Conservation of momentum

If the external forces are zero — or if their total impulse is negligible over the interval considered — the total momentum of the system is conserved:

Principle — Conservation of momentum

$\vv{p}_{\text{tot}}^{\,\text{ini}} = \vv{p}_{\text{tot}}^{\,\text{fin}}$

When it is conserved

$\vv{p}$ is conserved when the external forces are zero or negligible. Being a vector equation, it holds component by component: it can be conserved along $x$ and not along $y$ (for example if an external force acts only vertically).

This condition is realised, excellently, in three typical situations:

• in explosions: a stationary grenade breaks into fragments under the push of internal (chemical) forces; the total momentum stays equal to the starting one (often zero);
• in collisions: two bodies collide over a very short time, during which the internal contact forces are enormous and the external forces (weight, friction) give a negligible impulse;
• in recoil: a weapon fires a projectile forwards and moves backwards, so that the sum of the momenta stays unchanged.

In all these cases the forces at play are internal to the system, and by Newton’s third law their impulses cancel in pairs: that is why the total does not change.

▶ The Bullet Block Experiment — Veritasium

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Topics: Quantità di moto e urti Concepts: Conservazione della quantità di moto · Quantità di moto Skills: Conservazione della quantità di moto

Related exercises: Razzo nel vuoto · Terzo principio rotto · Massa che dimezza