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Mechanics. 6.7 Review and Summary. Chapter 6. Dynamics of particle systems. 6.7 Review and Summary. Particle system: a collection of two or more particles. Dynamics of particle system:. Extend the kinetic analysis methods for one particle to particle system The center-of-mass system
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Mechanics 6.7 Review and Summary Chapter 6. Dynamics of particle systems Chapter 6 Particle system
6.7 Review and Summary Particle system:a collection of two or more particles Dynamics of particle system: • Extend the kinetic analysis methods for one particle to particle system • The center-of-mass system • The impact(or collision) of particles Chapter 6 Particle system
6.7 Review and Summary Kinetics: Force-Mass-Acceleration Method • Center of mass of the particle system: • Velocity and acceleration of center of mass: • External and inter forces • The equation of motion of the mass center Chapter 6 Particle system
6.7 Review and Summary Work Energy principle • Work done on the particle system: • Work done by gravity on the system: • The work done by a pair of internal forces depends only on the relative displacement of the two particles. • Principle of work and kinetic energy for a particle system Chapter 6 Particle system
6.7 Review and Summary • Principle of Work and mechanical energy • Principle of conservation of mechanical energy: If Aext =0, (Aint)noncon= 0, then Ek + Ep = Ek0 + Ep0 = constant Chapter 6 Particle system
Principle of impulse and momentum 6.7 Review and Summary • Linear momentum of the system • Momentum theorem of a particle system: • The impulse-momentum principle for a particle system • The principle of conservation of momentum for a particle system: If I = 0, then p1 = p2 or p = 0 Chapter 6 Particle system
6.7 Review and Summary Principle of angular impulse and momentum • The angular momentum of the system about reference point A LA = LAi= ri mivi • The resultant torque acting on a system about point A A= Ai = (Ai)ext +(Ai)int Resultant torque of internal forces Resultant torque of external forces Torque of gravity: (Ai)int = 0 Chapter 6 Particle system
6.7 Review and Summary • Torque-angular momentum relationship • The angular momentum theorem of a particle system: A: fixed point or mass center • Angular momentum theorem about z-axis Chapter 6 Particle system
6.7 Review and Summary • Angular impulse-momentum principle • Principle of conservation of angular momentum about a fixed point A If (Ai)ext = 0, then LAis a constant vector Chapter 6 Particle system
Center of mass system 6.7 Review and Summary A reference frame in which the mass center of a particle system is at rest. • Work-energy principle: • kinetic energy Konig theorem • Work-kinetic energy principle in CM frame The total work done by the inertial forces is zero • work-mechanical energy principle in CM frame Chapter 6 Particle system
6.7 Review and Summary • Angular impulse momentum principle • The angular momentum of the system about mass center C LC = LCi= rCi mivCi • Angular momentum theorem in CM frame • angular impulse momentum theorem • Angular momentum about an arbitrary A Chapter 6 Particle system
6.7 Review and Summary Impact Direct central impact Oblique central impact Chapter 6 Particle system
v2 n t Line of impact m2 m1 v1 v20 v10 6.7 Review and Summary • For bothdirect and obliqueimpact problems, the following equations applyalongthe line of impact (n-dir.): • Forobliqueimpact problems, the following equations are also required, appliedperpendicularto the line of impact (t-dir.): Chapter 6 Particle system
6.7 Review and Summary Chapter 6 Particle system
