# What is the angular momentum of a rod with a mass of 8 kg and length of 6 m that is spinning around its center at 3 Hz?

Jan 25, 2018

The angular momentum is $= 452.4 k g {m}^{2} {s}^{-} 1$

#### Explanation:

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

The mass of the rod is $m = 8 k g$

The length of the rod is $L = 6 m$

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

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

$= \frac{1}{12} \cdot 8 \cdot {6}^{2} = 24 k g {m}^{2}$

The frequency is $f = 3 H z$

The angular velocity is $\omega = 2 \pi f = 2 \cdot 3 \cdot \pi = 6 \pi r a {\mathrm{ds}}^{-} 1$

The angular momentum is

$L = I \omega = 24 \cdot 6 \pi = 452.4 k g {m}^{2} {s}^{-} 1$