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The momentum of a mass $ m$ is usually defined by

$\displaystyle p = m v,

where $ v$ is the velocity of the mass. Note that momentum is a vector quantity in general, so we should more clearly write

$\displaystyle \underline{p}= m \underline{v},

where $ \underline{p}$ and $ \underline{v}$ are vectors in 3D space. We will return to vector momentum in §B.4.1 below.

Conservation of Momentum

Like energy, momentum is conserved in physical systems. For example, when two masses collide and recoil from each other, the total momentum after the collision equals that before the collision. Since the momentum is a three-dimensional vector in Euclidean space, momentum conservation provides three simultaneous equations, in general.B.10

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