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 `24 Hz`?

Answer 1

`L=81430` #kg.m^2//s#

Explanation:

By definition, angular momentum is the cross product of the position vector from the axis of rotation to the rotating object and the linear momentum of the object.
That is, `vecL=vecr xx vecp` where `vecp=mvecv`.

So in this case, the magnitude of the angular momentum is
`L=rmvsin90^@`
`=6xx15xx((2pi6xx24)/1)`, since `v=x/t` and the object completes 24 circumferences or cycles per second).
`therefore L=81430kg.m^2//s`.

The direction of `L` will be obtained by the right hand rule as per normal vector cross-products - curl the fingers of your right hand from `vecr` to `vecp` and then your thumb will point in the direction of `vecL`, which will be perpendicular to the plane formed by `vecr and vecp`.
So for example if the circular rotation is in the xy-plane formed by the basis unit vectors `hati and hatj`, then the angular momentum will be along the basis unit vector `hatk`.