# Principle of Linear Impulse and Momentum for a System of Particles

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Mechanical Engineering
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JoVE Core Mechanical Engineering
Principle of Linear Impulse and Momentum for a System of Particles

### Nächstes Video14.4: Conservation of Linear Momentum for a System of Particles

Consider a system of particles moving relative to an inertial frame of reference. The equation of motion for such a system can be written as the sum of external forces acting on each particle. Since the internal forces between particles occur in equal and opposite collinear pair, they are excluded from the equation. Integrating the equation of motion and substituting the limits yields the equation for the principle of linear impulse and momentum for the system of particles. This principle states that the initial linear momentum of the system, combined with the impulses of all external forces from the initial to the final time, equals the final linear momentum of the system. Now, consider the equation of the system's center of mass. Differentiating it, the total linear momentum of the particles can be related to the linear momentum of the center of mass. This relationship is then substituted into the equation for linear impulse and momentum. The modified equation implies the applicability of the principle to the system of particles that compose a rigid body.

## Principle of Linear Impulse and Momentum for a System of Particles

In the context of a system of particles moving relative to an inertial frame of reference, the equation of motion is a crucial tool for understanding the dynamics of the system. This equation, which accounts for external forces acting on each particle, plays a fundamental role in describing the system's behavior.

Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the analysis, focusing on the impact of external forces on the system.

The principle of linear impulse and momentum for the system of particles emerges upon integrating the equation of motion and substituting the limits. According to this principle, the combined initial linear momenta of the particles, along with the impulses of all external forces from the initial to the final time, equals the final linear momenta of the system.

To extend the applicability of this principle, we delve into the equation governing the system's center of mass. By differentiating it, a relationship between the total linear momentum of the particles and the linear momentum of the center of mass is established. This crucial relationship is then incorporated back into the linear impulse and momentum equation, resulting in a modified equation that aptly applies to the broader context of a system of particles composing a rigid body. This nuanced approach enhances our understanding of the dynamic interactions within such systems.