Mechanics

Gravitational acceleration - formula in LaTeX

The pendulum period formula solved for g: this is how g is measured in the classic lab exercise, by timing many swings of a string of known length. The period is squared, so its relative uncertainty counts twice in the result. Pi is written \pi.

g = \dfrac{4\pi^2 L}{T^2}

LaTeX code

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$$
g = \dfrac{4\pi^2 L}{T^2}
$$

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What the symbols mean

$g$: gravitational acceleration (m/s²)
$L$: length of the pendulum (m)
$T$: period of oscillation (s)

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

Worked example

A 0.80 m pendulum makes 10 swings in 18.0 s, so T = 1.80 s; timing many swings is more accurate than timing one. Keep the trailing zeros in 0.80 and 1.80: they state how precisely the length and time were measured.

g = \dfrac{4\pi^2 \cdot 0.80\,\mathrm{m}}{(1.80\,\mathrm{s})^2} \approx 9.75\,\mathrm{m/s^2}

LaTeX commands in this formula

\dfrac: fraction (display)
\pi: Greek letter pi
x^{2}: superscript (power); wrap several characters in braces

How to use this formula in LaTeX?

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