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  2 Hz?

Aug 13, 2016

$\text{The angular momentum of rod is } 96 \pi$

Explanation:

$\text{The angular momentum of a rod spinning its center can be calculated using } L = I \cdot \omega$

$L : \text{represents angular momentum}$
$I : \text{represents moment of inertia}$
$\omega : \text{represents angular velocity }$

$\omega = 2 \cdot \pi \cdot f \text{ where f is frequency}$

$\omega = 2 \cdot \pi \cdot 2 = 4 \pi$

$I = \frac{1}{12} \cdot m \cdot {l}^{2} \left(\text{ moment of inertia for a rod spinning around its center}\right)$

$m = 8 \text{ kg ";l=6" m}$

$I = \frac{1}{12} \cdot 8 \cdot {6}^{2} = \frac{8 \cdot 36}{12} = 8 \cdot 3 = 24$

$I = 24 \cdot 4 \pi = 96 \pi$