Unit of Momentum -SI Unit, CGS Unit & Other Units, FAQs

Edited By Vishal kumar | Updated on Jul 02, 2025 04:59 PM IST

In this article students will learn about the Newton’s third law of motion, momentum, SI units of the momentum, Linear momentum , SI Unit of the Linear momentum, CGS unit of the momentum, rate of change of momentum, unit of rate of change of momentum,

What is Momentum?

Momentum is an outcome of Newton's third law of motion. When two objects collide, the colliding objects exert equal and opposite forces on each other. Each of these objects can sense unequal forces acting on them, but the entire system has no force acting at all. According to Newton's law of motion, the total impulse experienced by an object depends on the force acting on it. The momentum remains unchanged in the absence of external forces. An important idea in Newtonian mechanics is that when two objects collide, the overall momentum remains unchanged before and after the collision. An impulse can be mathematically defined as the product of an object's mass and its velocity. The sum of the mass multiplied by the velocity before and after the impact should be the same.

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What is Momentum?
Define momentum and its SI Unit
Conservation of Linear Momentum Principle

Unit of Momentum -SI Unit, CGS Unit & Other Units, FAQs

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Mathematically, it’s a product of mass and velocity of the objects. In the physics community it is denoted by the letter p

Hence p=m*v

………1

Where m – Mass of the object

v- Velocity of the object

Units of the Momentum

SI unit of the momentum (Unit of linear momentum is)	kg•m/s.
CGS Unit of the momentum	g⋅cm/s
SI unit of rate of change of momentum	Newton (N)
Unit of angular momentum	kg-m2/sec

Define momentum and its SI Unit

Momentum can be defined as "moving mass". All items have mass; so if an object moves, it has momentum, and its mass is in motion. The amount of momentum an object has depends on two variables: the amount of material it moves and the speed of the material's movement. The momentum depends on the mass and speed variables. In terms of the mathematical equation, the momentum of a body is nothing but the product of the mass of the object times its velocity.

Momentum = Mass • Speed

………2

In physics, the lowercase p is the symbol for momentum. Thus, the equation for the momentum can be rewritten as

p = m • v

………3

In above equation it can be seen that, the momentum of the object is directly proportional to the mass of the object m and velocity of the object v. Equation 3 is also called as the linear momentum and its SI unit is Kg. m/s

So if the velocity of the object is increases keeping mass constant the momentum of object are also increases same is true for vice versa.

Momentum units are units of mass multiplied by units of velocity. The SI unit of momentum is kg • m / s. Although kg • m / s is the standard metric unit of momentum, there are many other units that are accepted (though not traditional) units of momentum. Examples include kg · mph, kg · km / h, and g · cm / s. In each of these examples, the unit of mass is multiplied by the unit of speed to obtain the unit of momentum. This is in line with the momentum equation.

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For the two mass systems total momentum of the system can be written as

P = m1v1+ m2v2

………4

Now consider the system whose mass is constant, then differentiating above equation with respect to time will give

dpdt=m1dV1dt+m2dV2dt

………5

In above equation dv1dt is rate of change of velocity called as the acceleration unit being m/s2

dpdt=m1a1+m2a2

………6

But we know that from Newton’s 2nd Law of motion rate of change of momentum is equal to the force. Hence above equation can be expressed in terms of force as

F=m1a1+m2a2

………7

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Conservation of Linear Momentum Principle

From our last equation 7, we now consider the special case when F = 0. This means that no external forces act on the isolated particle system. This situation implies that the rate of change of the total momentum of the system does not change, which means that this value is constant and confirms the principle of conservation of linear momentum: When there is no net external force acting on the particle system, the total momentum of the system is preserved. It's that simple. Regardless of the nature of the interactions occurring in a given system, its overall momentum will remain the same. To see exactly how this concept works, let's look at an example.

Keep the linear pulse in action. Consider cannon that fire a cannonball. Initially, both the cannon and the cannonball are stationary. Since the gun, bullet and explosive are in the same particle system, we can conclude that the total momentum of the system is zero. What happens after cannon is fired? It is clear that the cannonball is thrown with considerable speed and therefore with momentum. Since the system is not acted on by purely external forces, this impulse must be compensated for by an impulse in the direction opposite to the speed of the ball. In this way, the gun itself gains reverse speed while maintaining overall momentum. This conceptual example explains the "strike" associated with a firearm. Each time a gun, cannon, or artillery element fires a projectile, it must move in the opposite direction of the projectile. The heavier the firearm, the slower it moves. This is a simple example of conservation of momentum.

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Frequently Asked Questions (FAQs)

1. Define and explain Newton's third law of motion?

According to Newton's third law, forces act in pairs, and the forces are equal and opposite. For example, when two objects collide, the colliding objects exert equal and opposite forces on each other.

2. What is centripetal and centrifugal acceleration?

A sphere orbiting someone's head demonstrates the forces of centripetal and centrifugal acceleration. The force applied to hold the ball in place is called centripetal acceleration. At the same time, the force that the ball perceives from them is called centrifugal acceleration.

3. What is an example of the law of conservation of angular momentum?

The law of conservation of angular momentum says that when an object is not affected by any external force, the angular momentum does not change. An example of this is a spinning top where it will spin unless friction slows it down.

4. What is the relationship between the momentum of a body and the force acting on it?

According to the Newton’s law, Force is a rate of change of momentum over time. It can be written as F = mass x acceleration. In practical terms, the momentum of an any body increases when a force is acting upon it increases, because the force is responsible for it to accelerate, and to have an increase in its velocity.

5. What is angular momentum? Explain with an example.

In physics there are systems which are rotational in motion for example planetary motion. The angular momentum is equivalent to the linear momentum in term of rotations. It is also a conserved quantity. The angular momentum of any system which is closed is always remain constant. It is denoted by the letter L and mathematically can be expressed as

L = mvr

Example of the angular momentum conservation is planetary motion.

6. Why is momentum conserved but kinetic energy isn't always conserved?

Momentum is always conserved due to Newton's Third Law, which applies in all situations. Kinetic energy, however, can be converted to other forms of energy (like heat or sound) during collisions, so it's not always conserved.

7. Why is understanding momentum important in collision analysis?

Understanding momentum is crucial in collision analysis because total momentum is conserved in collisions, even when energy isn't. This allows us to predict the motion of objects after a collision.

8. How does momentum relate to kinetic energy?

Both momentum and kinetic energy depend on mass and velocity, but in different ways. Momentum is proportional to velocity (p = mv), while kinetic energy is proportional to velocity squared (KE = ½mv²).

9. How does air resistance affect an object's momentum?

Air resistance creates a force opposing the object's motion, which decreases the object's velocity over time. As momentum is the product of mass and velocity, decreasing velocity leads to decreasing momentum.

10. How does momentum relate to Newton's First Law of Motion?

Newton's First Law states that an object will maintain its velocity (and thus its momentum) unless acted upon by an external force. This law essentially describes the conservation of momentum in the absence of external forces.

11. What is the SI unit of momentum?

The SI unit of momentum is kilogram-meter per second (kg⋅m/s). This unit is derived from the fundamental units of mass (kg) and velocity (m/s).

12. How is the CGS unit of momentum different from the SI unit?

The CGS unit of momentum is gram-centimeter per second (g⋅cm/s). It differs from the SI unit in scale: 1 kg⋅m/s = 100,000 g⋅cm/s.

13. Why is momentum a vector quantity?

Momentum is a vector quantity because it has both magnitude and direction. It inherits its vector nature from velocity, which is also a vector quantity.

14. Can momentum ever be negative?

Yes, momentum can be negative. The sign of momentum indicates direction. Negative momentum simply means the object is moving in the opposite direction of what is defined as positive.

15. How does mass affect momentum?

Mass is directly proportional to momentum. If an object's mass increases while its velocity remains constant, its momentum will increase proportionally.

16. Can an object have momentum if it's not moving?

No, an object at rest (not moving) has zero momentum. Momentum requires both mass and velocity, and if velocity is zero, momentum is zero regardless of the object's mass.

17. What happens to momentum when velocity doubles?

When velocity doubles, momentum also doubles, assuming mass remains constant. This is because momentum is directly proportional to velocity.

18. Is there a unit for momentum in the FPS system?

Yes, in the FPS (foot-pound-second) system, the unit of momentum is slug-foot per second (slug⋅ft/s).

19. Why isn't momentum measured in Newtons?

Momentum isn't measured in Newtons because Newton is a unit of force, not momentum. Force is the rate of change of momentum, while momentum itself is mass times velocity.

20. How does relativistic momentum differ from classical momentum?

Relativistic momentum accounts for the effects of special relativity at very high speeds. Unlike classical momentum (p = mv), relativistic momentum is p = γmv, where γ is the Lorentz factor.

21. How do you convert momentum from SI units to CGS units?

To convert momentum from SI units (kg⋅m/s) to CGS units (g⋅cm/s), multiply the SI value by 100,000. For example, 1 kg⋅m/s = 100,000 g⋅cm/s.

22. Is there a unit of momentum that doesn't involve time?

No, all units of momentum involve time because velocity, a component of momentum, is defined as distance per unit time. Time is an inherent part of the concept of momentum.

23. Can photons have momentum despite having no mass?

Yes, photons have momentum despite having no rest mass. Their momentum is given by p = h/λ, where h is Planck's constant and λ is the photon's wavelength.

24. What's the difference between momentum and impulse?

Momentum is a property of a moving object (p = mv), while impulse is the change in momentum (I = F⋅Δt = Δp). Impulse has the same units as momentum.

25. Can two objects with different masses have the same momentum?

Yes, two objects with different masses can have the same momentum if their velocities are inversely proportional to their masses. For example, a 2 kg object moving at 3 m/s has the same momentum as a 3 kg object moving at 2 m/s.

26. How does the concept of momentum apply to rotating objects?

For rotating objects, we use angular momentum, which is the rotational analog of linear momentum. Its unit is kg⋅m²/s in the SI system.

27. Can momentum be created or destroyed?

No, momentum cannot be created or destroyed, only transferred between objects. This is known as the law of conservation of momentum.

28. How does momentum relate to force in terms of units?

Force is the rate of change of momentum with respect to time. In terms of units, force (N) equals the change in momentum (kg⋅m/s) divided by time (s).

29. Why do we use different units for momentum in different unit systems?

Different unit systems use different base units for mass, length, and time. Since momentum is derived from these base units, it naturally has different units in different systems.

30. How does the momentum of a system of particles differ from that of a single particle?

The momentum of a system of particles is the vector sum of the momenta of all individual particles in the system. This is called the total momentum or center of mass momentum.

31. Can an object's momentum change without its speed changing?

Yes, an object's momentum can change without its speed changing if its direction changes. This is because momentum is a vector quantity, so a change in direction alone constitutes a change in momentum.

32. How does momentum relate to inertia?

Inertia is an object's resistance to change in motion, which is directly related to its mass. Momentum is the product of mass and velocity, so objects with more inertia (more mass) will have more momentum at the same velocity.

33. Why is momentum conserved in quantum mechanics?

Momentum conservation in quantum mechanics is a consequence of the translational symmetry of space. This is an application of Noether's theorem, which relates symmetries to conservation laws.

34. How does the uncertainty principle apply to momentum?

The Heisenberg uncertainty principle states that the more precisely the momentum of a particle is known, the less precisely its position can be known, and vice versa. This is expressed as ΔpΔx ≥ ħ/2, where ħ is the reduced Planck constant.

35. Can an object have momentum in a vacuum?

Yes, an object can have momentum in a vacuum. Momentum only requires mass and velocity, not a medium. In fact, objects maintain their momentum better in a vacuum due to the absence of friction or air resistance.

36. How does the concept of momentum apply to waves?

Waves also carry momentum, known as wave momentum. For electromagnetic waves, this is related to their energy and speed of propagation. The momentum of a photon, for instance, is given by p = E/c, where E is the photon's energy and c is the speed of light.

37. Why is momentum important in rocket propulsion?

Rocket propulsion relies on the conservation of momentum. As the rocket expels gas in one direction, it gains momentum in the opposite direction, allowing it to accelerate even in the vacuum of space.

38. How does the de Broglie wavelength relate to momentum?

The de Broglie wavelength (λ) of a particle is inversely proportional to its momentum (p), given by the equation λ = h/p, where h is Planck's constant. This relationship is fundamental to quantum mechanics.

39. Can momentum be negative in more than one dimension?

Yes, in multiple dimensions, momentum can be negative in any or all components. For example, in 3D space, an object could have momentum (2, -3, 1) kg⋅m/s, where the y-component is negative.

40. How does momentum transfer occur in elastic collisions?

In elastic collisions, both momentum and kinetic energy are conserved. Momentum is transferred between colliding objects in such a way that the total momentum before and after the collision remains the same.

41. What's the relationship between momentum and work?

Work is related to the change in an object's kinetic energy, which is in turn related to momentum. The work-energy theorem states that the work done on an object equals its change in kinetic energy: W = ΔKE = ½m(v₂² - v₁²), where v₁ and v₂ are related to the initial and final momenta.

42. How does the concept of momentum apply in fluid dynamics?

In fluid dynamics, we often consider momentum flux, which is the rate of momentum flow per unit area. This concept is crucial in understanding fluid flow and pressure.

43. Can momentum be quantized?

Yes, in quantum mechanics, momentum can be quantized in certain systems, such as particles in a box or electrons in an atom. This quantization is a fundamental aspect of quantum theory.

44. How does relativistic momentum affect particle accelerators?

In particle accelerators, particles are accelerated to very high speeds where relativistic effects become significant. The relativistic momentum increases more rapidly than classical momentum as speed increases, affecting the energy required to further accelerate particles.

45. Why is momentum important in the study of cosmology?

In cosmology, momentum conservation plays a crucial role in understanding the motion of galaxies, the expansion of the universe, and the behavior of cosmic rays. It's also important in theories about the early universe and its evolution.