What is the angular momentum of a rod with a mass of 5 kg and length of 4 m that is spinning around its center at  2 7 Hz?

Jun 19, 2017

The angular momentum is $= 1131 k g {m}^{2} {s}^{-} 1$

Explanation:

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

and $\omega$ is the angular velocity

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

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

$= \frac{1}{12} \cdot 5 \cdot {4}^{2} = \frac{20}{3} k g {m}^{2}$

The angular velocity is

$\omega = 2 \pi f = 2 \pi \cdot 27 = 54 \pi r a {\mathrm{ds}}^{-} 1$

The angular momentum is

$L = I \omega = \frac{20}{3} \cdot 54 \pi = 1131 k g {m}^{2} {s}^{-} 1$