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 `12 Hz`?

Answer 1

The answer is `256pi` `kgm^2/s` which to the nearest whole number is 804 `kgm^/s`

Explanation:

Angular momentum is similar in formula to linear momentum:

`L=Ixxomega` as compared to `p =m xx v`

To find the moment of interia `I`, most students would check a list of known expressions, as every different geometry and even a different axis of rotation will play a part in determining the nature of `I`.

In the case of a rod being rotated about its centre, the moment of inertia is

`I=(mL^2)/12`

`L` being the length of the rod, and `m` its mass.

The angular velocity `omega` is equal to the number of radians swept out by the rod each second. In this case, as each revolution equals `2pi` radians,

`omega=24pi`

Put it together:

`L=((mL^2)/12)xx 24pi` = `((8)(4^2)(24pi))/12` = `256pi" " kgm^2/s`

which is approximately 804 `kgm^2/s`