Methods of momentum
Methods of momentum: Linear momentum of a particle is mass times the velocity of the particle. Linear momentum of a mass system is the vector sum of the linear momenta of all its particles. If we denote this linear momentum by G and mass and velocity of the ith particle by mi and Vi respectively, then
When the mass of each particle remains constant, the above expression may be written as
If rG is the position vector of mass center and m is the total mass, then
,where VG is the velocity of the mass center.
This is true for rigid as well as non rigid body. Differentiating the above expression with respect to the time
Integrating the above relation between t1 and t2 ,
Note that all external forces exert impulses, whether they do work or not.
Angular momentum is defined as the moment of linear momentum.
For a system of particles, the angular momentum HG (about the mass center) is given by
where is the position vector of the particle about the center of mass as shown in the figure.