Question

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`?

Answer 1

`L = 53.3 quad "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 = 1/12 ML^2`

`= 1/12 (8 quad "kg") (4 quad "m")^2`

`= 10.67 quad "kgm"^2`

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

`L = I omega`

`= (10.67 quad "kgm"^2)(5 quad "Hz")`

`53.3 quad "kgm"^2"s"^{-2}`