Total momentum of a system The total momentum of a system of N particles is given by the vector sum of the momenta of all the individual particles; Where
The most fundamental and useful relationship in physics The conservation of momentum The total momentum of an isolated system does not change with time Isolated means no outside interactions (forces) The particles may interact among themselves. It is important we carefully state exactly what all is in our system. 2q
Conditions for a system to be considered isolated. Floating in space so far from other objects that gravity can be considered to be zero. The interaction time is so short that outside forces don’t have time to affect the system Collisions Functionally isolated A frictionless horizontal surface where gravity is compensated for by the upward force of the surface.
Center of mass The center of mass of a number N particles where particle N i has mass m i is given by: The total mass of the system (M) is given by:
Center of mass lab – In lab you will find the center of mass of systems where weights are hung on meter sticks. This is a special case of the last equation. m1m1 m2m2 r1r1 r2r2 When the meter stick is balanced at its center of mass, the following equation holds: m1m1 r3r3
Examples Find the center of mass of the following system of particles in three dimensions. massxyz 3345 4022 5413 xyz 3345 4022 5413
Examples Find the center of mass of the following system of particles. massxyz 2-807 62-34 741
Why we use the center of mass In many situations a system of particles may be treated as a single particle with all the mass located at the center of mass. For example, the momentum of a system of particles is given by: This is true only for inertial reference frames.
Inertial reference frames An inertial reference frame is one in which a particle at rest remains at rest. Is this room an inertial reference frame? Is an accelerating car? Is an elevator whose supporting cable has been cut. An inertial reference frame is one without external forces 3q
Homework Chapter C4 C4B.1, C4B.3, C4R.1 Due Wednesday