and Kinetic Energy ϖ 2 2 2 0 2 2 0 1 2 1 ( ) 2 1 1 2 2 P K I I MR I Mv = = = + = + 0 ( is thesameas ) cm I I

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Rolling down a ramp: velocity 2 2 0 2 0 2 2 0 2 2 1 2 2 1 / I mv mgh v R I mgh m v R gh v I mR ϖ = + = = + = + h v
Rolling down a ramp: acceleration 0 2 0 sin sin 1 / f f ma mg F I RF a R g a I mR θ α = - = - = - = + mg N F note signs! θ

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(similar to H&R 11-4) A uniform solid disc rolls down an incline. (a) what must be the incline angle if the linear acceleration of the center of the disc is to have a magnitude of 0.1g? (b) If a frictionless block were to slide down
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Chapter 11 - Announcements Practice Exams are posted on...

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