Mechanics

Momentum - formula in LaTeX

Momentum is a vector pointing along the velocity, and in an isolated system the total momentum is conserved. \vec puts an arrow over a single letter; over something longer, such as a segment AB, use \overrightarrow.

\vec{p} = m\vec{v}

LaTeX code

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$$
\vec{p} = m\vec{v}
$$

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What the symbols mean

$\vec{p}$: momentum (kg·m/s)
$m$: mass (kg)
$\vec{v}$: velocity (m/s)

A classical mechanics formula - it shows up in kinematics and dynamics problems and in physics lab reports.

Worked example

A 2 kg cart moving at 3 m/s. The number and unit are separated by a thin space \, and the units sit upright in \mathrm so they do not read as variables.

p = m v = 2\,\mathrm{kg} \cdot 3\,\mathrm{m/s} = 6\,\mathrm{kg \cdot m/s}

Other ways to write it

Bold vectors instead of arrows, as in many university textbooks.
$\mathbf{p} = m\mathbf{v}$
```
\mathbf{p} = m\mathbf{v}
```
Conservation of momentum in a two-body collision; the prime marks velocities after the collision.
$m_1\vec{v}_1 + m_2\vec{v}_2 = m_1\vec{v}_1' + m_2\vec{v}_2'$
```
m_1\vec{v}_1 + m_2\vec{v}_2 = m_1\vec{v}_1' + m_2\vec{v}_2'
```
Impulse: the change in momentum equals the force times the time it acts.
$\Delta\vec{p} = \vec{F}\,\Delta t$
```
\Delta\vec{p} = \vec{F}\,\Delta t
```

LaTeX commands in this formula

\vec: vector

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