Question

What is the angular momentum of a rod with a mass of `2 kg` and length of `9 m` that is spinning around its center at `12 Hz`?

Answer 1

The angular momentum is given by

`vec L=Ivec omega`

where

`I="moment of inertia " (kg*m^2)`

`omega="angular velocity "("rad/s")`

For a thin rod with uniform density rotating about the centre, the moment of inertia is given by

`I=1/12*ML^2`

`M="the total mass of the rod "(kg)`

`L="length of the rod "(m)`

You can find moment of inertia formulas for different shaped objects tabulated. In this case

`I=1/12*2*9^2=13.5 " kg"*m^2`

We want to work in SI units, so convert the frequency to angular velocity using

`omega=2pif=2pi*12=24pi " rad/s"`

This arises because each rotation is `2pi` radians and there are 12 rotations per second, so you are rotating through `24pi` radians per second.

Finally, substitute these values into the equation to calculate the angular momentum

`vec L=Ivec omega=13.5*24pi=1017.876=1.02*10^3" "(" kg"*m^2)/s`

Notice that we ditch the radians in the units. This is a a thing that I don't really understand but is due to the definition of the radian being a ratio of two lengths (so units cancel out). It gets used and dropped sporadically.

#equalrightsforallunits

Careful with significant figures too.