Center of Mass and Momentum Rensselaer Polytechnic Institue伦斯勒理工学院的质量和动量中心.pptVIP

Center of Mass and Momentum Lecture 08 Monday: 9 February 2004 A special point… If the net external force on a system of particles is zero, then (even if the velocity of individual objects changes), there is a point associated with the distribution of objects that moves with zero acceleration (constant velocity). This point is called the “center of mass” of the system. It is the balancing point for the mass distribution. CENTER OF MASS Position, Velocity and Acceleration of CENTER OF MASS MOMENTUM For a system of particles, total momentum is: P = p1 + p2 + p3 ··· or P = S mnvn along with P = Mvcm MOMENTUM CENTER OF MASS (CONT.) The overall translational motion of a system of particles can be analyzed using Newtons laws as if all the mass were concentrated at the center of mass and the total external force were applied at that point. MOMENTUM For a particle, translational momentum is: Momentum is a vector Its direction is the same as the object’s velocity Momenta must be added as vectors MOMENTUM (Review) For a particle, translational momentum is: Momentum is a vector Its direction is the same as the object’s velocity Momenta must be added as vectors MOMENTUM of a SYSTEM(Review) A system is any group of objects that we wish to consider as a group. For a system of particles, momentum is: This is a vector sum!! We have to take direction into account. What does imply? (Review) Internal and External Forces Only External Forces Change the Total Momentum of the System Conservation of Momentum Conservation of Momentum states that the momentum does not change over time. That is, it is constant. If you know the momentum at any one time, then you know it for all other times. EXAMPLE: FExt = 0, FInt 1 0 Two masses, initially at rest. PBefore = PAfter 0 = m1v1 + m2v2 m1v1 = – m2v2 If, m1 = m2 v1 = – v2 Relationship between Force and Momentum What does imply? Reworking IMPU