= Momentum
{title2=$\mathbf p$}
{wiki}
= Linear momentum
{synonym}
= Momenta
{synonym}
For a nonrelativistic <point mass> of fixed <mass> $m>0$, measured in an <inertial frame>, its <momentum> is
$$
\mathbf p=m\mathbf v.
$$
<Momentum> is a <vector> pointing along the <velocity>, with <International System of Units> unit $\mathrm{kg\,m/s}$. Doubling either <mass> or <velocity> doubles <momentum>. In one dimension, a chosen positive direction makes $p=mv$ a signed quantity: a $2\,\mathrm{kg}$ body moving right at $3\,\mathrm{m/s}$ has $p=+6\,\mathrm{kg\,m/s}$; moving left at the same <speed> gives $p=-6\,\mathrm{kg\,m/s}$. https://openstax.org/books/university-physics-volume-1/pages/9-1-linear-momentum[OpenStax University Physics Volume 1, section 9.1: Linear Momentum]{ref}
For a collection, total <momentum> is the <vector> sum $\mathbf P=\sum_i m_i\mathbf v_i$. Two equal <masses> moving with opposite <velocities> can have zero total <momentum> while both have positive <kinetic energy>. Direction is therefore essential when using <momentum conservation>; adding <speeds> instead of signed <velocities> gives the wrong balance.
<Newton's second law> connects the net <force> on one fixed-<mass> <point mass> to its <momentum> through $\mathbf F_{\mathrm{net}}=d\mathbf p/dt$. Integrating that change gives <impulse>. Here $\mathbf p$ denotes <mechanical momentum>; when <canonical momentum> differs from <mass> times <velocity>, the distinction in <mechanical momentum> below applies. The nonrelativistic formula also has a limited regime: <special relativity> is needed at <speeds> comparable with the <speed of light>.
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