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?

1 Answer
Jun 26, 2018

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.