THEORYMECHANICS902Chapter12 Theorem of moment of momentumCollege of Mechanical and Vehicle EngineeringWangXiaojun
College of Mechanical and Vehicle Engineering WangXiaojun THEORY MECHANICS Chapter12 Theorem of moment of momentum
Chapter12Theoremofmomentof momentum>12.1 Moment of momentum ofa particle and its system> 12.2 The moment of inertia of a rigid body against an axis12.3theoremofmomentofmomentum 12.4 Differential equation of a rigid body rotating about a fixed axis> 12.5 Theorem of moment of momentum of a system of particlesrelativetothecenterofmass 12.6 Differential equations of motion in a rigid body plane
Ø 12.1 Moment of momentum of a particle and its system Ø 12.2 The moment of inertia of a rigid body against an axis Ø 12.3 theorem of moment of momentum Ø 12.4 Differential equation of a rigid body rotating about a fixed axis Ø 12.5 Theorem of moment of momentum of a system of particles relative to the center of mass Ø 12.6 Differential equations of motion in a rigid body plane Chapter12 Theorem of moment of momentum
Chapter12Theoremof momentof momentummomentumtheoremprincipal vectorArbitrarySimplify at aplaneforceparticlesystemmoment ofprincipal momentmomentumtheorem
Arbitrary plane force system principal vector principal moment Chapter12 Theorem of moment of momentum Simplify at a particle momentum theorem moment of momentum theorem
12.1Moment of momentum of aparticleand its system1Moment of momentum of a particleTALet the momentaofa particle M be mv,and themo(mv)vector diameter of the particle relativeto thefixedmiparticle O be r.MAy0Moment of momentum of particle to particle OLo(mi) = r× mim。(mv) perpendicular △OMA , it's going to be twice the area △OMA , and thedirection is determined by the right-hand ruleMoment of momentum of a particle on a fixed axis:L,(mi) =[i。(mi)]It is the number of generations, whose sign can be determined by the right hand ruleMomentofmomentumis instantaneous.Theinternationalunitof momentofmomentum is kg-m / s
1、Moment of momentum of a particle x y z O M A r mv m (mv) O Let the momenta of a particle be , and the vector diameter of the particle relative to the fixed particle be . M mv O r 12.1 Moment of momentum of a particle and its system L mv r mv O ( ) perpendicular , it's going to be twice the area , and the direction is determined by the right-hand rule. m (mv ) O OMA OMA Moment of momentum of particle to particle O: Moment of momentum is instantaneous. The international unit of moment of momentum is z O z L (mv ) L (mv ) Moment of momentum of a particle on a fixed axis: kg m /s 2 It is the number of generations, whose sign can be determined by the right hand rule
12.1 Moment of momentum of a particle and its system2, Moment of momentum of a system of particlesNparticlesmass m, volecity , radius vectorconstitutetheparticleiparticle system:MomentofmomentumofaparticleThemomentof momentum ofasystem with respect to a fixed particleparticle system to any fixed particle isthe vector sum of themoment ofLo = Emo(m,j,) = Er, ×m,imomentumofeachparticleinthesystemtothefixed particleMomentofmomentumofaparticle system on a fixed axisThemoment of momentum ofaparticle system for any fixed axis isthe algebraic sum of the moment ofL, =[Emo(m,y)] = Em,(m,,)momentumofeachparticleinthesystem for the fixed axis
12.1 Moment of momentum of a particle and its system N particles constitute the particle system: particle i O O i i i i i L m m v r m v ( ) Moment of momentum of a particle system with respect to a fixed particle Moment of momentum of a particle system on a fixed axis ( ) ( ) z O i i z z i i L m m v m m v The moment of momentum of a particle system to any fixed particle is the vector sum of the moment of momentum of each particle in the system to the fixed particle The moment of momentum of a particle system for any fixed axis is the algebraic sum of the moment of momentum of each particle in the system for the fixed axis mass , volecity , radius vector ir mi i v 2、Moment of momentum of a system of particles