Question

A cylinder has inner and outer radii of `9 cm` and `16 cm`, respectively, and a mass of `4 kg`. If the cylinder's frequency of counterclockwise rotation about its center changes from `9 Hz` to `3 Hz`, by how much does its angular momentum change?

Answer 1

The change in angular momentum is `=2.54kgm^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=4kg`

The radii of the cylinder are `r_1=0.09m` and `r_2=0.16m`

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

So, `I=4*(0.09^2+0.16^2)/2=0.0674kgm^2`

The change in angular velocity is

`Delta omega=Deltaf*2pi=(9-3)*2pi=12pirads^-1`

The change in angular momentum is

`DeltaL=I Delta omega=0.0674*12pi=2.54kgm^2s^-1`