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# Lect_24 - Angular Momentum Lecture 24 Angular Momentum We...

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Lecture 24 Angular Momentum Angular Momentum Angular Momentum Units: kg m²/s = N m s = J s Just as linear momentum quantifies the amount of motion, angular momentum quantifies the amount of rotation. Note that as with torque, the value depends on the center used. We want an equivalent of and of p G dt p d F G G = net ) ( v r m p r L G G G G G × = × = Angular momentum: ACT: Angular momentum A bus of a mass m drives along Osborn Drive at speed v as shown in the figure below. The magnitude of its angular momentum relative to the Memorial Union is. A. mvd B. 2 mvd C. 2 mvd Memorial Union v d d Bus Osborn drive d d L r p mr v = × = × G G G G G r v r r Direction: into the sky (RHR) v r Magnitude: mvr = mvd

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r 1 r 3 r 2 Angular momentum for rigid bodies m 1 m 2 m 3 P v 3 v 2 v 1 ω Consider a rigid body being rotated around an axis perpendicular to the page and through point P. The body can be broken down into n particles. i i i i i L L r p = = × G G G G = , out of the page i i i i m rv i i i i r mv = × G G Rigid structure: i i v r ω = i i i i m rv 2 i i i m r ω = I ω = ω = z z L I Angular momentum for rigid bodies (for rotations about axis of symmetry) (if rotations about axis of symmetry) Relation between angular momentum and torque Let us look at the simplest case (one particle): ( ) d r p dL dt dt × = G G G dp dr p r dt dt = × + × G G G G net τ = G net v p r F = × + × G G G G ( 0) v p v mv × = × = G G G G net dL dt τ = G G net F dt p d G G = equivalent of
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Lect_24 - Angular Momentum Lecture 24 Angular Momentum We...

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