Question

A cylinder has inner and outer radii of `2 cm` and `4 cm`, respectively, and a mass of `12 kg`. If the cylinder's frequency of counterclockwise rotation about its center changes from `6 Hz` to `1 Hz`, by how much does its angular momentum change?

Answer 1

The change in angular momentum is `=0.38kgm^2s^-1`

Explanation:

The angular momentum is `L=Iomega`

where `I` is the moment of inertia

and `omega` is the angular velocity

The mass of the cylinder is `m=12kg`

The radii of the cylinder are `r_1=0.02m` and `r_2=0.04m`

For the cylinder, the moment of inertia is `I=m((r_1^2+r_2^2))/2`

So, `I=12*((0.02^2+0.04^2))/2=0.012kgm^2`

The change in angular velocity is

`Delta omega=Deltaf*2pi=(6-1) xx2pi=10pirads^-1`

The change in angular momentum is

`DeltaL=IDelta omega=0.012 xx10pi=0.38kgm^2s^-1`