Question

What is the angular momentum of an object with a mass of `7 kg` that moves along a circular path of radius `4 m` at a frequency of `4 Hz`?

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Answer 1

`vecL=2814.867kg.m^2//s hatk`

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^@`
`=4xx7xx((2pi4xx4)/1)`, since `v=x/t` and the object completes 4 circumferences or cycles per second).
`therefore L=2814.867kg.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`.