# What is the significance of momentum? [duplicate]

I just want to get an idea what momentum is. I know the mathematical meaning that momentum is $mv$ where $v$ is velocity. But I don't know its significance. Like I know that Acceleration is how velocity is changing with respect to time, I wanted to get feel of what momentum really is?

## marked as duplicate by sammy gerbil, Jon Custer, tpg2114♦, Yashas, Kyle KanosSep 13 '17 at 9:58

• @DavidRicherby When I commented the question was closed. Only comments allowed then. – MichaelK Sep 12 '17 at 15:41
• @a25bedc5-3d09-41b8-82fb-ea6c353d75ae Ah, OK. I suggest reposting as an answer, now that it's been reopened. – David Richerby Sep 12 '17 at 15:42
• – J... Sep 12 '17 at 18:05

Momentum is what makes it "tough" to stop moving things.

If you stand with an apple in each hand, then you feel their weight. If you throw one of them upwards and catch it again, it feels "heavier" in that moment. What you feel in addition to the weight is the momentum.

Stopping a motion can be an easy or tough task depending on the momentum, which encompasses both the speed $v$ to decelerate from as well as the mass $m$ that resists this deceleration.

At the same time there happens to exist a conservation law regarding momentum. All momentum before equals all after any event; momentum is always conserved $\sum P_{before}=\sum p_{after}$. So apart from the physical significance of momentum, it also happens to be a very useful tool.

That's why we see it and learn about it and use it all the time.

• Not to mention that force, like the force of the apple, is literally the change in momentum over time. In other words $\vec F=\frac{\text d\vec p}{\text d t}$. – Kris Walker Sep 12 '17 at 9:29
• It should be stressed that momentum conservation applies if the system is invariant under spatial translations, it is not a universal given. – JamalS Sep 12 '17 at 12:53
• Perhaps you could relate this answer to Newton's Laws of Motion, which are essentially the consequences of what you describe, e.g. the Third Law results from conservation of momentum. – Barmar Sep 12 '17 at 20:28
• I personally view it as how much it hurts when you try to stop something from moving (particularly if you use your face to do the stopping) – slebetman Sep 13 '17 at 7:24
• If you pasted this same answer to a hypothetical question "What is the significance of kinetic energy?", it would fit there equally well, or almost. That makes me suspect that you mentioned some important facts about the momentum, but not enough to fully pinpoint the concept for somebody who doesn't already have a grasp on it. – Jirka Hanika Sep 13 '17 at 7:52

Momentum is the conserved Noether Charge that corresponds to the invariance of the Newtonian dynamics Lagrangian under spatial translation. In less technically dense language, this means that momentum is a conserved quantity whose conservation arises because physical laws (or a particular, "Lagrangian" formulation of them) are invariant to a shift in the origin of the co-ordinate system that the laws are written in.

So as in the other answers, you can only change a body's motion state by having it transfer the change of momentum to you since the total system's momentum has to be conserved; you feel this transfer of momentum as a reaction force acting on you oppositely to the force you impart on the body. And every time you feel this force, you can think of the phenomenon ultimately as an expression of the principle that our physical laws don't care where we put the origin of our descriptive co-ordinate system.

For me, this is the deepest meaning for momentum, as I describe further in my answer to the Physics SE question What is momentum really?. I also discuss there some other slightly different usages of the word "momentum" in physics; the other usages are related to mechanical momentum in that they are defined analogously, but need not co-incide with it.

As the other answer says, the momentum is a "measurement" of the "inertia" that the body or the system of particles has.

My first teachers wanted us to call it "quantity of movement", because that's mostly what it is. (finally, the word mmentum conquered everything haha).

Think it this way, it's the velocity multiplied by the "mass", which is, after all, related to the number of particles of the body. It's the total amount of movement in that system. And then, as philosophers said, "the total amount of movement is constant in the Universe", it was finally true.

• +1 Very good point. In fact, in my native Danish language, we don't call it momentum but rather bevægelsesmængde among others, which literally translates to motion-amount. – Steeven Sep 12 '17 at 9:31