Lecture 12 - Angular Momentum

Lecture 12 - Angular Momentum - 2 1 2 mv 2 1 2 I ϖ...

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Translation and Rotation
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3 2 Kepler's Three Laws 1. Law of ellipses 2. Equal areas in equal times 3. T a
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Modern argument area of parallelogram 1 2 divide by 0 1 1 2 2 A B C C r r A t d A dr r r v dt dt × = = ×∆ = ∆ ∆ → = × = × ur ur ur r r ur ur r r r r
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1 1 2 2 0 constant constant d A M r p L dt d L r F dt L d A dt τ = × = = = × = = = ur r ur ur ur r r ur ur ur
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In quantum mechanics, c c L L r p L S J = + × = + ur ur r ur ur ur ur
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Vortex bowl constant 1 mvl v l =
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( 29 ( 29 rest of the universe always conserved dL r F dt dL r F dt τ = × = = × - = - ur r r ur ur r r ur
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x θ dx v dt = d dt ϖ= dv a dt = d dt ϖ α= Displacement Rotational
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Displacement Rotational m I
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Unformatted text preview: 2 1 2 mv 2 1 2 I ϖ Displacement Rotational I τ α = r ur F ma = ur r Body 2 k Thin ring 2 R disc 2 1 2 R solid sphere 2 2 5 R rod, length L 2 1 12 L Displacement Rotational p mv = ur r L r p = × ur r ur d p F dt = ur ur dL dt τ= ur r 2 1 2 K mv = 2 1 2 K I ϖ = Combined displacement and rotation c c L L r p = + × ur ur r ur 2 2 1 1 2 2 K mv I ϖ = + 2 c I I Ml = +...
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Lecture 12 - Angular Momentum - 2 1 2 mv 2 1 2 I ϖ...

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