**Subject :**Elements of Mechanical Engineering

## 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

*m*and

_{i}

*V**respectively, then*

_{i }

When the mass of each particle remains constant, the above expression may be written as

If * r_{G}* is the position vector of mass center and

*m*is the total mass, then

Thus,

,where V_{G } 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 *t*_{1} and *t*_{2} ,

Note that all external forces exert impulses, whether they do work or not.

**Angular Momentum:**

Angular momentum is defined as the moment of linear momentum.

For a system of particles, the angular momentum ** H_{G}** (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.