Question

What is the angular momentum of a rod with a mass of `15 kg` and length of `6 m` that is spinning around its center at `23 Hz`?

Answer 1

`vecL=6503.085kg.m^2//s` in direction of `vecrxxvecp`.

Explanation:

The moment of inertia of a thin rod about an axis through its centre is given by (can be proven - ask if you want me to show you the derivation)

`I=1/12ML^2`

`=1/12xx15xx6^2`

`=45kg.m^2`.

The angular velocity of the rod is given by

`omega=2pif`

`=2pixx23=144.513rad//s`.

Hence the angular momentum is given by

`L=Iomega`

`=45xx144.513`

`=6503.085kg.m^2//s`.

The direction hereof may be obtained by the right hand rule - curl the fingers of your right hand in the direction of the rotation and your thumb will point in the direction of the angular momentum `vecL`.