# Force vs momentum concept

Force is a push or pull right. If we have more force that means that we push harder. Now I if we have more momentum, what does it mean? Since momentum is the quantity of motion that means that we have more motion. But, what does it mean to have more motion. Do you move faster? If so, then why isnt momentum and velocity the same?

Momentum is the quantity of motion.

Word soup. You can stir them around all you like, but those words won't expain anything. The language of physics is math.

$$\vec{p}=m\vec{v}$$

The momentum of a particle in classical mechanics, $$\vec{p}$$, is equal to its mass, $$m$$, times its velocity, $$\vec{v}$$.

why isnt momentum and velocity the same?

Because $$m\vec{v}$$ is not the same as $$\vec{v}$$.

what does it mean to have more [momentum]?

Momentum is interesting because it obeys a conservation law. If you add up the momenta of all of the particles in a system, that total will never change as the state of the system evolves, so long as no force from outside of the system is applied to any of the particles.

You can use that fact (and some mathematical reasoning) to make accurate predictions about how a system (e.g., our Solar system) will evolve over time.

https://en.wikipedia.org/wiki/Momentum

• Maybe it will help the OP to point out that F=dp/dt=ma Feb 11, 2021 at 14:47

The simple explanation i can think of is that momentum describe how hard is it to stop that object. The more momentum an object have, the harder it is to stop. Momentum is not only about velocity, but also mass, it's stated in the definition of memontum $$\vec{p}=m\vec{v}$$

for example, compare a small ball with a mass of $$5$$ g and a big boulder with a mass of $$5000$$ kg, both are moving at $$2$$ m/s. You can see that of course it is harder to stop the boulder, even though they both are moving at $$2$$ m/s. So in this sense, momentum is very different from just velocity.

The more momentum an object has, the harder it is to stop, i.e. it either needs more force to stop, or it will take longer to stop. We can see that from the relation between force and momentum $$\vec{F} = \frac{d\vec{P}}{dt}\\ \int \vec{F} dt = \int\vec{dP}$$ to make it simpler we can consider simple case where the force is constant, so that $$\vec{F} \Delta t = \Delta\vec{P}$$ you can see that for bigger $$\Delta{P}$$, we either need bigger $$\vec{F}$$ (greater force) or bigger $$\Delta t$$ (longer time)

I believe your answer lies in this simple relation between momentum and force:

Although momentum is also a property of an object in motion, it does not simply mean to have "more motion" and is not the same as velocity. Momentum can be related to force in a simple derivation.

F= ma v= vi+at assume vi=0; F= m.v/t

Think of the case where an object with a velocity v collides with a stationary object. The stationary object may start to move. However, this means that a force must have acted on that object. This force is equal to the change in momentum of that object over the time over which the force has acted. Thus, momentum can explain the origin of this force by using a property of the motion described by m times v over t. In other words, the mass,time and velocity are the "essential" properties used to describe this force, so you cannot use just to velocity or just the kinetic energy.