# What is the exact definition for momentum?

## Main Question or Discussion Point

What is the exact definition for momentum other than the formula p=m.v? Is there a way to understand it as a real world concept? I mean, i can understand velocity or mass os acceleration but momentum appears too abstract. Can anyone help by explaining this?

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tiny-tim
Homework Helper
What is the exact definition for momentum other than the formula p=m.v? Is there a way to understand it as a real world concept? I mean, i can understand velocity or mass os acceleration but momentum appears too abstract. Can anyone help by explaining this?
Hi rakeshsugirth!

I don't know what level you're at - but if you're into fundamental theoretical physics, then one way of looking at momentum is:
the invariance of physical systems with respect to spatial translation (in other words, that the laws of physics do not vary with locations in space) gives the law of conservation of linear momentum;
In other words: if the laws of physics are to appear the same to two observers in different positions (but stationary), then if one observer calculates that the momentums in an experiment add up to zero, then so will the other observer.

(Usually, one thinks of a conservation law as applying to different experiments measured by the same observer, but one can also regard it as as applying to the same experiments as measured by different observers.)

Hi tim,
Thanks for the reply but the answer seems to explain more about conservation of momentum rather than momentum itself. How to define momentum as something perceivable?

Hootenanny
Staff Emeritus
Gold Member
Hi tim,
Thanks for the reply but the answer seems to explain more about conservation of momentum rather than momentum itself. How to define momentum as something perceivable?
I mean, i can understand velocity or mass os acceleration but momentum appears too abstract.
Okay then, could you define mass, velocity and acceleration for me?

tiny-tim
Homework Helper
Hi tim,
Thanks for the reply but the answer seems to explain more about conservation of momentum rather than momentum itself. How to define momentum as something perceivable?
Ok - momentum is the oomph something has when it hits you! Newton's second law is:
force = (rate of) change of momentum,​
so when a force hits you, momentum is what it gives you! (Unless, of course, some other force - possibly friction through your feet on the ground - cancels the first force out).

Ok - momentum is the oomph something has when it hits you! Newton's second law is:
force = (rate of) change of momentum,​
so when a force hits you, momentum is what it gives you! (Unless, of course, some other force - possibly friction through your feet on the ground - cancels the first force out).
That's quite a nice explaination rakeshsugirth

P=mv has units of kg*m/s and it indicates a bodies momentum.

Momentum has no force in itself since there is no acceleration involved and F=ma. However the greater the momentum the greater the potential abilty to apply a large force.

So a truck travelling at 50kph (14m/s) has the potential to apply a much larger force than a tennis ball travelling at 50kph (14m/s). A mass without a velocity has potential to apply a force but then it is called inertia. Inertia is only relative to mass, so inertial force is generated when the mass is accelerated.

The truck has a mass of 20000kg and the ball 0.02kg. F=ma so the ball would have to decelerate a million times faster than the truck to apply the same force to another object.

Therefore if the truck collides with a large object (large mass with a large inertia) it will have the potential to move that large object, the ball however will not.

So imagine a body with a large momentum acts on a second body. If the second body has a small mass the second body will accelerate much faster than if it had a much larger mass.

So I say, momentum is the measure of the potential magnitude of force available to accelerate another body that it acts on.

Also momentum is relative. So if you are on a train doing 100mph you have no momentum relative to the train but you do have a large momentum relative to a cow standing in a field watchinching you whizz by. If the train hits a bridge you will suddenly appear to accelerate to 100mph (which was the velocity you had before the train stopped). Now you have a large momentum relative to the trai, which now has an enourmous inertia. When you hit the carriage door at the end of your carriage your soft body will be splattered by the lagre force generated by you rapid deceleration.

But I'm not a physicist so you may want to look further.

Cheers Dave

Hi pals,

Well momentum is made of two things : inertia, that is mass, and velocity. You get a better idea of the motion with momentum, because the velocity is weigthed by the mass. Think about a real motion in real life! (Of course, a lot can be said about conseravtion laws, analytical mechanics and so on. )