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Moment of inertia of a collinear system of particles
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[QUOTE="Physgeek64, post: 5440361, member: 525932"] [h2]Homework Statement [/h2] Landau&Lifshitz Vol. Mechanics, p101 Q1 Find the moment of inertia of a collinear set of molecules [h2]Homework Equations[/h2] I=sum m_i*(r_i^2) [h2]The Attempt at a Solution[/h2] r_i= r_i'-r_cm where r_cm=sum m_i*r_i/sum m_i I=sum m_i r_i^2 I= 1/M sum m_i m_j (r_i' - r_cm)^2 I=1/M sum m_i m_j (r_i'^2 -2r_i' r_cm + r_cm^2) The central term will reduce to zero by definition of the COM leaving I=1/M sum m_i m_j (r_i'^2 + r_cm^2) The answer of 1/M sum m_i m_j r_ij is given, where r_ij is the distance between the ith and jth particle, and the summation is over i not equal to j, but I'm not sure how to simplify this into that expression- I have attempted it a few different ways but none have yet to work. Any help would be much appreciated Thanks in advance :) [/QUOTE]
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Moment of inertia of a collinear system of particles
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