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Momentum (more correctly linear momentum) is the product of mass and velocity $\bf{p}=m\bf{v}.$ It is a vector quantity and measured in Ns (Newton Seconds).
Newton's 2nd law of motion states that the force acting on a body is proportional to the rate of change of the momentum. (When the mass of the object is constant and with specially chosen units this law becomes the familiar F = ma).
There is also a quantity called angular momentum which is the product of the moment of inertia and angular velocity.
Albert Einstein, in his Special Theory of Relativity, revised the definition of momentum but that is not surprising as he revised the definitions of most of the quantities in classical mechanics e.g.  length, mass, velocity, time, energy etc. Perhaps a little surprisingly, the relativistic definition of momentum isn't that different from the classical: $\bf{p}=\gamma\.m\bf{v},$ where $\gamma=[1(v/c)^2]^{1/2}$ and c is the speed of light. Even more surprisingly, Newton's 2nd law in its original form ( $\bf{F}=d\bf{p}/dt$ ) still holds true for relativistic momentum.
On the other hand, the quantum mechanical definition of momentum is vastly different: $\bf{p}=i\hbar\nabla.$
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