# What is the angular momentum of a rod with a mass of  8 kg and length of 4 m that is spinning around its center at 5 Hz?

Mar 9, 2016

$L = 53.3 \quad {\text{kgm"^2"s}}^{- 2}$

#### Explanation:

The moment of inertia of a homogenous rod with mass $M$ and length $L$ about its center, $I$, is given by

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

$= \frac{1}{12} {\left(8 \quad \text{kg") (4 quad "m}\right)}^{2}$

$= 10.67 \quad {\text{kgm}}^{2}$

The angular momentum about the center of the rod is given by

$L = I \omega$

$= \left(10.67 \quad \text{kgm"^2)(5 quad "Hz}\right)$

$53.3 \quad {\text{kgm"^2"s}}^{- 2}$