Question

A cylinder has inner and outer radii of `8 cm` and `15 cm`, respectively, and a mass of `3 kg`. If the cylinder's frequency of counterclockwise rotation about its center changes from `14 Hz` to `12 Hz`, by how much does its angular momentum change?

Answer 1

The change in angular momentum is `=0.54kgm^2s^-1`

Explanation:

The angular momentum is `L=Iomega`

where `I` is the moment of inertia

The mass of the cylinder is `m=3kg`

The radii of the cylinder are `r_1=0.08m` and `r_2=0.15m`

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

So, `I=3*(0.08^2+0.15^2)/2=0.04335kgm^2`

The change in angular velocity is

`Delta omega=Deltaf*2pi=(14-12)*2pi=4pirads^-1`

The change in angular momentum is

`DeltaL=I Delta omega=0.04335*4pi=0.54kgm^2s^-1`