Momentum and Center of Inertia

Vocabulary flashcards covering key concepts from the lecture notes on momentum (quantité de mouvement), isolated and pseudo-isolated systems, and the center of inertia (center of mass), including the inertia principle and related formulas.

Momentum (quantity of motion)

A vector p = m v; for a system, total momentum P = sum of individual momenta; momentum is conserved in an isolated system (no external forces).

Isolated system

A system on which no external forces act; the total momentum remains constant in time.

Pseudo-isolated system

A system for which external forces exist but cancel at every instant, so the net external force is zero and momentum is conserved.

Center of inertia (center of mass)

The point whose motion represents the translation of the whole system; for a system of particles, rG = (1/M) ∑ mi ri and velocity vG corresponds to the system’s translational motion.

Center of gravity vs Center of inertia

In a uniform gravitational field, the center of gravity coincides with the center of inertia; otherwise they may differ.

Movement d’ensemble (translation)

The motion of the center of inertia describing the ensemble (overall) movement of the system.

Mouvement propre (relative motion)

The motion of a point of the solid relative to the center of inertia; internal or relative motion within the system.

Two-mass system center of inertia formula

For masses m1 and m2 with centers G1 and G2, the center of inertia is G = (m1 G1 + m2 G2) / (m1 + m2).

Principle of inertia

In a Galilean (inertial) frame, the center of inertia of an isolated or pseudo-isolated system remains at rest if initially at rest, and moves with constant velocity if initially in motion.

Galilean frame (inertial frame)

An inertial reference frame in which Newton’s laws hold and there are no fictitious forces.

Velocity of the centre of inertia

The velocity vG of the center of inertia equals the translational velocity of the system; in uniform motion, vG is constant (MRU for the center of inertia).

External forces

For isolated or pseudo-isolated systems, external forces are zero or cancel out, ensuring momentum conservation.