What Is The Equation For Momentum?

What is the equation for momentum? The equation for momentum is p=mv. Mass and velocity are the two factors that directly affect momentum which is donated by m (mass) and v (velocity).

equation for momentum

:eight_pointed_black_star: What is the equation for momentum?

According to the definition of momentum, an item has a big momentum vector if its mass and velocity are both large. Both variables affect an object’s momentum.

The Mack truck’s higher bulk provides it more momentum. If the Mack truck stopped, the least large roller skate would have the greatest momentum. Any object at rest has zero momentum. Objects at rest have no momentum, no “mass in motion.”

Comparing two things’ momentum requires both variables, mass, and velocity. Linear momentum is the sum of mass and velocity. Linear momentum p is an equation.

p = mv

The equation shows that momentum is proportional to mass (m) and velocity (v) (v). Thus, the more mass or velocity an item has, the more momentum it has. Large, quick objects have more momentum than tiny, sluggish objects.

Newton termed momentum the amount of motion because it is so vital to understanding motion. Force affects momentum, and we can use Newton’s second rule of motion to illustrate this.

Similarly, a 2.0-kg cart moving at 8.0 m/s would have a momentum of 16.0 kg•m/s instead of 4.0 kg•m/s. A quadrupling of velocity quadruples the momentum. That p = m•v is more than “a plug-and-chug recipe for algebraic problem-solving” is shown in these two cases.

Remember Newton’s second law of motion (Fnet = ma)? Newton defined his second law of motion in terms of momentum: net external force = change in momentum/time. The difference in momentum vector between the end and beginning values.

The momentum equation can help us think about how changing one of two variables affects an object’s momentum. Consider a 0.5-kg physics cart carrying one 0.5-kg brick at 2.0 m/s. The laden cart weighs 1 kilogram and has a momentum of 2 kg•m/s. The same cart laden with three 0.5-kg bricks would have a total mass of 2.0 kg and a momentum of 4.0 kg•m/s. Doubling mass doubles momentum.


Momentum is a vector that follows velocity v. Because mass is a scalar when velocity is negative (opposed to motion), momentum is also negative; when velocity is positive, momentum is also positive. Weight per second is kg/s.

:eight_pointed_black_star: Momentum In Sports

Momentum In Sports

Sports use the term “momentum.” A squad with a momentum vector is hard to stop. A squad with a lot of momentum vector is hard to stop. Momentum is a physics word that describes how much motion an item possesses. A moving sports team has momentum. A thing in motion has momentum.

Momentum is “mass in motion.” Objects have mass, thus if they move, they have momentum or mass in motion. The amount of momentum an item possesses is dependent on two variables: the quantity of movement and the speed of movement. Mass and velocity determine momentum.

Momentum = mass • velocity

where m represents mass and v is speed. The equation shows that momentum vector is directly proportional to mass and velocity.


Metric momentum is expressed in kg•m/s. While the kg•m/s is the official metric measure of momentum, there are several additional acceptable (but non-standard) quantities. Kg•mi/hr, Kg•km/hr, and Gcm/s. In each case, a mass unit plus a velocity unit equals a momentum unit. This matches the momentum equation.

:eight_pointed_black_star: What Exactly Is Momentum?


In Newtonian physics, linear momentum is the product of mass and velocity. It has a magnitude and a direction. If an object’s mass is m and its velocity is v, then its momentum is p.

p = m v

The SI unit of momentum is the kilogram meter per second (kgm/s), which is equivalen to the newton-second.

Newton’s second law of motion states that a body’s momentum changes at the same rate as its net force. The total linear momentum of a closed system does not change if it is not impacted by external influences.

Classical mechanics’ advanced formulations, Lagrangian and Hamiltonian mechanics, enable choosing coordinate systems with symmetry and limitations.

The preserved quantity in these systems is generalized momentum, which is distinct from kinetic momentum. Generalized momentum is an operator on a wave function in quantum physics. The Heisenberg uncertainty principle links momentum and position operators.

A momentum density may be described in continuous systems like electromagnetic fields, fluid dynamics, and deformable bodies, leading to equations like the Navier–Stokes equations for fluids or the Cauchy momentum equation for deformable solids or fluids.

:small_red_triangle_down: Momentum as a Vector Quantity

A measure of momentum is a vector quantity. The size and direction of a vector quantity have already been examined in a previous unit. It’s important to specify both the amount and the direction of the bowling ball’s motion to accurately characterize its momentum. While it is true that a ball possesses 10 kg•m/s of momentum vector, this does not provide a complete picture of that momentum.

The ball’s velocity is directly proportional to the direction of the momentum vector. In a previous lesson, we learned that the velocity vector points in the same general direction as the object’s path of travel.

The momentum of a bowling ball traveling westward may be accurately defined as 10 kg•m/s westward. The amount and direction of an object’s momentum may be completely defined as a vector quantity.


Momentum is preserved in electrodynamics, quantum mechanics, quantum field theory, and general relativity. Translational symmetry is one of the fundamental symmetries of space and time.

:eight_pointed_black_star: Types Of Momentum

Momentum is defined as the result of multiplying the momentum mass by speed. The more this equation is multiplied, the more momentum is generated. It is important to note that there are two forms of momentum in science: angular and linear. However, the definition doesn’t end there. One of the few physics concepts whose metaphorical definition is the same as its real one is the term “momentum.”

:small_red_triangle_down: Angular Momentum

The mass of a body is converted to angular momentum by multiplying the momentum mass by the angular velocity. Thus, a single object may possess two distinct forms of angular momentum. Earth, for example, has two types of momentum: one derived from its motion about the sun, and the other from the speed at which it spins on its axis.

As a result of angular momentum, the smaller the body is, the quicker it spins as it is being moved. Having their arms wrapped around their waist increases their rotational speed, which explains why figure skaters spin quicker when they are low to the ground.

:small_red_triangle_down: Linear Momentum

As the name implies, linear momentum (also known as force) is the amount of mass associated with a moving object. The trajectory of a linear momentum item can be altered by an external push. Your trajectory will be altered, which might result in a fall.

Because of the greater force of the vehicle, you’ve been unable to move the truck. The cue ball’s impact on a billiard ball is an example of how linear momentum may be utilized to better understand and anticipate how objects’ trajectories change when they contact.

:small_red_triangle_down: Conceptual Momentum

Regardless of the form of momentum, the daily definition of momentum is nearly identical to its scientific meaning. After a speech tour and a solid debate performance, for example, the media will often suggest that the candidate has acquired momentum.

A politician may build momentum by showing up to a small number of events, and by doing so promptly. Momentum is created by a campaign’s mix of several outreaches activities and the proximity of those events to one other.


If you’re struck by a truck with a high linear momentum due to its size and weight, you’re going to be lucky to make it out alive. However, because the dog had a comparable momentum to yours when it accidentally ran into you while you were jogging, you should not be seriously injured.

:eight_pointed_black_star: Difference Between Momentum and Inertia

Many people misunderstand the terms inertia and momentum because of their similar meanings. Inertia is a body’s ability to resist motion, whereas momentum is a body’s ability to keep going forward. To further grasp the notion, let’s contrast the two.

Momentum Inertia
Vector quantity momentum is the inclination of a body to continue its current motion. A scalar quantity known as inertia is the body’s ability to resist any change in velocity.
The letter ‘p’ stands for momentum. The symbol for inertia is ‘I.’
The momentum of a mass’s body traveling at a speed ‘v’ is given by the equation p=mv. There’s no formula for calculating inertia.
Momentum can be classified as either linear or angular. The three forms of inertia are inertia at rest, inertia in motion, and inertia in direction.
Momentum is a function of mass and speed. Only momentum mass is required for inertia.
There is no loss of momentum. Irreducible inertia has no bearing on energy conservation.

Momentum has an impact on motion components, even if it is not explicitly taken into account. Consider a figure skating scenario once again. The skating athlete’s speed must rise when her arms are drawn closer to her body according to the conservation of angular momentum. To keep the angular momentum constant, she must increase her angular velocity, by decreasing her inertia (I = mr2 where r is lowered).

A moving body isn’t necessarily required for inertia; instead, it’s the ability of an item to remain in motion that’s the emphasis of this concept. It is also important to note that inertia does not include these concepts, which are missing from the definition of momentum.


Many people think that inertia is the same as momentum. Inertia, on the other hand, is the tendency of a thing to remain in motion or at rest.

:eight_pointed_black_star: History Of The Concept: Momentum Physics

History of the concept

In his commentary on Aristotle’s Physics, Byzantine scholar John Philoponus established the concept of momentum around 530 AD. According to Aristotle, anything that moves must be propelled.

Air movements, for example, keep a thrown ball going. Until Galileo, most authors accepted Aristotle’s idea, although others were suspicious. Philoponus pointed out the folly of Aristotle’s assertion that air promotes object motion.

  • He suggested that the act of tossing the thing gave it momentum. In 1020, Ibn Sn (commonly known as Avicenna) established his theory of motion in The Book of Healing. He agreed that the thrower gives a projectile a boost, but unlike Philoponus, he thought it was a permanent quality that needed external factors like air resistance to dissipate.

  • The European philosopher’s Peter Olivi and Jean Buridan read and polished Philoponus’ and maybe Ibn Sn’s writings. Buridan, the rector of the University of Paris in 1350, defined impetus as weight times speed. Buridan’s hypothesis differed from his predecessor’s in that he believed a body would be detained by forces of air resistance and gravity opposing its momentum.

  • René Descartes thought that the whole “amount of motion” (Latin: quantitas motus) in the cosmos is preserved. This is not a statement of the contemporary law of momentum, as he had no idea of momentum mass apart from weight and size, and he thought speed rather than velocity was preserved.

  • According to Descartes, if a moving item bounces off a surface, it changes direction but not speed. Galileo used the same word impeto to characterize Descartes’ amount of motion in his Two New Sciences.

  • In his “Discourse on Metaphysics,” Leibniz used the example of dropping bricks of varying sizes to refute Descartes’ definition of “quantity of motion.” He points out that while force is conserved, the amount of motion (the product of size and speed) is not.

The precise principles governing the elastic collision of two bodies were developed by Christiaan Huygens. His observation of the difficulties’ Galilean invariance was significant. It took years for his ideas to spread. In 1661, he gave them to William Brouncker and Christopher Wren in London.


A secret was kept by Spinoza in 1666, during the Second Anglo-Dutch War, to Henry Oldenburg. Huygens had written them in 1652–6 in a manuscript called De Motu corporum ex percussion. After the battle, Huygens presented his findings to the Royal Society in 1668. Sçavans Journal, 1669.

:eight_pointed_black_star: What is the equation for conservation of momentum?

The law of conservation of momentum is mathematically determined from the plausible assumption that space is uniform, that is, that nothing in the laws of nature distinguishes one place in space from another.

  • This is the universal law of physics that says the quantity termed momentum that defines motion in an isolated collection of objects never changes, hence the overall momentum of a system stays constant. Momentum is the force necessary to bring an item to a complete stop in a unit of time.

  • Angular momentum conservation law defines rotational motion in the same manner as ordinary momentum characterizes linear motion. Although this law’s mathematical representation is more complex, instances abound. For example, all helicopters require two propellers (rotors) for stability.

  • If a helicopter had only one horizontal propeller, the body would rotate in the opposite direction to save angular momentum. Because angular momentum is conserved, ice skaters spin faster when their arms are close to their bodies and slower when they are extended.

Angular-momentum conservation also follows mathematically from the plausible assumption that space is uniform in orientation—that is, that nothing in the laws of nature distinguishes one direction in space from another.


The overall momentum of an array of objects is the sum of the individual moments. Because momentum is a vector including both direction and amplitude of motion, the momenta of objects moving in opposite directions can cancel out to provide a total of zero.

:eight_pointed_black_star: Momentum and Newton’s Second Law

Newton’s second law states that the acceleration of an object is dependent on two variables – the net force acting on the object and the momentum mass of the item – and that the acceleration of an object relies on the net force acting on the object. It is known that the acceleration of a body is related to the net force applied to the body and that the acceleration of the body is inversely proportional to the mass of the body.

The acceleration of an item increases in direct proportion to the increase in the force exerted on it, as shown in the diagram. In the same way, when the mass of a thing increases, the acceleration of the object decreases.

When expressed in its most general form, Newton’s second law states that the rate of change of a particle’s momentum p is given by a force acting on the particle; that is, F = dp/dt (force = rate of change of momentum of a particle). In the absence of any external force acting on the particle, the particle’s momentum must be constant or conserved, as shown by dp/dt = 0.

This remark is just a reiteration of Newton’s first rule, the principle of inertia, which states that if there is no force acting on a body, it will continue to travel at the same speed in a straight path indefinitely.


The law of conservation of momentum may be derived from this concept, which states that total momentum is always preserved in all interactions between all of the bodies in the universe, regardless of how they interact.

:eight_pointed_black_star: Application of Second Law

Newton’s second law is used to determine the amount of force required to move or stop an object. It is a mathematical formula. As an illustration], we have provided the following instances to help you grasp this concept:

:small_red_triangle_down: Kicking a soccer ball

The force we provide to a ball when we kick it is directed in a precise direction. The more force we apply to the ball, the further it will go. The more force we apply to the ball, the further it will travel.

:small_red_triangle_down: Pushing a shopping cart

In a supermarket, pushing an empty cart is much simpler than pushing a filled cart, because more heft necessitates greater acceleration.

:small_red_triangle_down: Two persons are walking.

If one of the two individuals walking is heavier than the other, the person weighing heavier will walk slower than the person weighing lighter because the acceleration of the person weighing lighter is larger than that of the other.


A particle’s momentum can be changed by the force exerted by an external agent, but this must be done in such a way that the total momentum of the particle and external agent remains constant, also known as conservation of momentum.

Frequently Asked Questions - FAQs

People asked many questions ab to momentum. We discussed a few of them below:

:one: What is the proper way to apply the P MV formula?

The Momentum Calculator makes use of the formula p=mv, which states that momentum (p) equals mass (m) times velocity (v). The third value can be calculated by the calculator using any two of the other numbers.

:two: What is the formula for momentum and what is the unit of momentum?

Momentum is defined as the quantity of motion experienced by a moving body. It may be represented theoretically as p = m * v and is measured in kilograms per minute per second (kg m/s).

:three: What is the difference between angular and linear momentum?

Linear momentum is a characteristic of objects that are changing their location concerning a reference point during a certain period. When objects change the angle of their position vector concerning a reference point, this is referred to as angular momentum.

:four: How linear momentum is different than momentum?

Momentum is defined as the product of a system’s mass times its velocity multiplied by its acceleration. Linear momentum is denoted by the sign p = m * v in symbols. The amount of momentum an item has is directly proportional to the amount of mass it has as well as the amount of velocity it has. So the higher the mass or the greater the velocity of an item, the greater the amount of momentum it possesses.

:five: Why do we use the letter p to represent momentum?

If the letter “m” were to be used, there would be some misunderstanding with the term “mass.” The German name for the present moment is der Impuls, whereas the French phrase for it is l’impulsion. The use of the letter “I” as its sign might confuse with the concepts of the moment of inertia and inertia. As a result, the Germans and the French adopted the letter “p” to represent momentum.

:six: When it comes to mathematics, what is the definition of momentum?

In the simplest terms, momentum may be described as “mass in motion.” All objects have mass, and if an item is moving, it has momentum, which means that it is putting its momentum mass into motion. The momentum of an item may be expressed mathematically as the product of the mass of the object multiplied by the velocity of the object.

:seven: What is the principle of conservation of momentum Igcse?

The conservation of momentum principle asserts that, for two or more bodies in an isolated system operating on one other, their total momentum remains constant unless an external force is applied, which is not the case. In this way, neither new nor existing momentum can be produced or eliminated.

:eight: Is it possible to have negative momentum?

It is true that Momentum is a vector quantity, and that it is defined as the product of an object’s mass and its velocity. If the item’s velocity is negative, i.e., if the object is moving in the direction that has been designated as the negative direction, the object’s momentum will likewise be negatively oriented.

:nine: What is the difference between inertia and momentum?

The resistance of an item to change in motion (or absence of motion) is described by inertia, while the amount of motion it possesses is described by momentum. Momentum is the force or speed with which you move, whereas inertia is the force that keeps you moving. The automobile experienced a shift in motion (or momentum), but the giraffe was unconvinced that this was the case.

:keycap_ten: What are the two most important things that affect momentum?

Both the number of things moving and the pace at which it is moving play a role in determining an object’s amount of momentum. Momentum is mostly determined by mass and velocity.

:closed_book: Conclusion

Momentum is a term that you are most likely extremely acquainted with. Regularly, you’ll hear people talk about something growing or collecting momentum. It might refer to a physical moving item, or it could refer to something more symbolic, such as a sports team. Momentum is defined as the quantity of motion experienced by a moving body. In a nutshell, the more momentum a moving thing possesses, the more difficult it is to bring it to a halt.

Thus, the phrase is often used figuratively, as seen by the example of a sports team in the above paragraph. It indicates that the squad is on a roll (usually, a winning streak) and is developing into a stronger team as a result of this trend. The opposing teams will have a more difficult time slowing down the team’s momentum as time goes on.

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