Lecture 9 Single particle F m a New idea compare time before to time after T Impulse causes momentum change System of particles Combine Newton s Second and Third Laws Momentum of a single part p m v Force F m a m Newtons Second Law Fdt dp Impulse momentum time after momentum time before Momentum and Impulse Obeys a conservation law Simpli es complicated motions Describes Collisions Basis of rocket propulsion and space travel System of particles Newton s Second Law Force changes the momentum of the system Internal forces in a system of particles is zero The momentum of a system of N particles is de ned as the sum of individual momenta of the particles The internal force on the ith particle is sum of the internal interaction forces with all the other particles The sum of the internal forces on each particle in the system is Newton s Third Law internal forces cancel in pairs So the sum of the internal forces on the system is zero Newton s third law the force on a system of particles is the external force because internal forces cancel in pairs Newton s second law The total external force is equal to the rate of change of the momentum of the system Newton s second and third laws for system of particles Position of center of mass system of particles Mass for collection of discrete bodies system Position of center of mass
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