# The relation between impulse and momentum

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## Summary:

I've studied momentum and impulse a long time ago, don't judge the silliness of this question
I get that the impulse is I=FΔt, but why is it even equal to change in momentum caused by the force under consideration?

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etotheipi
Gold Member
2019 Award
$$\vec{I} = \int_{t_1}^{t_2} \vec{F} dt = \int_{t_1}^{t_2} \frac{d\vec{P}}{dt} dt = \vec{P}(t_2) - \vec{P}(t_1) = \Delta \vec{P}$$##\vec{F}## is the net force on the particle or extended body.

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vanhees71 and Dale
$$I = \int_{t_1}^{t_2} \vec{F} \cdot dt = \int_{t_1}^{t_2} \frac{d\vec{P}}{dt} dt = \vec{P}(t_2) - \vec{P}(t_1) = \Delta \vec{P}$$##\vec{F}## is the net force on the particle or extended body.
I still haven't studied integrals...

etotheipi
Gold Member
2019 Award
For constant ##\vec{F}##,$$\vec{I} = \vec{F} \Delta t = \frac{d\vec{P}}{dt} \Delta t = \Delta \vec{P}$$

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vanhees71
For constant ##\vec{F}##,$$I = \vec{F} \Delta t = \frac{d\vec{P}}{dt} \Delta t = \Delta \vec{P}$$
Thank you so much, now it's clear!

vanhees71
Summary:: I've studied momentum and impulse a long time ago, don't judge the silliness of this question

I get that the impulse is I=FΔt, but why is it even equal to change in momentum caused by the force under consideration?
https://en.m.wikipedia.org/wiki/Impulse_(physics)

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

"A resultant force causes acceleration and a change in the velocity of the body for as long as it acts. A resultant force applied over a longer time therefore produces a bigger change in linear momentum than the same force applied briefly: the change in momentum is equal to the product of the average force and duration. Conversely, a small force applied for a long time produces the same change in momentum—the same impulse—as a larger force applied briefly."

etotheipi
https://en.m.wikipedia.org/wiki/Impulse_(physics)

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

"A resultant force causes acceleration and a change in the velocity of the body for as long as it acts. A resultant force applied over a longer time therefore produces a bigger change in linear momentum than the same force applied briefly: the change in momentum is equal to the product of the average force and duration. Conversely, a small force applied for a long time produces the same change in momentum—the same impulse—as a larger force applied briefly."
Really exhaustive explanation, thank you!

Lnewqban
You are welcome.
These basic concepts are very important.
Note units related to impulse and momentum in each system.

etotheipi