1. Center of Mass

2. Motion with Many Particles  Real objects consist of many particles.  The particles are bound by internal forces. The object moves as if it were a single particleThe object moves as if it were a single particle  Parts of the object may appear to move independently.

3. Forces on One Particle  There is a net force on each particle in an object.  This corresponds to the particle’s acceleration. mimi riri

4. Force on a System  For N particles in a system the forces add.  Some forces are internal and some are external to the system. m2m2 m3m3 m4m4 m1m1

5. Internal Forces  Within an object all the forces are in pairs.  These forces must cancel out in the sum.

6. Total Mass  The sum of all the individual masses in a system is the total mass.

7. Center of Mass  The weighted average of the positions of the particles is the center of mass. m2m2 m3m3 m4m4 m1m1 r CM

8. Translational Motion  The motion of the center of mass of a system of particles depends on the net external force on the system. next M F net r CM