# What is the angular momentum of a rod with a mass of 15 kg and length of 7 m that is spinning around its center at 19 Hz?

Jan 16, 2018

The angular momentum is $= 7312.1 k g {m}^{2} {s}^{-} 1$

#### Explanation:

$\text{Angular momentium" (kgm^2s^-1)="Moment of inertia"(kgm^2)xx"Angular velocity } \left(r a {\mathrm{ds}}^{-} 1\right)$

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

and $\omega$ the angular velocity

The mass of the rod is $m = 15 k g$

The length of the rod is $L = 7 m$

The moment of inertia of a rod, rotating about the center is

$I = \frac{1}{12} \cdot m {L}^{2}$

$= \frac{1}{12} \cdot 15 \cdot {7}^{2} = 61.25 k g {m}^{2}$

The frequency is $f = 19 H z$

The angular velocity is $\omega = 2 \pi f = 2 \cdot 19 \cdot \pi = 38 \pi r a {\mathrm{ds}}^{-} 1$

The angular momentum is

$L = I \omega = 61.25 \cdot 38 \pi = 7312.1 k g {m}^{2} {s}^{-} 1$