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

1 Answer
Jun 26, 2018

The angular momentum is given by

L=Iω

where

I=moment of inertia (kgm2)

ω=angular velocity (rad/s)

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

I=112ML2

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=112292=13.5 kgm2

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

ω=2πf=2π12=24π rad/s

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

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

L=Iω=13.524π=1017.876=1.02103 kgm2s

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.