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Mechanics of Solids 2011 Part 4

Tham khảo tài liệu 'mechanics of solids 2011 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 1-42 Section 1 Work and Energy The work and energy equation for a system of particles is similar to the equation stated for a single particle. n n n ị U ị V ị T U AV AT 1.3.36 Momentum Methods for a System of Particles Moments of Forces on a System of Particles. The moments of external forces on a system of particles about a point O are given by n n n ị r X F .ị M ị X m a i 1 1 1 1.3.37 Linear and Angular Momenta of a System of Particles. The resultant of the external forces on a system of particles equals the time rate of change of linear momentum of that system. G ị mvt ị F G 1.3.38 i 1 The angular momentum equation for a system of particles about a fixed point O is H ị r Xm a 1.3.39 ị Mo HO ị X m a 1 The last equation means that the resultant of the moments of the external forces on a system of particles equals the time rate of change of angular momentum of that system. Angular Momentum about the Center of Mass The above equations work well for reference frames that are stationary but sometimes a special approach may be useful noting that the angular momentum of a system of particles about its center of mass C is the same whether it is observed from a fixed frame at point O or from the centroidal frame which may be translating but not rotating. In this case HO Hc rc X mvC ị MO HC rC X maC 1.3.40 Conservation of Momentum The conservation of momentum equations for a system of particles is analogous to that for a single .