# On what ground do you multiply $m$ with $v$ in the momentum equation $p=mv$? [duplicate]

I've read several other posts that says the momentum equation is the definition of momentum, and it has no proof. However, I would like to know what is the experimental observation where the multiplication of m = mass and v=velocity is justified.

In other words, what is the meaning of this multiplication of 2 physical quantities of mass and velocity?

• There is no need to justify a definition. It's just made for convenience --- as are all definitions. We know that $F=ma$ (which is the definition of $F$, and $a=dv/dt$, so $F= dp/dt$. Apr 28 at 21:03
• Related question: Why is momentum defined as mass times velocity? Apr 28 at 21:05
• @mikestone so the multiplication here is arbitrary? and I can replace multiplication with division? Apr 28 at 21:06
• If you want to define some quantity other than momentum you can certainly form $z=m/v$. It may b useful for something..... All defintions are made as a convenient packaging of something. For example the cosine is defined as the adjacent over the hypotenuse. Apr 28 at 21:09
• Does this answer your question? Why is momentum defined as mass times velocity? Apr 28 at 21:22

Strictly speaking, a definition doesn’t need justification. However, some definitions are useful and important, and it is relatively easy to show why they are useful. In the case of momentum, basically all of the experimental observations that confirm Newton’s third law justify using $$\vec p=m\vec v$$ as an important quantity.

If Newton’s 3rd law holds then for any isolated mechanical system the quantity $$m \vec v$$ is constant, or conserved, regardless of the details. This is a very useful property and so it makes sense to give it a specific name and traditional symbol.

Observations supporting Newton’s 3rd law include (in no particular order):

Recoil of a gun

Rocket thrust