# About Principle of Consevation of Momentum

If the net external force $$F^{\text{ext}}$$ on an $$N$$ - particle system is zero, the system's total momentum $$P$$ is constant.

This is the Principle of Consevation of Momentum.

But I think the net external force $$F^{\text{ext}}$$ on an $$N$$ - particle system is always non-zero in the real world.

Is the Principle of Consevation of Momentum nonsense?

Is the Principle of Consevation of Momentum an example of vacuously true statement?

## 2 Answers

No, it’s not nonsense and it’s not vacuously true. Even though there are always external forces, they can be negligible and momentum can be conserved within experimental error.

Part of learning physics is understanding what you have to take into account and what you can safely ignore. For example, when navigating a spacecraft to Mars, we don’t worry about the pull of the Andromeda galaxy on it.

Conservation laws are incredibly useful throughout all branches of physics. Far from being vacuous, they are consequences of fundamental symmetries of nature. For example, the conservation of momentum arises from the fact that fundamental physical laws are unchanged under spatial translations. This way of looking at conservation laws is generally not encountered until graduate-school-level physics.

I think you have to consider the statement in the context of Newton's other observations, namely that force equals mass times acceleration, and action and reaction are equal and opposite. Taken together, the three allow a vast range of physical situations to be modelled. They are neither vacuously true, nor nonsense, but crisp insightful summaries of the way in which nature acts that have been put to use for an incredible variety of practical purposes.