Question

A cylinder has inner and outer radii of `6 cm` and `12 cm`, respectively, and a mass of `1 kg`. If the cylinder's frequency of counterclockwise rotation about its center changes from `15 Hz` to `9 Hz`, by how much does its angular momentum change?

Answer 1

The change in angular momentum is `=0.34kgm^2s^-1`

Explanation:

The angular momentum is `L=Iomega`

where `I` is the moment of inertia

The mass of the cylinder is `m=1kg`

The radii of the cylinder are `r_1=0.06m` and `r_2=0.12m`

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

So, `I=1*(0.06^2+0.12^2)/2=0.009kgm^2`

The change in angular velocity is

`Delta omega=Deltaf*2pi=(15-9)*2pi=12pirads^-1`

The change in angular momentum is

`DeltaL=I Delta omega=0.009*12pi=0.34kgm^2s^-1`