Lect20 - PHYS 172: Modern Mechanics Fall 2009 Lecture 20...

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Fall 2009 PHYS 172: Modern Mechanics Lecture 20 – Angular Momentum - Multiparticle systems Read 10.5–10.7
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CLICKER QUESTION #1 Reading Question (Sections 10.5 – 10.7) (This is a closed-book quiz, no consulting with neighbors, etc.) A yo-yo is in the xy plane. You pull up on the string with a force of magnitude 0.6 N. What is the direction of the torque you exert on the yo-yo? you F G A. +y B. -y C. +z D. -z E. zero magnitude x y +z out of the page
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Exam #3 is next week Tuesday November 17th at 8 pm in Elliott Hall Alternative testing at same time in Room 8 in Physics Lectures both days next week, and labs & recitations as usual
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Last Time AA L rp G GG single particle system: multiparticle system: , A trans A rot LL L =+ G ,, trans A cm A tot L rP G 1, 1 2, 2 rot cm cm Lr p r p + × + G G G " 1 p G 2 p G 3 p G cm r G 2, cm r G 3, cm r G , cm A r G θ p A r A sin A rr =
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Last Time Angular velocity ω : Moment of inertia I : 22 2 11 2 2 3 3 Im r m r m r ⊥⊥ =+ + + " rot LI ω = G G
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Moment of inertia: masses not in plane Moment of inertia 22 11 2 2 ... Im r m r ⊥⊥ =+ + Masses not in plane: r is distance from axis of rotation Example : solid disk of uniform density: 2 1 2 IM R = R R In respect to its axle
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•Let’s consider what the time derivative of the angular momentum of a single particle is. Recall the Momentum Principle: d G p dt = G F net d ( G r A × G p ) dt = d G r A dt × G p + G r A × d G p dt d G r A dt × G p = G v × G p = 0 G r A × d G p dt = G r A × G F net G τ= G r A × G F net dL JK A dt = r K A × F net = τ K A or Δ L A = r K A × F net () Δ t = τ K A Δ t
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Lect20 - PHYS 172: Modern Mechanics Fall 2009 Lecture 20...

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