Momentum. Law of conservation

01/04/2026

The online momentum simulations on this page will help you to deepen your understanding of the important concept of momentum in physics and to study and understand the law of conservation of momentum.

Concept of momentum

Momentum is a physical vector quantity used to describe the motion of an object in relation to its mass and velocity. The concept of momentum is fundamental in physics.

Momentum formula

Momentum formula is calculated by multiplying the mass (m) of the object by its velocity (v).

Quantity of motion (p) = mass (m) * velocity (v)

Law of conservation of momentum

A direct consequence of Newton’s third law (action – reaction) is the law of conservation of momentum which states that the total momentum of an isolated system remains constant unless acted upon by external forces. Therefore, in an isolated system, if there are no external forces acting on the objects, the total amount of momentum before an event will be equal to the total amount of momentum after that event.

Applications of the law of conservation of momentum

The law of conservation of momentum is especially useful in situations where several objects interact, such as collisions or explosions. In these cases, equations based on momentum formula can be used to determine the final velocities of the objects after the event.

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Momentum simulations

Momentum

Momentum

The momentum of an object is the product of mass times velocity. Is the amount of motion a scalar or vector quantity?

Momentum
Rocket

Momentum

The momentum of an object is the product of mass times velocity. Is the amount of motion a scalar or vector quantity?

Water rocket

A water rocket contains water under high pressure. When the water is released, it is ejected downward and the rocket is propelled upward. Can you explain why this happens?

Giants of science

“If I have seen further, it is by standing on the shoulders of giants”

Isaac Newton

Gottfried Wilhelm Leibniz

1646

–

1716

Gottfried Wilhelm Leibniz was one of the founders of infinitesimal calculus, created modern mathematical notation, and contributed to mechanics and optics with groundbreaking theories

“Music is the hidden exercise of arithmetic of the soul, which does not know it is calculating.”

René Descartes

1596

–

1650

René Descartes developed analytic geometry and contributed to classical mechanics and the study of optics

“Pienso, luego existo”

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Giants of science

“If I have seen further, it is by standing on the shoulders of giants”

Isaac Newton

Joseph-Louis Lagrange

1736

–

1813

Joseph-Louis Lagrange formulated the Lagrangian equations, key in classical mechanics to describe motion. He also founded variational calculus, applying it to algebra and mathematical physics

“As soon as a mathematical truth is established, it always serves as a starting point for new truth”

Léon Foucault

1819

–

1868

Léon Foucault demonstrated Earth’s rotation with his famous pendulum and measured the speed of light with great precision, revolutionizing experimental optics

“The pendulum does not lie: the Earth moves beneath our feet”

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Test your knowledge

What is linear momentum, and why is it considered a fundamental physical quantity?

Linear momentum is a physical quantity that describes how an object moves by considering both its mass and its velocity. It is a vector quantity, meaning that its direction is just as important as its magnitude. This concept is fundamental because it allows us to analyze interactions between objects, especially in situations involving pushes, impacts or explosions. Momentum helps explain how motion is transferred from one object to another and how systems respond when external forces act on them. It is also essential for studying isolated systems, where the total momentum remains constant. Thanks to this idea, it is possible to predict how objects behave before and after an interaction without knowing every internal detail of the process.

What does the law of conservation of momentum state, and how is it applied in physical systems?

The law of conservation of momentum states that, in an isolated system with no external forces acting on it, the total momentum remains constant. This means that even if the objects inside the system interact, the overall “balance” does not change. The law follows directly from the principle of action and reaction: when one object exerts a force on another, both experience changes in motion that compensate each other. This principle is especially useful when studying collisions, explosions or any situation where several bodies exchange forces. It allows us to determine how motion is redistributed among the objects and to predict their final velocities without needing to know every detail of the interaction.

Why does an object with a lot of mass or a lot of speed have more momentum?

An object has more momentum when it is very heavy, very fast or both. This is because it is harder to change its motion. For example, stopping a light ball is easy, but stopping a moving car requires much more force. The same happens with speed: a small object moving very fast can have a significant amount of momentum. In short, the harder it is to stop or redirect an object, the greater its momentum.

What happens to momentum when two objects collide?

When two objects collide, the total momentum of the system remains constant as long as no significant external forces act on it. This means that even though each object may change its speed after the collision, the overall balance stays the same. One object may gain momentum while the other loses it, but the total does not change. This principle helps analyze collisions between cars, billiard balls or any system where two bodies interact suddenly.

What is the conservation of momentum useful for in real life?

The conservation of momentum is useful for understanding and predicting situations where several objects interact. In traffic accidents, it helps reconstruct how vehicles were moving before the impact. In sports, it explains how force is transmitted in football, boxing or billiards. In engineering, it helps design mechanisms that remain stable when they receive impacts or sudden pushes. Even in modern physics, it is used to study particles that collide or separate. It appears in many contexts because it describes how motion is shared during any interaction.