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Conservation of momentum

Review your understanding of the conservation of momentum in this free article aligned to NGSS standards.

Key terms

TermMeaning
SystemThe collection of objects that are of interest.
Closed systemA system in which masses do not enter or leave.
Isolated systemA system in which no net external forces act on the objects within it.
MomentumThe quantity of motion. Momentum is the product of mass and velocity, and because velocity is a vector, momentum is also a vector.
Δ(mv)The change in momentum.
ΔtThe change in time, or the time interval.
FnetThe net external force.

Equations

EquationSymbol breakdownMeaning
p=mvp is momentum, m is mass, and v is velocity.The momentum of an object is the mass of the object multiplied by the velocity of the object.
Δ(mv)=FΔtF is the external force, Δt is the time interval, and Δ(mv) is the change in momentum.The change in momentum is the product of the external force acting and the length of time that force acts.

Momentum and force in a system

Momentum of an object is the product of the object’s mass and velocity. We also know that a net force acting on the mass will result in the acceleration of that mass: F=ma.
A net force acting on an object can change the object's velocity, and therefore its momentum. The change in velocity due to a net force will increase the longer that force acts on an object: FΔt=maΔt=mΔv=Δmv.
The relationship FΔt=Δ(mv) also applies to a system, or collection of objects.
Two people on ice skates actively push their hands together, each person pushing toward the other person. An arrow, labeled direction of motion, points to the left behind the person on the left. Another arrow, labeled direction of motion, points to the right behind the person on the right.
In a closed, isolated system, the net external force is 0, so the change in momentum is also 0. In other words, momentum is conserved for closed, isolated systems.
However, how the system is defined is important. For instance, consider two ice skaters who are at rest and facing each other, as shown above. They push off of each other and move in opposite directions. Taking both skaters together as a system, the total momentum is 0 both before and after they push off each other, because the push off is an internal force.
Taken separately as two different systems, the push off is an external force acting on both skaters, and their momenta both change. The momentum lost by one skater is taken up by the other skater.

What else should I know about conservation of momentum?

  • The conservation of momentum has practical consequences. The relationship between momentum and force can help us study forces using easily measured quantities. For instance, by knowing the masses and velocities of objects before and after a collision, we can learn about the forces involved during that collision.
  • FnetΔt is referred to as the impulse. The quantity FnetΔt is referred to as the impulse, for which the symbol J is used. The equation FnetΔt=Δmv is thus often referred to as the impulse-momentum theorem in many textbooks.
  • Internal forces do not affect the momentum of the system. Because of Newton’s Third law, the forces acting between masses within a system cancel in pairs and do not contribute to the system’s momentum.
  • Momentum may be conserved in one direction but not in another. Momentum is conserved in the direction of Fnet, but it is not conserved in the perpendicular direction. For example, in projectile motion, the momentum changes vertically because of the force of gravity downwards. However, momentum does not change horizontally, because there are no horizontal forces.

Want to join the conversation?

  • scuttlebug yellow style avatar for user jasmine harvey
    How does one slay the day in regards to physics?
    (18 votes)
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  • duskpin ultimate style avatar for user Diana
    So I get the problem when you have the mass of the object and the velocity of the object. I just don't understand it when you have just kg*m/s
    (10 votes)
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  • blobby green style avatar for user 686247
    how is 40 N equivalent to 40kg * m/s2
    (4 votes)
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    • blobby green style avatar for user Anonymouse14
      I just posted this in the comment section that follows, so well, I hope u can understand why kg m/s^2 is the unit for force.

      Well, we humans are too lazy to write the whole thing, that is, 'kg m/s^2' every time we talk about force and its units. So, we decided to keep another unit, N, that is , Newton.

      Consider this, when we are given a math problem of this type , " *insert name* has 5 apples which amount to 25 (unit currency). Now, the person wishes to buy 3 more apples from the same shop. Calculate the extra money he needs to pay." We simply divide 25 by 5 to get the cost of one apple, and then multiply it by three. Well, this is not so lengthy at this stage for most of us, but it does cause quite some silly calc errors. It would have been way easier if we just had the cost of one apple from the beginning, right?

      Similarly, in force, what we do is this:

      We consider a case where an acceleration of 1 m/s^2 is produced for a mass of 1 kg when a certain force is applied. And, according to the formula, we get the answer as 1 kg m/s^2 . This 1 kg m/s^2 is given the name Newton and the symbol 'N'.
      Thus, in your case, when we say 40N, we say 40 x 1 N that is 40 x 1 kg m/s^2 . This is why they're equal.

      Hope this helps, and sorry for such a lengthy explanation. I seem incapable of explaining in short.
      (8 votes)
  • starky tree style avatar for user disantojoshua
    so if I get this right, Momentum and force are correlated?
    since by my understanding saying 40 Netowns is the same as saying 40 kg * m/s^2 momentum.

    fun fact: a force of 40Newtons is around 4KG of weight force.
    1 meter / second is 3.60km/h
    (6 votes)
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  • blobby green style avatar for user kea241199
    In the last bullet it says, "Momentum is conserved in the direction of Fₙₑₜ..." is it implied here that Fₙₑₜ = zero because conservation of momentum only applies when the net external force is zero?
    (5 votes)
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  • piceratops ultimate style avatar for user JJ999
    Can anyone help me with this question:
    Two model cars collide and then move together in one dimension. Car 1 has a mass of 2 kg and an initial velocity of 2m/s. Car 2 has a mass of 1 kg 1, point, and an initial velocity of -3 m/s before two model cars have a perfectly inelastic collision. What is their final velocity immediately after the collision?
    (This is actually a question in the practice, but I did not understand their solution.)
    (5 votes)
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    • duskpin seedling style avatar for user Janice Tang
      I haven't encountered a problem like this, I think in this unit the problem will give you one of the final momentums/velocities or (imply) that they are moving with the same momemtum/velocity. Otherwise I don't think this problem is designed for momemtum conservation.
      (1 vote)
  • aqualine ultimate style avatar for user MaxS0348
    Im having trouble understanding conservation of momentum,
    I understand the other lessons well but not this one.
    Ive watched and read the articles and videos, can someone explain in simpler terms.
    (3 votes)
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  • eggleston blue style avatar for user dena escot
    could you explain more "The change in velocity due to a net force will increase the longer that force acts on an object"

    and in strikers example is the push off force internal or external force? I do not understand

    and how are the forces acting between masses within a system cancel in pairs ? I knew from the newton's third law the pair force does not cancel each other
    (1 vote)
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  • blobby green style avatar for user s
    if the external force on an isolated system is supposed to be -0- and the internal force does not affect the momentum how would force affect the momentum
    (1 vote)
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    • stelly green style avatar for user Rosemary Monson
      It helps to have the external force equal 0 so that it does not have an effect on the system and we can just focus on the variables inside the system.
      The internal force does affect the momentum in a system.
      For example: (the objects IN the system are the hand and notebook) when a hand pushes a notebook across a desk, assuming the effect of friction and gravity(external forces) are negligible, the hand's momentum is the FORCE (in Newtons) applied to push the notebook multiplied by the time(usually in seconds) during which that force was applied.
      (1 vote)
  • male robot johnny style avatar for user David Ratliff
    i watched the video 3 or 4 times and I dont get it,it may be because im tired,but still i dont understand Sal shouldv explained it
    (1 vote)
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