# What is the angular momentum of a rod with a mass of 8 kg and length of 7 m that is spinning around its center at 19 Hz?

Jan 28, 2018

$4387.23 \frac{k g {m}^{2}}{s}$

#### Explanation:

The angular momentum of a rod is given by $L = I \omega$, where $I$ is the moment of inertia and $\omega$ the angular velocity.

Furthermore, $I = \frac{1}{12} m {l}^{2}$, where $m$ is the mass and $l$ the length of the rod.

Also, $\omega = 2 \pi f$, where $f$ is the frequency.

Calculate $I$.

$I = \frac{1}{12} \left(8\right) {\left(7\right)}^{2}$
$\textcolor{w h i t e}{I} = \frac{3}{4} \left(49\right)$
$I = 36.75 k g {m}^{2}$

Calculate $\omega$.

$\omega = 2 \pi \left(19\right)$
$\omega = 38 \pi \frac{r a d}{s}$

Using these values, multiply:

$L = I \omega$
$L = 36.75 \cdot 38 \pi$
$L = 4387.23 \frac{k g {m}^{2}}{s}$