Question

A cylinder has inner and outer radii of `2 cm` and `6 cm`, respectively, and a mass of `1 kg`. If the cylinder's frequency of counterclockwise rotation about its center changes from `10 Hz` to `15 Hz`, by how much does its angular momentum change?

Answer 1

The change in angular momentum is `=0.13kgm^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=0.02m` and `r_2=0.06m`

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

So, `I=1*(0.02^2+0.06^2)/2=0.004kgm^2`

The change in angular velocity is

`Delta omega=Deltaf*2pi=(15-10)*2pi=10pirads^-1`

The change in angular momentum is

`DeltaL=I Delta omega=0.004*10pi=0.13kgm^2s^-1`