Momentum

Momentum is the measure of 'how' much motion a body posses and is of prime importance to Mechanics, Mathematically if we have a body of mass $m$ moving with velocity $\vec{v}$ then it's momentum $\vec{p}$ is defined as

$\vec{p}=m \vec{v}$ The central importance of momentum is due Newton's second law which states or rather defines Force $\vec{F}$ acting on a body to be equal to it's rate of change of momentum.That is if $\vec{F}$ is the net force acting on a body then we have $\vec{F}=\frac{d \vec{p}}{dt}$ This means if a body moves such that it's momentum vector remains invariant with time then we can conclude that there is no net Force acting on it

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Momentum