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# lec04 - Systems of Particles 1 2.003J/1.053J Dynamics and...

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Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 1 Systems of Particles 2.003J/1.053J Dynamics and Control I, Spring 2007 Professor Thomas Peacock 2/20/2007 Lecture 4 Systems of Particles: Angular Momentum and Work Energy Principle Systems of Particles Angular Momentum (continued) d τ ext = H B + v B × P B dt τ ext : Total External Torque B H B : Total Angular Momentum P : Total Linear Momentum From now on, τ ext = τ B . B If τ B = 0 and v B = 0 or if B is the center of mass or if v B v C then H B = constant (Conservation of Angular Momentum). You may be familiar with τ B = d H B (only valid if v B = 0 or v B P ). dt Angular momentum H B of a collection of particles about point B is given by: N H B = h B i i =1 where h B i = r i × m i v i . If ( H B ) is the sum of the angular momenta of the individual particles about point B,

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Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. Figure 1: Angular momentum about B for a system of particles. Each particle has mass m i positions r i with respect to the origin and r i with respect to B . The center of mass C has positions r c with respect to B and ρ i with respect to each point mass m i . Figure by MIT OCW.
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